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1 1. Uvod mathematical computational engine / software OBSAH PREDMETU: zakladni principy/uvod - Maple 18 ABSOLVOVANI PREDMETU: klasifikovany zapocet 1) test na cviceni (90 min, 14. tyden, povoleny vsechny materialy) 2) vypracovani projektu (zadani v prubehu semestru tyden) 2. Maple - verze - Maple 18: Standard Worksheet (.mw) -!! my budeme pouzivat!! - Classic Worksheet Maple 18 (.mws) - starsi pocitace, mene pameti - Command-line Maple 18 - komplexni vypocty - a jine (kalkulacka, vlastni aplikace - maplets) 3. Maple - prostredi Ikonky novy subor (Create a new file ulozeni (Save the active file T (Insert plain text after the current execution group radek) [ (Insert Maple Input after the current execution group (vytvori novy radek, executable) Math mode - text je cerny + radek nemusi byt ukoncen ; nebo : Text mode - text je cerveny + radek musi byt ukoncen ; nebo : novy blok (Enclose the current selection in a document mode, or create a new one) odstavce (Enclose the selection in a subsection Z Remove any section enclosing the selection) restart (Restart Maple server) Poznamka: - "tlacitko" restart - vyhodnoceni az pri prvnim spusteni ve worksheetu - "napsany" restart - vyhodnoceni hned po [Enter]:!!! (Execute the entire worksheet)! (Execute all selected groups) preruseni operace (Interrupt the current operation) Priklad: Warning, computation interrupted

! - Classic Worksheet Maple 18 (.mws) - starsi pocitace, mene pameti - Command-line Maple 18 - komplexni vypocty - a jine (kalkulacka, vlastni aplikace - maplets) 3.

2 help (Open the help system (help), F2 (napoveda pro dany prikaz) Palety - viz leva cast pracovniho okna - umoznuji rychlejsi zadavani matematickeho vstupu, specialnich symbolu, Reseni problemu Cisla (symbol v Open Face palete) - cele cisla ; (4.1.1) = Z/; - racionalni cisla 2/4; evalf(2/3); (4.1.2) (4.1.3) - realne cisla 2/4.; (4.1.4) - komplexne cisla (1+2*I)*(1-2*I); # I imaginární jednotka 5 5+0*I; 5 (4.1.5) (4.1.6) Zakladni operace: +, -, *, / Konstanty - cislo evalf(pi); (4.2.1) (4.2.2)

3456789; 123456789 (4.1.1) = Z/; - racionalni cisla 2/4; evalf(2/3); 1 2 0.6666666667 (4.1.2) (4.1.3) - realne cisla 2/4.; 0.

3 - hodnota (cislo) Pi; evalf(pi); evalf(gamma); (4.2.3) (4.2.4) (4.2.5) exponenciala exp(1); exp(1); evalf(exp(1)); evalf(exp(2)); evalf(e); e e e (4.2.6) (4.2.7) (4.2.8) (4.2.9) (4.2.10) Promenne nazvy - kombinace: male/velke pismena + cislice + "_" mezery v nazvech promennych nepouzivat - Maple chape mezery jako nasobeni (az na 1-D mode) Priklady: promenna1; promenna1 := 2; promenna1; x := a[123]*b; a[123] := 3; x; promenna1 2 (4.3.1) (4.3.2) (4.3.3) (4.3.4) (4.3.5) (4.3.6) x := 'x'; x+1; (4.3.7) (4.3.8) Document Mode vs. Worksheet Mode

promennych nepouzivat - Maple chape mezery jako nasobeni (az na 1-D mode) Priklady: promenna1; promenna1 := 2; promenna1; x := a[123]*b; a[123] :=

4 Maple offers two primary modes of problem entry and content creation: Document mode and Worksheet mode. Both modes have respective advantages and you can easily switch from one mode to the other for maximum flexibility. See worksheet for more information on the worksheet interface. Document Mode Quick problem-solving and free-form, rich content composition No prompt () displayed Math is entered and displayed in 2-D Solve math problems with right-click menu on input and output Worksheet Mode Traditional Maple problem-solving environment Enter problems at a prompt () Math entered and displayed in 2-D or 1-D Solve math problems with right-click menu on output Document mode lets you create rich content. For example, the following solves for x without any commands: solutions for x The command to perform the same operation in Worksheet mode is in 2-D (Math) Input: (4.4.1) or in 1-D (Maple) Input: solve((x-2)/alpha=1,x); (4.4.2) Toggle Math/Text entry mode [F5] Toggle 2-D/1-D Math entry mode [F5] 2-D black font, 1 -D red font on toolbar Evaluate math expression and display result inline [Ctrl][=] Evaluate math expression and display result on new line [Enter] Evaluate math expression and display result on new line [Enter] Continue on next line without executing [Shift][Enter] Switch to Worksheet mode (insert prompt) on toolbar Switch to Document mode Format Create Document Block Show hidden commands View Expand Document Block Hide commands. Show only results. Highlight commands to be hidden. Format Create Document Block Zapis matematickych vyrazu 1-D Math vs. 2-D Math Math Input Z 2-D Math Input)

Document Mode Quick problem-solving and free-form, rich content composition No prompt () displayed Math is entered and displayed in 2-D Solve math problems with right-click menu on input and output

5 int(exp(-x^2), x = 0.. infinity); (4.5.1) (4.5.2) (4.5.3)!!! Pozor na mezery!!! : = ale = Vyhodnoceni vyrazu Document mode: 3 (4.6.1) = 3 Worksheet mode (s [): a) Math (cerny text) (+ Enter) 3 (4.6.2) 10 (+Shift+Enