Praktyczne wprowadzenie 
do Mathematici

Obliczenia numeryczne

Arytmetyka

2.3 + 5.63

2.4 / 8.9 ^ 2

2 3 4

(3 + 4) ^ 2 - 2 (3 + 1)

2.4 ^ 45

({{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"^\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "potegowanie "}, {"\!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) ", "minus "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"/\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "dzielenie "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)  lub  \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"*\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"*\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\) ", "mnozenie  "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"+\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"+\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\) ", "dodawanie  "}})

Obliczenia dokladne i przyblizone

2 ^ 100

2 ^ 100 //N

1/3 + 2/7

1/3 + 2/7 //N

({{"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"//N\\\"\", \"MR\"]\) ", "zwroc przyblizona wartosc numeryczna wyrazenia \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}})

452/62

452.3/62

452./62

1. + 452/62

Funkcje matematyczne

({{"\!\(\*StyleBox[\"\\\"Sqrt[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pierwiastek kwadratowy ("(Sqrt[x])")  "}, {"\!\(\*StyleBox[\"\\\"Exp[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "funkcja wykladnicza ("(e^x)")  "}, {"\!\(\*StyleBox[\"\\\"Log[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "logarytm naturalny ("(Subscript[log, e])x")  "}, {"\!\(\*StyleBox[\"\\\"Log[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "logarytm o podstawie "b" ("(Subscript[log, b])x") "}, {"\!\(\*StyleBox[\"\\\"Sin[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\),  \!\(\*StyleBox[\"\\\"Cos[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\),  \!\(\*StyleBox[\"\\\"Tan[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "funkcje trygonometryczne (z argumentami w radianach) "}, {"\!\(\*StyleBox[\"\\\"ArcSin[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\),  \!\(\*StyleBox[\"\\\"ArcCos[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\),  \!\(\*StyleBox[\"\\\"ArcTan[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "odwrotne funkcje trygonometryczne "}, {"\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"!\\\"\", \"MR\"]\) ", "silnia "}, {"\!\(\*StyleBox[\"\\\"Abs[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wartosc bezwzgledna "}, {"\!\(\*StyleBox[\"\\\"Round[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "liczba calkowita najblizsza "x"  "}, {"\!\(\*StyleBox[\"\\\"Mod[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", n" modulo "m" "}, {"\!\(\*StyleBox[\"\\\"Random[\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "liczba pseudolosowa pomiedzy 0 a 1 "}, {"\!\(\*StyleBox[\"\\\"Max[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\),  \!\(\*StyleBox[\"\\\"Min[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "maksimum, minimum z "x", "y", "…"    "}, {"\!\(\*StyleBox[\"\\\"FactorInteger[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", rozklad na liczby pierwsze}})

({{"◼ Argumenty wszystkich funkcji \!\(\*StyleBox[\"\\\"Mathematici\\\"\", \"TI\"]\) sa zawarte w \!\(\*StyleBox[\"\\\"nawiasach kwadratowych\\\"\", \"TI\"]\). "}, {"◼ Nazwy funkcji wbudowanych w \!\(\*StyleBox[\"\\\"Mathematice\\\"\", \"TI\"]\) zaczynaja sie z \!\(\*StyleBox[\"\\\"duzych liter\\\"\", \"TI\"]\). "}})

Log[8.4]

Sqrt[16]

Sqrt[2]

Sqrt[2] //N

Sqrt[2.]

({{"\!\(\*StyleBox[\"\\\"Pi\\\"\", \"MR\"]\) ", π≃3.14159"  "}, {"\!\(\*StyleBox[\"\\\"E\\\"\", \"MR\"]\) ", e≃2.71828"   "}, {"\!\(\* StyleBox[\"\\\"Degree\\\"\",\n\"MR\"]\) ", π/180":  stopnie naradiany  "}, {"\!\(\*StyleBox[\"\\\"I\\\"\", \"MR\"]\) ", i=(Sqrt[-1])"  "}, {"\!\(\*StyleBox[\"\\\"Infinity\\\"\", \"MR\"]\) ", ∞" "}})

Pi ^ 2 //N

Sin[Pi/2]

Sin[20 Degree] //N

Log[E ^ 5]

Log[2, 256]

Obliczenia o zadanej dokladnosci

({{"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"//N\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"N[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przyblizona wartosc numeryczna wyrazenia \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"N[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wartosc numeryczna wyrazenia\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) obliczona z zadana precyzja "}})

N[Pi]

N[Pi, 40]

Liczby zespolone

Sqrt[-4]

(4 + 3 I) / (2 - I)

Exp[2 + 9 I] //N

({{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"+\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"I\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "liczba zespolona "x+i y" "}, {"\!\(\*StyleBox[\"\\\"Re[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "czesc rzeczywista "}, {"\!\(\*StyleBox[\"\\\"Im[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "czesc urojona "}, {"\!\(\*StyleBox[\"\\\"Conjugate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "liczba zespolona sprzezona "(SuperStar[z])" lub "(OverBar[z])"  "}, {"\!\(\*StyleBox[\"\\\"Abs[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wartosc bezwzgledna "|z|"   "}, {"\!\(\*StyleBox[\"\\\"Arg[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "argument "ϕ" w "|z|(e^(iϕ))"  "}})

Techniki obliczeniowe

Wykorzystywanie poprzednich wynkiow

({{"\!\(\*StyleBox[\"\\\"%\\\"\", \"MR\"]\) ", "ostatnio wygenerowany wynik "}, {"\!\(\*StyleBox[\"\\\"%%\\\"\", \"MR\"]\) ", "przedostatnio wygenerowany wynik "}, {"\!\(\*StyleBox[\"\\\"%%\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"%\\\"\", \"MR\"]\) ("k" razy) ", ""k"-ty od konca wynik "}, {"\!\(\*StyleBox[\"\\\"%\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) ", "wynik z linii \!\(\*StyleBox[\"\\\"Out[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) (ostroznie!) "}})

77 ^ 2

% + 1

3 % + % ^ 2 + %%

%2 + %3

Definiowanie zmiennych

x = 5

x ^ 2

x = 7 + 4

pi = N[Pi, 40]

pi

pi ^ 2

({{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\) ", "przypisz wartosc zmiennej \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\) ", "przypisz wartosc zmiennym \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) i \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=.\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"Clear[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "usun wartosci przypisane do \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) "}})

Tworzenie list obiektow

{3, 5, 1}

{3, 5, 1}^2 + 1

{6, 7, 8} - {3.5, 4, 2.5}

Exp[ % ] // N

v = {2, 4, 3.1}

v / (v - 1)

Operowanie elementami list

({{{"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"c\\\"\", \"TI\"]\)"}" ", "lista "}, {"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", " \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)""-ty element listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) (pierwszym elementem jest \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[1]]\\\"\", \"MR\"]\)) "}, {"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)"{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", lista i, j,...-tych elementow listy list}})

{5, 8, 6, 9}[[2]]

{5, 8, 6, 9}[[ {3, 1, 3, 2, 4} ]]

v = {2, 4, 7}

v[[ 2 ]]

({{"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"v\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"v\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", zwroc i-ty element listy}, {"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"v\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\)  lub  \!\(\*StyleBox[\"\\\"v\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\) ", zmien wartosc i-tego elementu listy}})

v = {4, -1, 8, 7}

v[[3]] = 0

v

Cztery rodzaje nawiasow w Mathematice

({{"\!\(\*StyleBox[\"\\\"(\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"term\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\")\\\"\", \"MR\"]\) ", "okragle nawiasy grupujace "}, {"\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "nawiasy kwadratowe argumentow funkcji "}, {{"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"c\\\"\", \"TI\"]\)"}" ", "nawiasy klamrowe list "}, {"\!\(\*StyleBox[\"\\\"v\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", "podwojne nawiasy kwadratowe indeksow (\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"v\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)) "}})

Sekwencje operacji

({{(Subscript["\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)", 3])" ", "wykonaj kilka operacji i wypisz wynik ostatniej "}, {(Subscript["\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) ", "wykonaj operacje, nie wypisuj wyniku "}})

x = 4; y = 6; z = y + 6

({{"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) ", "wykonaj opeacje i nie wypisuj jej wyniku "}})

x = 67 - 5 ;

%

Praca z Mathematica

({{"\!\(\*StyleBox[\"\\\"Mathematica\\\"\", \"TI\"]\) kernel ", "czesc systemu wykonujaca obliczenia "}, {"\!\(\*StyleBox[\"\\\"Mathematica\\\"\", \"TI\"]\) front end ", "czesc systemu odpowiedzialna za wspolprace z uzytkownikiem "}})

System pomocy w Mathematice

({{"\!\(\*StyleBox[\"\\\"Getting Started\\\"\", \"SR\"]\) ", "szybkie wprowadzenie do \!\(\*StyleBox[\"\\\"Mathematici\\\"\", \"TI\"]\)"}, {"\!\(\*StyleBox[\"\\\"Help Browser\\\"\", \"SR\"]\) ", "poszukiwanie okreslonych funkcji "}, {"\!\(\*StyleBox[\"\\\"Mathematica Book\\\"\", \"SR\"]\) ", "podrecznik do systemu w wersji on-line "}, {"\!\(\*StyleBox[\"\\\"Answers\\\"\", \"SR\"]\) ", "baza danych z odpowiedziami na najczesciej zadawane pytania "}})

({{"\!\(\*StyleBox[\"\\\"?\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"Name\\\"\", \"TI\"]\) ", "pokaz informacje o \!\(\*StyleBox[\"\\\"Name\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"??\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"Name\\\"\", \"TI\"]\) ", "pokaz dodatkowa informacje o \!\(\*StyleBox[\"\\\"Name\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"?\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"Aaaa\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"*\\\"\", \"MR\"]\) ", "pokaz informacje o obiektach, ktorych nazw zaczynaja sie od \!\(\*StyleBox[\"\\\"Aaaa\\\"\", \"TI\"]\) "}})

?Log

??Log

?Lo*

?:=

Pakiety Mathematici

({{"\!\(\*StyleBox[\"\\\"<<\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"package\\\"\", \"TI\"]\) ", "wczytaj pakiet \!\(\*StyleBox[\"\\\"Mathematici\\\"\", \"TI\"]\) "}})

<< DiscreteMath`CombinatorialFunctions`

Subfactorial[10]

({{"\!\(\*StyleBox[\"\\\"Remove[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"name\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", "usun funkcje "}})

Ostrzezenia i komunikaty w Mathematice

Sqrt[4, 5]

Off[Sqrt::argx]

Sqrt[4, 5]

On[Sqrt::argx]

({{"\!\(\*StyleBox[\"\\\"Off[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"Function\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"::\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"tag\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "nie wyswietlaj komunikatow "}, {"\!\(\*StyleBox[\"\\\"On[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"Function\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"::\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"tag\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wyswietlaj komunikaty "}})

Przerywanie obliczen w Mathematice

({{"Command-Comma  lub  Alt-Comma ", "interfejs typu notebook "}, {"Control-C ", "interfejs tekstowy "}})

({{"\!\(\*StyleBox[\"\\\"continue\\\"\", \"MR\"]\) ", "kontynuuj obliczenia "}, {"\!\(\*StyleBox[\"\\\"show\\\"\", \"MR\"]\) ", "pokaz co robi \!\(\*StyleBox[\"\\\"Mathematica\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"inspect\\\"\", \"MR\"]\) ", "przedstaw stan obliczen "}, {"\!\(\*StyleBox[\"\\\"abort\\\"\", \"MR\"]\) ", "przerwij obliczenia "}, {"\!\(\*StyleBox[\"\\\"exit\\\"\", \"MR\"]\) ", "wyjdz z \!\(\*StyleBox[\"\\\"Mathematici\\\"\", \"TI\"]\) calkowicie"}})

Obliczenia algebraiczne

Obliczenia symboliczne

({{"obliczenia numeryczne ", "\!\(\*StyleBox[\"\\\"3\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"+\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"62\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\)  "⟶"  \!\(\*StyleBox[\"\\\"64\\\"\", \"MR\"]\) "}, {"obliczenia symboliczne ", "\!\(\*StyleBox[\"\\\"3x\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"+\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"2\\\"\", \"MR\"]\)  "⟶"  \!\(\*StyleBox[\"\\\"2\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"+\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"2\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"MR\"]\) "}})

-1 + 2x + x^3

x^2 + x - 4 x^2

x y + 2 x^2 y + y^2 x^2 - 2 y x

(x + 2y + 1)(x - 2)^2

Expand[%]

Factor[%]

Sqrt[2]/9801 (4n)! (1103 + 26390 n) / (n!^4 396^(4n))

Sqrt[1 + x]^4

Log[1 + Cos[x]]

Podstawowa zasada  Mathematici.

"◼ Wez wyrazenie i zastosuj do niego reguly przeksztalcania tak dlugo dopoki wynik przestanie sie zmieniac. "

Podstawianie wartosci pod symbole

({{"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"/.\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\) ", "zamien \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) przez \!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\) w \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"/.\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xval\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"yval\\\"\", \"TI\"]\)"}" ", "wykonaj szereg podstawien "}})

1 + 2x /. x -> 3

1 + x + x^2 /. x -> 2 - y

x -> 3 + y

x^2 - 9  /.  %

(x + y) (x - y)^2 /. {x -> 3, y -> 1 - a}

({{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\) ", "nadaj wartosc zmiennej \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) globalnie "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=.\\\"\", \"MR\"]\) ", "usun wartosc zwiazana ze zmienna \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) "}})

x = 3

x^2 - 1

x = 1 + a

x^2 - 1

x + 5 - 2x

x =.

x + 5 - 2x

t = 1 + x^2

t /. x -> 2

t /. x -> 5a

t /. x -> Pi //N

Przeksztalcanie i upraszczanie wyrazen algebraicznych

({{"\!\(\*StyleBox[\"\\\"Expand[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wylicz iloczyny i potegi i zwroc wynik w postaci sumy skladnikow "}, {"\!\(\*StyleBox[\"\\\"Factor[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zapisz wyrazenie \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) jako iloczyn jak najprostszych czynnikow "}})

Expand[ (1 + x)^2 ]

Factor[ % ]

Factor[ x^10 - 1 ]

Expand[ % ]

({{"\!\(\*StyleBox[\"\\\"Simplify[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz jak najprostsza postac wyrazenia \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) stosujac standardowe przeksztalcenia algebraiczne "}, {"\!\(\*StyleBox[\"\\\"FullSimplify[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz jak najprostsza postac wyrazenie stosujac mozliwe znane przeksztalcenia algebraiczne "}})

Simplify[x^2 + 2x + 1]

Simplify[x^10 - 1]

Integrate[1/(x^4-1), x]

D[%, x]

Simplify[%]

Simplify[Gamma[x] Gamma[1 - x]]

FullSimplify[Gamma[x] Gamma[1 - x]]

Inne funkcje: ExpandAll[], Together[], Apart[], Cancel[], Collect[], FactorTerms[], TrigExpand[], ComplexExpand[], PowerExpand[], TrigReduce[], TrigToExp[], ExpToTrig[]

Uzyskiwanie fragmentow wyrazen algebraicznych

({{"\!\(\*StyleBox[\"\\\"Coefficient[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc wspolczynniki przy wyrazeniach postaci \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\) w wyrazeniu \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Exponent[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc najwyzsza potege wyrazenia postaci \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\) w wyrazeniu \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", n-ty skladnik wyrazenia expr}})

e = Expand[(1 + 3x + 4y^2)^2]

Coefficient[e, x]

Exponent[e, y]

Part[e, 4]

({{"\!\(\*StyleBox[\"\\\"Numerator[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "licznik \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Denominator[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "mianownik \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}})

r = (1 + x)/(2 (2 - y))

Denominator[%]

Wyswietlanie wynikow obliczen

({{"\!\(\*StyleBox[\"\\\"command\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) ", "wykonaj polecenie \!\(\*StyleBox[\"\\\"command\\\"\", \"TI\"]\), nie wyswietlaj jego wyniku "}, {"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"//\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"Short\\\"\", \"MR\"]\) ", "pokaz w jednej linii zawartosc wyrazenia \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Short[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pokaz w \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) liniach zawartosc wyrazenia \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}})

Expand[(x + 5 y + 10)^8] ;

% //Short

Short[%, 3]

Length[%]

Matematyka symboliczna

Operacje podstawowe

({{"\!\(\*StyleBox[\"\\\"D[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pochodna (czastkowa) "((∂f)/(∂x))" "}, {"\!\(\*StyleBox[\"\\\"Integrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "calka nieoznaczona "∫f dx" "}, {"\!\(\*StyleBox[\"\\\"Sum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "suma "(∑_(i="\!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)")) f" "}, {"\!\(\*StyleBox[\"\\\"Solve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwiazanie rownania ze wzgledu na "x" "}, {"\!\(\*StyleBox[\"\\\"Series[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"order\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwiniecie w szereg potegowy funkcji "f" w punkcie "x=(Subscript[x, 0])" "}, {"\!\(\*StyleBox[\"\\\"Limit[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "granica "(lim_(x->(Subscript[x, 0])))f" "}})

Rozniczkowanie

({{"\!\(\*StyleBox[\"\\\"D[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pochodna czastkowa "(∂/(∂x)) f" "}, {"\!\(\*StyleBox[\"\\\"D[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pochodna wielokrotna "(((∂/(∂(Subscript[x, 1])))∂)/(∂(Subscript[x, 2]))) ... f" "}, {"\!\(\*StyleBox[\"\\\"D[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pochodna wielokrotna "((∂^nf)/(∂(x^n)))" "}, {"\!\(\*StyleBox[\"\\\"Dt[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozniczka "df" "}, {"\!\(\*StyleBox[\"\\\"Dt[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozniczka "(d/(dx)) f" "}})

D[ x^n, x ]

D[ ArcTan[x], x ]

D[ x^n, {x, 3} ]

Dt[ x^n, x ]

Dt[ x^n ]

D[ f[x], x ]

D[ 2 x f[x^2], x ]

Calkowanie

({{"\!\(\*StyleBox[\"\\\"Integrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "calka nieoznaczona "∫f dx" "}, {"\!\(\*StyleBox[\"\\\"Integrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "calka wielokrotna "∫dx dy f" "}, {"\!\(\*StyleBox[\"\\\"Integrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "calka oznaczona "(∫_("\!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"))f dx" "}, {"\!\(\*StyleBox[\"\\\"Integrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wielokrotna calka oznaczona "(∫_("\!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"))dx(∫_("\!\(\*StyleBox[\"\\\"ymin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"ymax\\\"\", \"TI\"]\)"))dy f" "}})

Integrate[x^n, x]

Integrate[1/(x^4 - a^4), x]

Integrate[ x^x, x ]

Integrate[ Log[x], {x, a, b} ]

Integrate[Exp[-x^2], {x, 0, Infinity}]

Integrate[ x^x, {x, 0, 1} ]

N[ % ]

Integrate[ x^2 + y^2, {x, 0, 1}, {y, 0, x} ]

Sumy i iloczyny

({{"\!\(\*StyleBox[\"\\\"Sum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "suma "(∑_(i="\!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)")) f" "}, {"\!\(\*StyleBox[\"\\\"Sum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"di\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "suma z indeksem \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) zwiekszanym z krokiem \!\(\*StyleBox[\"\\\"di\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Sum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"jmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"jmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "suma zagniezdzona "(∑_(i="\!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"))(∑_(j="\!\(\*StyleBox[\"\\\"jmin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"jmax\\\"\", \"TI\"]\)")) f" "}, {"\!\(\*StyleBox[\"\\\"Product[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "iloczyn "(∏_(i="\!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)")) f" "}})

Sum[x^i/i, {i, 1, 7}]

Sum[x^i/i, {i, 1, 5, 2}]

Product[x + i, {i, 1, 4}]

Sum[1/i^4, {i, 1, Infinity}]

Sum[1/(i^4 + 2), {i, 1, Infinity}]

Sum[1/(i! + (2i)!), {i, 1, Infinity}]

N[%]

Sum[x^i y^j, {i, 1, 3}, {j, 1, i}]

({{{"\!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}" ", "powtarzaj \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) razy bez zwiekszania zadnej zmiennej "}, {{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}" ", "zwiekszaj \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) od \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) do \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) o \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) "}, {{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}" ", "zwiekszaj \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) od \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) o \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) "}, {{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"di\\\"\", \"TI\"]\)"}" ", "zwiekszaj \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) od \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) o \!\(\*StyleBox[\"\\\"di\\\"\", \"TI\"]\) "}, {{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"jmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"jmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) …  ", "zwiekszaj \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) od \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) i dla kazdej wartosci \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) zwiekszaj \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\) od \!\(\*StyleBox[\"\\\"jmin\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"jmax\\\"\", \"TI\"]\), itd. "}})

Rownania

({{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "przypisz zmiennej \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) wartosc \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "sprawdz czy \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) i \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) sa rowne "}})

2 + 2 == 4

x = 4

x

x == 6

x =.

x == 5

% /. x -> 4

x^2 + 2 x - 7 == 0

eqn = %

eqn

Relacje i operacje logiczne

({{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "rowne (inna postac \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) == \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"!=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "nierowne (inna postac \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) ≠ \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "wieksze niz "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "wieksze lub rowne (inna postac \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) ≥ \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\))"}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"<\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "mniejsze niz "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"<=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "mniejsze lub rowne (inna postac \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) ≤ \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\))"}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\) ", "wszystkie rowne "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"!=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"!=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\) ", "wszystkie nierowne (scisle) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\),  itd. ", "scisle malejace, itd. "}})

10 < 7

3 != 2 != 3

3 < 5 <= 6

Pi^E < E^Pi

({{"\!\(\*StyleBox[\"\\\"!\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\) ", "nie (inna postac ¬\!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\)) "}, {"\!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"&&\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"q\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"&&\\\"\", \"MR\"]\) …  ", "i (inna postac \!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\) ∧ \!\(\*StyleBox[\"\\\"q\\\"\", \"TI\"]\) ∧ … ) "}, {"\!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"||\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"q\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"||\\\"\", \"MR\"]\) …  ", "lub (inna postac \!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\) ∨ \!\(\*StyleBox[\"\\\"q\\\"\", \"TI\"]\) ∨ … ) "}, {"\!\(\*StyleBox[\"\\\"Xor[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"q\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wylaczne lub "}, {"\!\(\*StyleBox[\"\\\"If[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"then\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"else\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc \!\(\*StyleBox[\"\\\"then\\\"\", \"TI\"]\) gdy \!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\) jest \!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) a \!\(\*StyleBox[\"\\\"else\\\"\", \"TI\"]\) gdy \!\(\*StyleBox[\"\\\"p\\\"\", \"TI\"]\) jest \!\(\*StyleBox[\"\\\"False\\\"\", \"MR\"]\) "}, {"\!\(\*StyleBox[\"\\\"LogicalExpand[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwin wyrazenie logiczne "}})

7 > 4 && 2 != 3

(p || q) && !(r || s)

LogicalExpand[ % ]

Rozwiazywanie rownan algebraicznych

({{"\!\(\*StyleBox[\"\\\"Solve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwiaz rownanie zwracaj wynik w postaci listy regul na \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"/.\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"solution\\\"\", \"TI\"]\) ", "uzyj listy regul w celu uzyskania wartosci \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"/.\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"solution\\\"\", \"TI\"]\) ", "uzyj listy regul w celu okreslenia wartosci wyrazenia "}})

Solve[x^2 + 2x - 7 == 0, x]

N[ % ]

x /. %

x^2 + 3 x /. %%

Mathematica zawsze rozwiaze rownanie algebraiczne jesli jego stopien jest nizszy niz piec.

Solve[x^4 - 5 x^2 - 3 == 0, x]

Solve[2 - 4 x + x^5 == 0, x]

N[ % ]

Solve[ Sin[x] == a, x ]

Solve[ Cos[x] == x, x ]

FindRoot[ Cos[x] == x, {x, 1} ]

Inny przyklad: Przecinanie sie okregu z prosta

Show[{Graphics[Circle[{0,0},1]],Plot[1-x,{x,-2,2}]}]

Manipulate[Show[{Graphics[Circle[{0,0},1]],Plot[a-x,{x,-2,2}]}],{a,-2,2}]

Solve[x^2+y^2==1 && x+y==a,{x,y},Reals]  (* w 10.0 && a>0 *)

Rozwiazywanie rownan rozniczkowych

({{"\!\(\*StyleBox[\"\\\"DSolve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"eqns\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"],\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwiaz rownanie rozniczkowe dla \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\), biorac \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) jako zmienna niezalezna "}, {"\!\(\*StyleBox[\"\\\"DSolve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"eqns\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) w postaci funkcji prymitywnej "}})

DSolve[ y'[x] == a y[x] + 1, y[x], x ]

DSolve[ {y'[x] == a y[x] + 1, y[0] == 0}, y[x], x ]

DSolve[ {x'[t] == y[t], y'[t] == x[t]},{x[t], y[t]}, t ]

DSolve[ y'[x] == x + y[x], y, x ]

y''[x] + y[x]  /.  %

Granice

({{"\!\(\*StyleBox[\"\\\"Limit[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "granica z \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) gdy \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) zdaza do "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])" "}})

t = Sin[x]/x

t /. x->0

t /. x->0.01

Limit[t, x->0]

Matematyka numeryczna

Operacje podstawowe

({{"\!\(\*StyleBox[\"\\\"N[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", numeryczna wartosc wyrazenia}, {"\!\(\*StyleBox[\"\\\"NIntegrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "numeryczne przyblizenie "(∫_("\!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)")) f dx}, {"\!\(\*StyleBox[\"\\\"NSum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"Infinity\\\"\", \"MR\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "numeryczne przyblizenie "(∑_("\!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)")^∞) f" "}, {"\!\(\*StyleBox[\"\\\"NSolve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "numeryczne przyblizenie rozwiazania rownania wielomianowego "}, {"\!\(\*StyleBox[\"\\\"FindRoot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz numeryczne rozwiazanie rownania startujac z \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])" "}, {"\!\(\*StyleBox[\"\\\"FindMinimum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz minimum funkcji \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) startujac z \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])" "}})

Numeryczne sumowanie, mnozenie, calkowanie

({{"\!\(\*StyleBox[\"\\\"NSum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"Infinity\\\"\", \"MR\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "numeryczne przyblizenie "(∑_("\!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)")^∞) f" "}, {"\!\(\*StyleBox[\"\\\"NProduct[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"Infinity\\\"\", \"MR\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "numeryczne przyblizenie "(∏_("\!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)")^∞) f" "}, {"\!\(\*StyleBox[\"\\\"NIntegrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "numeryczne przyblizenie "(∫_("\!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)")) f dx}, {"\!\(\*StyleBox[\"\\\"NIntegrate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "numeryczne przyblizenie "(∫_("\!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"))dx(∫_("\!\(\*StyleBox[\"\\\"ymin\\\"\", \"TI\"]\)")^("\!\(\*StyleBox[\"\\\"ymax\\\"\", \"TI\"]\)"))dy f" "}})

NSum[1/i^3, {i, 1, Infinity}]

NIntegrate[1/Sqrt[x (1-x)], {x, 0, 1}]

NIntegrate[Exp[-x^2], {x, -Infinity, Infinity}]

NIntegrate[ Sin[x y], {x, 0, 1}, {y, 0, x} ]

Numeryczne rozwiazywanie rownan algebraicznych

({{"\!\(\*StyleBox[\"\\\"NSolve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwiaz numerycznie rownanie wielomianowe "}, {"\!\(\*StyleBox[\"\\\"NSolve[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwiaz numerycznie uklad rownan wielomianowych "}, {"\!\(\*StyleBox[\"\\\"FindRoot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz rozwiazanie numeryczne rownania  zaczynajac od \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])" "}, {"\!\(\*StyleBox[\"\\\"FindRoot[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"lhs\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\"==\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"rhs\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz rozwiazanie numeryczne ukladu rownan "}})

NSolve[ x^5 + x + 1 == 0, x ]

NSolve[{x + y == 2, x - 3 y + z == 3, x - y + z == 0},
         {x, y, z}]

FindRoot[ 3 Cos[x] == Log[x], {x, 1} ]

FindRoot[ 3 Cos[x] == Log[x], {x, 10} ]

Numeryczne rozwiazywanie rownan rozniczkowych

({{"\!\(\*StyleBox[\"\\\"NDSolve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"eqns\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz numeryczna postac funkcji \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) spelniajaca rownania \!\(\*StyleBox[\"\\\"eqns\\\"\", \"TI\"]\)  ze zmienna niezalezna \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) w zakresie od \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"NDSolve[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"eqns\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "rozwiaz uklad rownan ze wzgledu na funkcje "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", i])" "}})

NDSolve[{y'[x] == y[x], y[0] == 1}, y, {x, 0, 2}]

y[1.5] /. %

({{"\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"/.\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"solution\\\"\", \"TI\"]\) ", "uzyj listy regul na \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) w celu okreslenia \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) "}, {"\!\(\*StyleBox[\"\\\"InterpolatingFunction[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"data\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"][\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wylicz wartosc funkcji przyblizajacej w punkcie \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Plot[Evaluate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"/.\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"solution\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"],\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wykresl rozwiazanie rownania rozniczkowego "}})

NDSolve[ {y'[x] == z[x], z'[x] == -y[x], y[0] == 0,
                    z[0] == 1}, {y, z}, {x, 0, Pi} ]

z[2] /. %

Plot[Evaluate[z[x] /. %3], {x, 0, Pi}]

(* Atraktor Lorenza *)
rozw=NDSolve[{x'[t]==-3 (x[t]-y[t]),y'[t]==-x[t] z[t]+26.5 x[t]-y[t],z'[t]==x[t] y[t]-z[t],x[0]==z[0]==0,y[0]==1},{x,y,z},{t,0,200},MaxSteps-> ∞]

ParametricPlot3D[Evaluate[{x[t], y[t], z[t]} /. rozw], {t, 0, 100}, PlotPoints -> 1000]

Optymalizacja numeryczna

({{"\!\(\*StyleBox[\"\\\"ConstrainedMin[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ineqs\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zminimalizuj funkcje liniowa \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) przy ograniczeniach liniowych \!\(\*StyleBox[\"\\\"ineqs\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"FindMinimum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz lokalne minimum dowolnej funkcji \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) startujac z \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])" "}, {"\!\(\*StyleBox[\"\\\"FindMinimum[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 0])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "znajdz lokalne minimum funkcji kilku zmiennych "}})

Zadanie programowania liniowego

ConstrainedMin[x - y - z, {y + z < 3, x > 7},
                                       {x, y, z}]

FindMinimum[x Cos[x], {x, 1}]

FindMinimum[x Cos[x], {x, 10}]

FindMinimum[Sin[x y], {x, 2}, {y, 2}]

Operowanie danymi numerycznymi

({{"\!\(\*StyleBox[\"\\\"Fit[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przybliz wartosci "(Subscript[y, n])" liniowa kombinacja funkcji "(Subscript[f, i])" "}, {"\!\(\*StyleBox[\"\\\"Fit[\\\"\", \"MR\"]\)"{{(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 1])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 2])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przybliz punkty "((Subscript[x, n]),(Subscript[y, n]))" liniowa kombinacja funkcji "(Subscript[f, i])" "}})

data = Table[ Exp[x/5.] , {x, 7}]

Fit[data, {1, x, x^2}, x]

Fit[data, {1, x, x^3, x^5}, x]

data = Table[ {x, Exp[Sin[x]]} , {x, 0., 1., 0.2}]

Fit[%, {1, Sin[x], Sin[2x]}, x]

Statystyka

<<Statistics`DescriptiveStatistics`

data = {4.3, 7.2, 8.4, 5.8, 9.2, 3.9}

Mean[data]

Variance[data]

DispersionReport[data]

Funkcje i programy

Definiowanie funkcji

({{"\!\(\*StyleBox[\"\\\"f[x_]\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\":=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"x^2\\\"\", \"MR\"]\) ", "zdefiniuj funkcje \!\(\*StyleBox[\"\\\"f\\\"\", \"MR\"]\) "}, {"\!\(\*StyleBox[\"\\\"?\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) ", "wyswietl definicje \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Clear[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "usun definicje \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) "}})

f[x_] := x^2

f[a+1]

f[4]

f[3x + x^2]

Expand[f[(x+1+y)]]

?f

hump[x_, xmax_] := (x - xmax)^2 / xmax

2 + hump[x, 3.5]

hump[x_, xmax_] := (x - xmax)^4

?hump

Funkcje jako procedury

({{(Subscript["\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\";\\\"\", \"MR\"]\) …  ", "sekwencja wyrazen do wyliczenia "}, {"\!\(\*StyleBox[\"\\\"Module[\\\"\", \"MR\"]\)"{"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"proc\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "procedura ze zmiennymi lokalnymi \!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\), \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\), …  "}})

Expand[ Product[x + i, {i, 3}] ]

Expand[ Product[x + i, {i, 4}] ]

exprod[n_] := Expand[ Product[ x + i, {i, 1, n} ] ]

exprod[5]

cex[n_, i_] := ( t = exprod[n]; Coefficient[t, x^i] )

ncex[n_, i_] :=
       Module[{u}, u = exprod[n]; Coefficient[u, x^i]]

cex[5, 3]

Petle

({{"\!\(\*StyleBox[\"\\\"Do[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wylicz \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) dla \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) zmieniajacego sie od \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) do \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Do[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"di\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wylicz \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) dla \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) zmieniajacego sie od \!\(\*StyleBox[\"\\\"imin\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) z krokiem \!\(\*StyleBox[\"\\\"di\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Print[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wypisz \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Table[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz liste wartosci wyrazenia \!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) dla \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) zmieniajacego sie od \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) do \!\(\*StyleBox[\"\\\"imax\\\"\", \"TI\"]\) "}})

Do[ Print[i!], {i, 5} ]

Table[ i!, {i, 5} ]

r = 1; Do[ r = 1/(1 + r), {100} ]; r

Reguly przeksztalcania dla funkcji

1 + f[x] + f[y] /. x -> 3

1 + f[x] + f[y] /. f[x] -> p

1 + f[x] + f[y] /. f[t_] -> t^2

f[a b] + f[c d] /. f[x_ y_] -> f[x] + f[y]

1 + x^2 + x^4 /. x^p_ -> f[p]

Listy

Laczenie obiektow w listy

{2, 3, 4}

x^% - 1

D[%, x]

% /. x -> 3

Wektory i macierze

({{{"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"c\\\"\", \"TI\"]\)"}" ", "wektor "(a,b,c)" "}, {{{"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"c\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"d\\\"\", \"TI\"]\)"}}" ", "macierz "(({{a, b}, {c, d}}))" "}})

m = {{a, b}, {c, d}}

m[[1]]

m[[1,2]]

v = {x, y}

p v + q

v + {xp, yp} + {xpp, ypp}

{x, y} . {xp, yp}

m . v

m . m

Funkcje do tworzenia wektorow

({{"\!\(\*StyleBox[\"\\\"Table[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz wektor o dlugosci "n" wyliczajac \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) dla \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\), \!\(\*StyleBox[\"\\\"2\\\"\", \"MR\"]\), … , \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Array[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz wektor o dlugosci "n" postaci "{"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[1],\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[2],\\\"\", \"MR\"]\) … "}" "}, {"\!\(\*StyleBox[\"\\\"Range[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz liste "{"\!\(\*StyleBox[\"\\\"1,\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"2,\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"3,\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)"}" "}, {"\!\(\*StyleBox[\"\\\"Range[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz liste "{(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\"+1,\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])}" "}, {"\!\(\*StyleBox[\"\\\"Range[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"dn\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz liste "{(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\"+\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"dn\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])}" "}, {"\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)""-ty element wektora \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Length[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc liczbe elementow wektora \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"MatrixForm[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wyswietl elementy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) jako macierz "}, {"\!\(\*StyleBox[\"\\\"c\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"v\\\"\", \"TI\"]\) ", "pomnoz przez skalar "}, {"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\".\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\) ", "iloczyn skalarny "}, {"\!\(\*StyleBox[\"\\\"Cross[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "iloczyn wektorowy (inna postac \!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\) × \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\)) "}})

Funkcje do tworzenia macierzy

({{"\!\(\*StyleBox[\"\\\"Table[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz macierz "m×n"wyliczajac \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\) dla \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) w zakresie od \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) do \!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\) i \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\) w zakresie od \!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) do \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Array[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz macierz "m×n" z "i,j"-tym elementem postaci \!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) "}, {"\!\(\*StyleBox[\"\\\"IdentityMatrix[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz macierz jednostkowa "n×n" "}, {"\!\(\*StyleBox[\"\\\"DiagonalMatrix[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "utworz macierz kwadratowa z elementami na diagonali z listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)""-ty rzad macierzy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc "i,j"-ty element macierzy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Dimensions[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zwroc wymiary macierzy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"MatrixForm[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wyswietl macierz \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) w formacie macierzowym "}})

s = Table[i+j, {i, 3}, {j, 3}]

MatrixForm[s]

({{"\!\(\*StyleBox[\"\\\"c\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\) ", "pomnoz przez skalar "}, {"\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\".\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"b\\\"\", \"TI\"]\) ", "iloczyn macierzy "}, {"\!\(\*StyleBox[\"\\\"Inverse[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "macierz odwrotna "}, {"\!\(\*StyleBox[\"\\\"MatrixPower[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)""-ta potega macierzy "}, {"\!\(\*StyleBox[\"\\\"Det[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wyznacznik "}, {"\!\(\*StyleBox[\"\\\"Transpose[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "transpozycja "}, {"\!\(\*StyleBox[\"\\\"Eigenvalues[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wartosci wlasne "}, {"\!\(\*StyleBox[\"\\\"Eigenvectors[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wektory wlasne "}, {"\!\(\*StyleBox[\"\\\"Eigenvalues[N[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\),  \!\(\*StyleBox[\"\\\"Eigenvectors[N[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", "numeryczne wartosci wlasne i wektory wlasne "}})

m

Det[m]

Inverse[m]

r = Table[i+j+1, {i, 3}, {j, 3}]

Eigenvalues[r]

Operowanie elementami list

({{"\!\(\*StyleBox[\"\\\"First[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pierwszy element listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Last[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "element ostatni "}, {"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", " \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)""-ty element "}, {"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[-\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", " \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)""-ty element od konca "}, {"\!\(\*StyleBox[\"\\\"Part[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\)  lub  \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", "lista elementow z pozycji "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])", "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])", …  "}})

({{"\!\(\*StyleBox[\"\\\"Take[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pierwszych \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) elementow z listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Take[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "ostatnich \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) elementow "}, {"\!\(\*StyleBox[\"\\\"Take[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "elementy od \!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) (wlacznie) "}, {"\!\(\*StyleBox[\"\\\"Rest[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "lista \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) z pominietym pierwszym elementem "}, {"\!\(\*StyleBox[\"\\\"Drop[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "lista \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) z pominietymi \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) pierwszymi elementami "}, {"\!\(\*StyleBox[\"\\\"Drop[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "lista \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) z pominietymi \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) ostatnimi elementami "}, {"\!\(\*StyleBox[\"\\\"Drop[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "lista \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) z pominietymi elem. od \!\(\*StyleBox[\"\\\"m\\\"\", \"TI\"]\) do \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) "}})

t = {a,b,c,d,e,f,g}

Take[t, 3]

Take[t, -3]

Take[t, {2, 5}]

Rest[t]

Drop[t, 3]

Drop[t, {3, 3}]

Testowanie i poszukiwanie elementow listy

({{"\!\(\*StyleBox[\"\\\"Position[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "pozycje na ktorych wzorzec \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\) wystepuje w liscie \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)"}, {"\!\(\*StyleBox[\"\\\"Count[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "liczba wystapien wzorca \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\) na liscie \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"MemberQ[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "sprawdz czy wzorzec \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\) jest elementem listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"FreeQ[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "sprawdz czy nie ma wzorca \!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\) na liscie \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}})

Position[{a, b, c, a, b}, a]

Count[{a, b, c, a, b}, a]

MemberQ[{a, b, c}, a]

MemberQ[{a, b, c}, d]

m = IdentityMatrix[3]

FreeQ[m, 0]

Position[m, 0]

Extract[m, %]

Dodawanie usuwanie i zamiana elementow list

({{"\!\(\*StyleBox[\"\\\"Prepend[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "dodaj \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\) na poczatku listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Append[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "dodaj \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\) na koncu listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Insert[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wstaw \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\) na pozycji \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Insert[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wstaw na pozycji \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) liczac od konca listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)"}, {"\!\(\*StyleBox[\"\\\"Insert[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wstaw na pozycji \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\), \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\), …  listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Delete[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "usun element na pozycji \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"Delete[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "usun element na pozycji \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\), \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\), …  listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}})

Prepend[{a, b, c}, x]

Append[{a, b, c}, x]

Insert[{a, b, c}, x, 2]

Insert[{a, b, c}, x, -2]

Delete[{a, b, c, d}, 3]

({{"\!\(\*StyleBox[\"\\\"ReplacePart[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zamien element na pozycji \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"ReplacePart[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zamien na pozycji \!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\) liczac od konca "}, {"\!\(\*StyleBox[\"\\\"ReplacePart[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zamien element \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) "}, {"\!\(\*StyleBox[\"\\\"ReplacePart[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{{(Subscript["\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zamien elementy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)", k])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"j\\\"\", \"TI\"]\)", k])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) tym samym elementem "}, {"\!\(\*StyleBox[\"\\\"ReplacePart[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{{(Subscript["\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\", \\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zamien element \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"i\\\"\", \"TI\"]\)", k])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) przez \!\(\*StyleBox[\"\\\"element\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"[[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)", k])"\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) "}})

ReplacePart[{a, b, c, d}, x, 3]

ReplacePart[{a, b, c, d}, x, {{1}, {4}}]

IdentityMatrix[3]

ReplacePart[%, x, {2, 2}]

Laczenie list

({{"\!\(\*StyleBox[\"\\\"Join[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "polacz listy "}, {"\!\(\*StyleBox[\"\\\"Union[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "polacz listy usuwajac powtarzajace sie elementy i sortujac wynik "}})

Join[{a, b, c}, {x, y}, {c, {d, e}, a}]

Union[{a, b, c}, {c, a, d}, {a, d}]

Reorganizowanie list

({{"\!\(\*StyleBox[\"\\\"Sort[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "posortuj elementy listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)  "}, {"\!\(\*StyleBox[\"\\\"Union[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "posortuj elementy usuwajac elementy powtarzajace sie "}, {"\!\(\*StyleBox[\"\\\"Reverse[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "odwroc porzadek elementow listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"RotateLeft[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przesun cyklicznie elementy listy \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) pozycji w lewo "}, {"\!\(\*StyleBox[\"\\\"RotateRight[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przesun \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) pozycji w prawo"}, {"\!\(\*StyleBox[\"\\\"RotateLeft[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\),  \!\(\*StyleBox[\"\\\"RotateRight[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przesun o jedna pozycje "}})

Sort[{b, a, c, a, b}]

Union[{b, a, c, a, b}]

Reverse[{a, b, c, d}]

RotateLeft[{a, b, c, d, e}, 2]

RotateLeft[{a, b, c, d, e}, -2]

Grupowanie elementow list

({{"\!\(\*StyleBox[\"\\\"Partition[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "podziel liste \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) na \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\) elementowe czesci "}, {"\!\(\*StyleBox[\"\\\"Partition[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"n\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"d\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "zastosuj przesuniecie \!\(\*StyleBox[\"\\\"d\\\"\", \"TI\"]\) dla kolejnych czesci "}, {"\!\(\*StyleBox[\"\\\"Split[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "podziel liste \!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\) na czesci zlozone z identycznych elementow "}})

t = {a, b, c, d, e, f, g}

Partition[t, 2]

Partition[t, 3]

Partition[t, 3, 1]

Split[{a, a, b, b, b, a, a, a, b}]

Grafika i dzwiek

Podstawowe funkcje graficzne

({{"\!\(\*StyleBox[\"\\\"Plot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl  funkcje f zalezna od x dla x w zakresie od xmin do xmax}, {"\!\(\*StyleBox[\"\\\"Plot[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl  kilka funkcji rownoczesnie}})

Plot[Sin[x], {x, 0, 2Pi}]

Plot[Tan[x], {x, -3, 3}]

Plot[{Sin[x], Sin[2x], Sin[3x]}, {x, 0, 2Pi}]

Wizualizacja wynikow obliczen

NDSolve[{y'[x] == Sin[y[x]], y[0] == 1}, y, {x, 0, 4}]

Plot[Evaluate[ y[x] /. % ], {x, 0, 4}]

Zmiana opcji wykresow

({{"\!\(\*StyleBox[\"\\\"Plot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"option\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", przedstaw wykres z uwzglednieniem wymienionych opcji        }})

({{ nazwa opcji ,  wartosc domyslna , }, {"\!\(\*StyleBox[\"\\\"AspectRatio\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"1/GoldenRatio\\\"\", \"MR\"]\) ", stosunek wysokosci do szerokosci; Automatic wylicza na podstawie akutalnych wartosci x i y}, {"\!\(\*StyleBox[\"\\\"Axes\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", wyswietlanie osi wspolrzednych  }, {"\!\(\*StyleBox[\"\\\"AxesLabel\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"None\\\"\", \"MR\"]\) ", opis osi wspolrzednych}, {"\!\(\*StyleBox[\"\\\"DisplayFunction\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"$DisplayFunction\\\"\", \"MR\"]\) ", sposob wyswietlania wykresu; Identity wylacza wyswietlanie}, {"\!\(\*StyleBox[\"\\\"Frame\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"False\\\"\", \"MR\"]\) ", wyswietlenie ramki wokol wykresu}, {"\!\(\*StyleBox[\"\\\"FrameLabel\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"None\\\"\", \"MR\"]\) ", etykiety wokol ramki}, {"\!\(\*StyleBox[\"\\\"FrameTicks\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", podzialka na ramce;None - brak}, {"\!\(\*StyleBox[\"\\\"GridLines\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"None\\\"\", \"MR\"]\) ", wyswietlanie siatki;   Automatic - dobor automatyczny}, {"\!\(\*StyleBox[\"\\\"PlotLabel\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"None\\\"\", \"MR\"]\) ", podpis wykresu}, {"\!\(\*StyleBox[\"\\\"PlotRange\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", zakres wspolrzednych pokazanych na rysunku;All powoduje wyswietlenie calego wykresu}, {"\!\(\*StyleBox[\"\\\"Ticks\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", podzialka na osiach; None- brak }})

Plot[Sin[x^2], {x, 0, 3}]

Plot[Sin[x^2], {x, 0, 3}, Frame->True]

Plot[Sin[x^2], {x, 0, 3},
               AxesLabel -> {"x value", "Sin[x^2]"} ]

Plot[Sin[x^2], {x, 0, 3}, Frame -> True,
               GridLines -> Automatic]

Plot[Sin[x^2], {x, 0, 3}, AspectRatio -> 1]

Mozliwe wartosci opcji

({{"\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", dobierz automatycznie}, {"\!\(\*StyleBox[\"\\\"None\\\"\", \"MR\"]\) ", nie wyswietlaj}, {"\!\(\*StyleBox[\"\\\"All\\\"\", \"MR\"]\) ", wyswietl wszystko}, {"\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) ", zrob}, {"\!\(\*StyleBox[\"\\\"False\\\"\", \"MR\"]\) ", nie rob}})

Opcja PlotRange

({{"\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", pokaz mozliwie duza czesc wykresu z uwydatnieniem miejsc ciekawych (wartosc domyslna)}, {"\!\(\*StyleBox[\"\\\"All\\\"\", \"MR\"]\) ", pokaz caly wykres}, {{"\!\(\*StyleBox[\"\\\"ymin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymax\\\"\", \"TI\"]\)"} , pokaz wykres w podanym zakresie y}, {{"\!\(\*StyleBox[\"\\\"xrange\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"yrange\\\"\", \"TI\"]\)"}" ", pokaz wykres w podanym zakresie x i y}})

Plot[Sin[x^2], {x, 0, 3}, PlotRange -> {0, 1.2}]

Plot[Sin[1/x], {x, -1, 1}]

Manipulowanie wykresami

({{"\!\(\*StyleBox[\"\\\"Show[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", przerysuj wykres}, {"\!\(\*StyleBox[\"\\\"Show[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"option\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", przerysuj wykres ze zmienionymi opcjami                                      }, {"\!\(\*StyleBox[\"\\\"Show[\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", polacz kilka wykresow}, {"\!\(\*StyleBox[\"\\\"Show[GraphicsArray[\\\"\", \"MR\"]\)"{{(Subscript["\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]]\\\"\", \"MR\"]\) ", pokaz tablice wykresow}, {"\!\(\*StyleBox[\"\\\"InputForm[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wyswietl informacje na temat wykresu }})

Przerysowywanie wykresow

Plot[ChebyshevT[7, x], {x, -1, 1}]

Show[%]

Show[%, PlotRange -> {-1, 2}]

Show[%, PlotLabel -> "A Chebyshev Polynomial"]

Laczenie wykresow

gj0 = Plot[BesselJ[0, x], {x, 0, 10}]

gy1 = Plot[BesselY[1, x], {x, 1, 10}]

gjy = Show[gj0, gy1]

Show[GraphicsGrid[{{gj0,gjy},{gy1,gjy}}]]

Show[%, Frame->True, FrameTicks->None]

Show[ % /. (Ticks -> Automatic) -> (Ticks -> None) ]

Zmiana wartosci domyslnych opcji

({{"\!\(\*StyleBox[\"\\\"Options[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"function\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", aktualne wartosci opcji danej funkcji}, {"\!\(\*StyleBox[\"\\\"Options[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"function\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"option\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wartosc wskazanej opcji funkcji }, {"\!\(\*StyleBox[\"\\\"SetOptions[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"function\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"option\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"value\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", zmiana wartosci opcji funkcji}})

Options[Plot, PlotRange]

SetOptions[Plot, PlotRange->All] ;

Options[Plot, PlotRange]

({{"\!\(\*StyleBox[\"\\\"Options[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wartosci opcji wskazanego wykresu}, {"\!\(\*StyleBox[\"\\\"Options[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"option\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wartosc wskazanej opcji wykresu}, {"\!\(\*StyleBox[\"\\\"FullOptions[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"option\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wyliczona wartosc wskazanej opcji}})

g = Plot[SinIntegral[x], {x, 0, 20}]

Options[g, PlotRange]

FullOptions[g, PlotRange]

Wykresy trojwymiarowe

({{"\!\(\*StyleBox[\"\\\"Plot3D[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl funkcje f zalezna od x i y}})

Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}]

({{ nazwa opcji ,  wartosc domyslna , }, {"\!\(\*StyleBox[\"\\\"Lighting\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) ", czy powierzchnia ma byc pokolorowana czy tez nie                   }, {"\!\(\*StyleBox[\"\\\"Mesh\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) ", czy siatka ma byc wyswietlana czy tez nie}, {"\!\(\*StyleBox[\"\\\"Shading\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) ", czy powierzchnia ma byc wycieniowana czy tez nie }, {"\!\(\*StyleBox[\"\\\"ViewPoint\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"{1.3,\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"-2.4,\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"2}\\\"\", \"MR\"]\) ", punkt z ktorego wykres jest widziany }})

Show[%, PlotRange -> {-0.5, 0.5}]

Plot3D[10 Sin[x + Sin[y]], {x, -10, 10}, {y, -10, 10},
                                PlotPoints -> 40]

Zmiana punktu widzenia

Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}]

Show[%, ViewPoint -> {0, -2, 0}]

g = Plot3D[Exp[-(x^2+y^2)], {x, -2, 2}, {y, -2, 2}]

Show[g, Mesh -> False]

Show[g, Shading -> False]
Show[g, ColorFunction -> (White &)]

Wykresy na podstawie list danych

({{"\!\(\*StyleBox[\"\\\"ListPlot[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wykresl wartosci "(Subscript[y, 1])", "(Subscript[y, 2])", "..." dla "x" rownego "1", "2", "..." "}, {"\!\(\*StyleBox[\"\\\"ListPlot[\\\"\", \"MR\"]\)"{{(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 1])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)", 2])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wykresl punkty "((Subscript[x, 1]),(Subscript[y, 1]))", "..." "}, {"\!\(\*StyleBox[\"\\\"ListPlot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"PlotJoined\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"True]\\\"\", \"MR\"]\) ", "polacz punkty liniami "}, {"\!\(\*StyleBox[\"\\\"ListPlot3D[\\\"\", \"MR\"]\)"{{(Subscript["\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)", 11])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)", 12])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)", 21])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"z\\\"\", \"TI\"]\)", 22])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przedstaw na wykresie 3D punkty "(Subscript[z, yx])" "}})

t = Table[i^2, {i, 10}]

ListPlot[t]

ListPlot[t,Joined->True]

Table[{i^2, 4 i^2 + i^3}, {i, 10}]

ListPlot[%]

t3 = Table[Mod[x, y], {y, 20}, {x, 30}] ;

ListPlot3D[t3]

Show[%, ViewPoint -> {1.5, -0.5, 0}]

Wykresy parametryczne

({{"\!\(\*StyleBox[\"\\\"ParametricPlot[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", x])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", y])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wykresl funkcje dana w postaci parametrycznej "}, {"\!\(\*StyleBox[\"\\\"ParametricPlot[\\\"\", \"MR\"]\)"{{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", x])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", y])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{(Subscript["\!\(\*StyleBox[\"\\\"g\\\"\", \"TI\"]\)", x])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"g\\\"\", \"TI\"]\)", y])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wykresl zestaw funkcji zadanych w postaci parametrycznej"}, {"\!\(\*StyleBox[\"\\\"ParametricPlot[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", x])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", y])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"AspectRatio\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"Automatic]\\\"\", \"MR\"]\) ", wykresl funkcje parametryczna z zachowaniem jej ksztaltu}})

ParametricPlot[{Sin[t], Sin[2t]}, {t, 0, 2Pi}]

ParametricPlot[{Sin[t], Cos[t]}, {t, 0, 2Pi}]

Show[%, AspectRatio -> Automatic]

({{"\!\(\*StyleBox[\"\\\"ParametricPlot3D[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", x])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", y])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", z])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "wykresl krzywa trojwymiarowa dana w postaci parametrycznej "}, {"\!\(\*StyleBox[\"\\\"ParametricPlot3D[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", x])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", y])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", z])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"u\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"umin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"umax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl powierzchnie trojwymiarowa dana w postaci parametrycznej  }})

ParametricPlot3D[{Sin[t], Cos[t], t/3}, {t, 0, 15}]

ParametricPlot3D[{t, u, Sin[t u]},
                    {t, 0, 3}, {u, 0, 3}]

ParametricPlot3D[{u Sin[t], u Cos[t], t/3},
                        {t, 0, 15}, {u, -1, 1}]

ParametricPlot3D[{Sin[t], Cos[t], u},
                   {t, 0, 2Pi}, {u, 0, 4}]

ParametricPlot3D[
   {Cos[t] (3 + Cos[u]), Sin[t] (3 + Cos[u]), Sin[u]},
             {t, 0, 2Pi}, {u, 0, 2Pi}]

ParametricPlot3D[
        {Cos[t] Cos[u], Sin[t] Cos[u], Sin[u]},
                 {t, 0, 2Pi}, {u, -Pi/2, Pi/2}]

Inne rodzaje wykresow

({{"\!\(\*StyleBox[\"\\\"<<Graphics`\\\"\", \"MR\"]\) ",  zaladuj pakiet z dodatkowymi funkcjami graficznymi        }, {"\!\(\*StyleBox[\"\\\"LogPlot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl funkcje w skali logary-
tmiczno-liniowej                                       }, {"\!\(\*StyleBox[\"\\\"LogLogPlot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl funkcje w skali logary- tmiczno-logarytmicznej}, {"\!\(\*StyleBox[\"\\\"LogListPlot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", jw. dla listy danych}, {"\!\(\*StyleBox[\"\\\"LogLogListPlot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", jw. dla listy danych}, {"\!\(\*StyleBox[\"\\\"PolarPlot[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"r\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl funkcje dana w ukladzie biegunowym}, {"\!\(\*StyleBox[\"\\\"BarChart[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", przedstaw wykres slupkowy}, {"\!\(\*StyleBox[\"\\\"PieChart[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", przedstaw wykres kolowy}, {"\!\(\*StyleBox[\"\\\"PlotVectorField[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", x])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)", y])}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"xmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"ymax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl pole wektorowe odpowiadajace funkcji f                     }, {"\!\(\*StyleBox[\"\\\"ListPlotVectorField[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"list\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl pole wektorowe
odpowiadajace tablicy
dwuwymiarowej list}, {"\!\(\*StyleBox[\"\\\"SphericalPlot3D[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"r\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"theta\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"min\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"max\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"phi\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"min\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"max\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykresl funkcje zadana w ukladzie sferycznym                           }})

<<Graphics`

LogPlot[ Exp[-x] + 4 Exp[-2x], {x, 0, 6} ]

p = Table[Prime[n], {n, 10}]

BarChart[p]

PieChart[p]

Graph[{1 -> 3, 1 -> 2, 2 -> 4, 4 -> 5, 5 -> 1}]

Animacja

({{"\!\(\*StyleBox[\"\\\"<<Graphics`Animation`\\\"\", \"MR\"]\) ", zaladuj pakiet Animation jesli potrzeba}, {"\!\(\*StyleBox[\"\\\"Animate[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"plot\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmin\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wykonaj szereg wykresow zgodnie z funkcja plot i przedstaw ich animacje}, {"\!\(\*StyleBox[\"\\\"ShowAnimation[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"g\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"g\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", przedstaw animacje sekwencji obiektow graficznych}})

Table[ Plot3D[ BesselJ[0, Sqrt[x^2 + y^2] + t],
       {x, -10, 10}, {y, -10, 10}, Axes -> False,
       PlotRange -> {-0.5, 1.0}],
   {t, 0, 8} ] // Short

Show[GraphicsGrid[Partition[%,3]]]

Animate[Plot3D[BesselJ[0,Sqrt[x^2+y^2]+t],{x,-10,10},{y,-10,10},Axes->False,PlotRange->{-0.5,1.0}],{t,0,8}]

Dzwiek

({{"\!\(\*StyleBox[\"\\\"Play[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"0,\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", odtworz dzwiek o apmlitudzie f danej jako funkcja czasu t wyrazonego w sekundach}})

Play[Sin[2Pi 440 t], {t, 0, 1}]

Play[Sin[1000/t], {t, 0, 5}]

Play[ Sin[700 t + 25 t Sin[350 t]], {t, 0, 4} ]

Play[RiemannSiegelZ[2000 t] , {t, 0, 6},PlayRange -> {-20,20} ]

<< Music`
Show[MusicScale[JustMinor[[{1, 3, 5, 8, 5, 3, 1}]], Aflat3, 3]]

wynik = NDSolve[{x'[t] == x[t] Cos[t + x[t]], x[0] == 1}, x, {t, 0, 100}]

Plot[x[t] /.wynik, {t, 0, 100}, PlotRange -> All]

Play[Evaluate[Sin[2000 x[4t] t] /. wynik], {t, 0, 25}]

wynik = NDSolve[{x''[t] + x[t]^3 == Sin[t], x[0] == x'[0] == 0},x, {t, 0, 100}]

Plot[x[t] /.wynik, {t, 0, 50}]

ParametricPlot[Evaluate[{x[t], x'[t]} /. wynik], {t, 0, 50}]

Play[Evaluate[Sin[2000(2+ x[2t]) t] /. wynik], {t, 0, 50}]

s=NDSolve[{x'[t]==-3 (x[t]-y[t]),y'[t]==-x[t] z[t]+26.5 x[t]-y[t],z'[t]==x[t] y[t]-z[t],x[0]==z[0]==0,y[0]==1},{x,y,z},{t,0,200},MaxSteps->∞]

ParametricPlot3D[Evaluate[{x[t], y[t], z[t]} /. s], {t, 0, 200}, PlotPoints -> 1000, ColorFunction -> (Hue[#4] &)]

Plot[x[t] /. s, {t, 0, 50}]

Play[Evaluate[Sin[100(10+x[2t]) t] /. s], {t, 0, 50}]

Sound[SoundNote[DeleteCases[3 Range[31] Reverse[#], 0] - 48, .1] & /@ Transpose[CellularAutomaton[150, {{1}, 0}, 30]]]

PieChart[Table[
With[{j = i}, Button[1, EmitSound[Sound@SoundNote[j]]]], {i, 14}]]

Speak["this is some text"]

({{"\!\(\*StyleBox[\"\\\"Play[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "{"\!\(\*StyleBox[\"\\\"t\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"0,\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"tmax\\\"\", \"TI\"]\)"}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"SampleRate\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"r\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", odtworz dzwiek z probkowaniem o czestotliwosci r                }})

({{"\!\(\*StyleBox[\"\\\"ListPlay[\\\"\", \"MR\"]\)"{(Subscript["\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) "(Subscript["\!\(\*StyleBox[\"\\\"a\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … "}"\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"SampleRate\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"r\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", odtworz dzwiek o amplitudzie danej lista                                               }})

({{"\!\(\*StyleBox[\"\\\"Show[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"sound\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", odtworz ponownie dzwiek}})

Wprowadzanie wyrazen w Mathematice

Greckie litery

({{"zaznacz myszka ""α"" ", "wybierz odpowiednie pole palety "}, {"∖\!\(\*StyleBox[\"\\\"[Alpha]\\\"\", \"MR\"]\) ", "wykorzystaj pelna nazwe litery "}, {"Esc\!\(\*StyleBox[\"\\\"aEsc\\\"\", \"MR\"]\)  lub  Esc\!\(\*StyleBox[\"\\\"alphaEsc\\\"\", \"MR\"]\) ", "wykorzystaj alias (oznaczane jako \!\(\*StyleBox[\"\\\"a\\\"\", \"MR\"]\)) "}, {"Esc\!\(\*StyleBox[\"\\\"\\\\\\\\alphaEsc\\\"\", \"MR\"]\) ", "wykorzystaj alias w formacie TeX'a"}, {"Esc\!\(\*StyleBox[\"\\\"&agrEsc\\\"\", \"MR\"]\) ", "wykorzystaj alias w formacie  SGML "}})

Greckie litery jako nazwy zmiennych

Expand[(α + β)^3]

Expand[(α + β)^3]

Expand[(Rαβ + Ξ)^4]

Factor[πα^4 - 1]

Uwaga: π oznacza Pi.

N[π]

Wyrazenia wielowymiarowe

Standardowy sposob wprowadzania wyrazen

x^y

Wyrazenie dwuwymiarowe wprowadzone bezposrednio...

(x^y)

...przez wykorzystanie palety

...przez wykorzystanie kombinacji klawiszy

({{"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) Ctrl[\!\(\*StyleBox[\"\\\"^]\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) Ctrl[␣] ", "uzyj klawiszy kontrolnych, ktore znajduja sie na wiekszosci klawiatur "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) Ctrl[\!\(\*StyleBox[\"\\\"6]\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) Ctrl[␣] ", "uzyj klawiszy kontrolnych znajdujacych sie na kazdej klawiaturze "}, {"∖\!\(\*StyleBox[\"\\\"!∖(\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"x∖\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"^\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"y∖\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\")\\\"\", \"MR\"]\) followed by \!\(\*StyleBox[\"\\\"Make 2D\\\"\", \"SR\"]\) ", "wykorzystaj podstawowe znaki ASCII "}})

x \[ControlKey]\[LeftModified]^\[RightModified] y

x \[ControlKey]\[LeftModified]^\[RightModified] y + z

x \[ControlKey]\[LeftModified]^\[RightModified] y \[ControlKey]\[LeftModified]␣\[RightModified] + z

x \[ControlKey]\[LeftModified]_\[RightModified] y

x \[ControlKey]\[LeftModified]^\[RightModified] y \[ControlKey]\[LeftModified]%\[RightModified] z

({{"Ctrl[^]  lub  Ctrl[6] ", "przejdz na pozycje indeksu gornego"}, {"Ctrl[_]  lub  Ctrl[-] ", "przejdz na pozycje indeksu "dolnego}, {"Ctrl[@]  lub  Ctrl[2] ", "wprowadz pierwiastek kwadratowy "}, {"Ctrl[%]  lub  Ctrl[5] ", przejdz z indeksu gornego na dolny
lub vice versa,wejdz na pozycje
stopnia pierwiastka}, {"Ctrl[/] ", "przejdz na pozycje mianownika ulamka "}, {"Ctrl[␣] ", powroc do pozycji normalnej}})

Wprowadzanie wzorow

({{"\!\(\*StyleBox[\"\\\"znak\\\"\", \"SO10\"]\) ", "\!\(\*StyleBox[\"\\\"alias\\\"\", \"SO10\"]\) ", "\!\(\*StyleBox[\"\\\"symbol\\\"\", \"SO10\"]\) "}, {π" ", "\!\(\*StyleBox[\"\\\"p\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Pi\\\"\", \"MR\"]\) "}, {∞" ", "\!\(\*StyleBox[\"\\\"inf\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Infinity\\\"\", \"MR\"]\) "}, {"°"" ", "\!\(\*StyleBox[\"\\\"deg\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Degree\\\"\", \"MR\"]\) "}})

"" oznacza klawisz "Esc".

Sin[60°]

Sin[60 °]

Sin[60 deg]

Sin[(π/3)]

({{"\!\(\*StyleBox[\"\\\"znak\\\"\", \"SO10\"]\) ", "\!\(\*StyleBox[\"\\\"alias\\\"\", \"SO10\"]\) ", "\!\(\*StyleBox[\"\\\"oznaczenie\\\"\", \"SO10\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) ≤ \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"<=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"<=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) ≥ \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) ≠ \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"!=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"!=\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) -> \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) ", "\!\(\*StyleBox[\"\\\"x\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\"->\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"y\\\"\", \"TI\"]\) "}})

x/(x+1) /. x -> 3 + y

x/(x+1) /. x -> 3 + y

x/(x+1) /. x -> 3 + y

({{"\!\(\*StyleBox[\"\\\"alias\\\"\", \"SO10\"]\) ", "\!\(\*StyleBox[\"\\\"wyrazenie pelne\\\"\", \"SO10\"]\) ", }, {"\!\(\*StyleBox[\"\\\"sum\\\"\", \"MR\"]\) ", "∖\!\(\*StyleBox[\"\\\"[Sum]\\\"\", \"MR\"]\) ", "znak sumy ∑ "}, {"\!\(\*StyleBox[\"\\\"prod\\\"\", \"MR\"]\) ", "∖\!\(\*StyleBox[\"\\\"[Product]\\\"\", \"MR\"]\) ", "znak iloczynu ∏ "}, {"\!\(\*StyleBox[\"\\\"int\\\"\", \"MR\"]\) ", "∖\!\(\*StyleBox[\"\\\"[Integral]\\\"\", \"MR\"]\) ", "znak calki ∫ "}, {"\!\(\*StyleBox[\"\\\"dd\\\"\", \"MR\"]\) ", "∖\!\(\*StyleBox[\"\\\"[DifferentialD]\\\"\", \"MR\"]\) ", "znak rozniczki d "}, {"\!\(\*StyleBox[\"\\\"pd\\\"\", \"MR\"]\) ", "∖\!\(\*StyleBox[\"\\\"[PartialD]\\\"\", \"MR\"]\) ", "znak pochodnej czastkowej ∂ "}})

int f[x] dd x

∫Exp[-(x^2)]\[DifferentialD]x

Integrate[Exp[-x^2], x]

(∂_x)(x^n)

D[x^n, x]

(∂_(x,x,x))(x^n)

D[x^n, x, x, x]

Tablice i macierze

({{"Ctrl[,] ", "dodaj kolumne "}, {"Ctrl[↵] (Control-Return) ", "dodaj rzad "}, {"Tab ", "przejdz do nastepnego pola □ lub ■ "}, {"Ctrl[␣] (Control-Space) ", "wyjdz poza tablice "}})

({{a, b, c}, {1, 2, 3}})

(({{a, b, c}, {1, 2, 3}}))

Wyrazenia w jezyku naturalnym

({{"= ", zrob cos z tym co potrafisz}})

=plot a sine function

=solve the equation a x^2+3b =c

=picture of a parrot

Operacje na plikach dyskowych

Wczytywanie i zapisywanie plikow Mathematici

({{"\!\(\*StyleBox[\"\\\"<<\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"name\\\"\", \"TI\"]\) ", "wczytaj plik w formacie \!\(\*StyleBox[\"\\\"Mathematici\\\"\", \"TI\"]\) "}, {"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">>\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"name\\\"\", \"TI\"]\) ", "zapisz wyrazenie do pliku tekstowego "}, {"\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\) \!\(\*StyleBox[\"\\\">>>\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"name\\\"\", \"TI\"]\) ", "dopisz wyrazenie do pliku tekstowego "}, {"\!\(\*StyleBox[\"\\\"!!\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"name\\\"\", \"TI\"]\) ", "wyswietl zawartosc pliku tekstowego "}})

Expand[ (x + y)^3 ]  >> tmp

Zawartosc pliku

!!tmp

Wczytanie pliku z wyliczeniem wyrazen znajdujacych sie w nim

<<tmp

({{"\!\(\*StyleBox[\"\\\"Save[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"name\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"f\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"g\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) … \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", umieszczenie definicji zmiennych lub funkcji w pliku tekstowym}})

f[x_] := x^2 + c

c = 17

Save["ftmp", f]

!!ftmp

<<ftmp;

({{"\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".m\\\"\", \"MR\"]\) ", plik tekstowy z wyrazeniami w formacie Mathematici}, {"\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".nb\\\"\", \"MR\"]\) ", plik typu notebook}, {"\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".mx\\\"\", \"MR\"]\) ", plik z wyrazeniami Mathematici w formacie DumpSave}})

Wskazanie przy uzyciu pola Cell menu pozwala na wskazanie cel, ktore maja byc wyliczone automatycznie przy wczytaniu notebooka.

({{"\!\(\*StyleBox[\"\\\"Directory[\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "podaj nazwe katalogu biezacego "}, {"\!\(\*StyleBox[\"\\\"SetDirectory[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"dir\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", "zmien katalog biezacy "}, {"\!\(\*StyleBox[\"\\\"FileNames[\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", wylistuj zawartosc katalogu biezacego}, {"\!\(\*StyleBox[\"\\\"FileNames[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"form\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", jw. z uwzglednieniem wzorca}, {"\!\(\*StyleBox[\"\\\"<<\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"name\\\"\", \"TI\"]\) ", wczytaj zawartosc pliku}, {"\!\(\*StyleBox[\"\\\"<<\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"context\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"`\\\"\", \"MR\"]\) ", wczytaj zawartosc pliku zwiazanego z biezacym kontekstem}, {"\!\(\*StyleBox[\"\\\"CopyFile[\\\\\\\"\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)", 1])"\!\(\*StyleBox[\"\\\"\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"\\\\\\\"\\\"\", \"MR\"]\)"(Subscript["\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)", 2])"\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", "skopiuj "(Subscript["\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)", 1])" do "(Subscript["\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)", 2])" "}, {"\!\(\*StyleBox[\"\\\"DeleteFile[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", "skasuj plik"}})

Directory[ ]

SetDirectory["Examples"]

FileNames["Test*.m"]

({{"\!\(\*StyleBox[\"\\\"FindList[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"text\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", "wypisz linie zawierajace text we wskazanym pliku"}, {"\!\(\*StyleBox[\"\\\"FindList[FileNames[\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"],\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"text\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", przeszukaj wszystkie pliki w biezacym katalogu}})

FindList["index", "Laplace"]

Wczytywanie plikow danych

({{"\!\(\*StyleBox[\"\\\"ReadList[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"Number]\\\"\", \"MR\"]\) ", wczytaj liczby z pliku i utworz z nich liste w formacie Mathematici}, {"\!\(\*StyleBox[\"\\\"ReadList[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"Number,\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"RecordLists->True]\\\"\", \"MR\"]\) ", jw., utworz oddzielna liste dla kazdej linii pliku }})

!!rand.dat

ReadList["rand.dat", Number]

ReadList["rand.dat", Number, RecordLists -> True]

Generowanie wyrazen w formacie Fortranu i C

({{"\!\(\*StyleBox[\"\\\"CForm[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przedstaw wyrazenie w formacie zgodnym z jezykiem C "}, {"\!\(\*StyleBox[\"\\\"FortranForm[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", "przedstaw wyrazenie w Fortrana"}})

Expand[(1 + x + y)^2]

FortranForm[%]

CForm[%]

Makra obiektow takich jak funkcja Power sa zdefiniowane w pliku naglowkowym C mdefs.h dostarczanym wraz z Mathematica.

Eksportowanie grafiki

({{"\!\(\*StyleBox[\"\\\"Display[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"graphics\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"format\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", zapisz obiekt graficzny w pliku w zadanym formacie}, {"\!\(\*StyleBox[\"\\\"Display[\\\\\\\"!\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"command\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"graphics\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"format\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"\\\\\\\"]\\\"\", \"MR\"]\) ", "podaj obiekt graficzny na wejscie polecenia systemowego"}})

Plot[Sin[x] + Sin[Sqrt[2] x], {x, 0, 10}]

Export["sinplot.eps",%,"EPS"]

Export["!lpr",%,"EPS"]

({{"\!\(\*StyleBox[\"\\\"\\\\\\\"MPS\\\\\\\"\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Mathematica\\\"\", \"TI\"]\) abbreviated PostScript "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"EPS\\\\\\\"\\\"\", \"MR\"]\) ", "Encapsulated PostScript "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"EPSI\\\\\\\"\\\"\", \"MR\"]\) ", "Encapsulated PostScript with \!\(\*StyleBox[\"\\\"image\\\"\", \"MR\"]\) preview "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"EPSTIFF\\\\\\\"\\\"\", \"MR\"]\) ", "Encapsulated PostScript with TIFF preview "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"PDF\\\\\\\"\\\"\", \"MR\"]\) ", "Adobe Acrobat portable document format "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"Illustrator\\\\\\\"\\\"\", \"MR\"]\) ", "Adobe Illustrator format "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"PICT\\\\\\\"\\\"\", \"MR\"]\) ", "Macintosh PICT "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"Metafile\\\\\\\"\\\"\", \"MR\"]\) ", "Microsoft Windows metafile "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"TIFF\\\\\\\"\\\"\", \"MR\"]\) ", "TIFF "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"GIF\\\\\\\"\\\"\", \"MR\"]\) ", "GIF "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"PSImage\\\\\\\"\\\"\", \"MR\"]\) ", "PostScript \!\(\*StyleBox[\"\\\"image\\\"\", \"MR\"]\) format "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"XBitmap\\\\\\\"\\\"\", \"MR\"]\) ", "X Windows bitmap "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"PCL\\\\\\\"\\\"\", \"MR\"]\) ", "Hewlett-Packard printer control language "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"PBM\\\\\\\"\\\"\", \"MR\"]\) ", "portable bitmap "}, {"\!\(\*StyleBox[\"\\\"\\\\\\\"MGF\\\\\\\"\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Mathematica\\\"\", \"TI\"]\) system-independent raster graphics format "}})

Formaty nad kreska - wektorowe

({{"\!\(\*StyleBox[\"\\\"ImageSize\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", rozmiar grafiki wyrazony w punktach drukarki}, {"\!\(\*StyleBox[\"\\\"ImageRotated\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"False\\\"\", \"MR\"]\) ", pionowe lub poziome ulozenie grafiki}, {"\!\(\*StyleBox[\"\\\"ImageResolution\\\"\", \"MR\"]\) ", "\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) ", rozdzielczosc grafiki w dpi}})

Opcje funkcji Display.

Generowanie wyrazen w formacie TeX'a i HTML

({{"\!\(\*StyleBox[\"\\\"TeXForm[\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"expr\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\"]\\\"\", \"MR\"]\) ", przedstaw wyrazenie w formacie TeX'a}})

(x + y)^2 / Sqrt[x y]

TeXForm[%]

({{"\!\(\*StyleBox[\"\\\"TeXSave[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".tex\\\\\\\"]\\\"\", \"MR\"]\) ", "zapisz biezacy notebook w formacie TeX'a "}, {"\!\(\*StyleBox[\"\\\"TeXSave[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".tex\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"source\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".nb\\\\\\\"]\\\"\", \"MR\"]\) ", "zapisz notebook \!\(\*StyleBox[\"\\\"source\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".nb w formacie TeX'a\\\"\", \"MR\"]\) "            }})

({{"\!\(\*StyleBox[\"\\\"HTMLSave[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".html\\\\\\\"]\\\"\", \"MR\"]\) ", zapisz biezacy notebook w  HTML}, {"\!\(\*StyleBox[\"\\\"HTMLSave[\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"file\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".html\\\\\\\",\\\"\", \"MR\"]\) \!\(\*StyleBox[\"\\\"\\\\\\\"\\\"\", \"MR\"]\)\!\(\*StyleBox[\"\\\"source\\\"\", \"TI\"]\)\!\(\*StyleBox[\"\\\".nb\\\\\\\"]\\\"\", \"MR\"]\) ", zapisz notebook source.nb w formacie HTML}})

Uruchamianie programow zewnetrznych

x^2 + y^2 >> "!lpr"

Uruchomienie zewnetrznego programu i wypisanie wyniku jego dzialania

!squares 4

Uruchomienie zewnetrznego programu i wczytanie na liste wyniku jego dzialania

ReadList["!squares 4", Number, RecordLists->True]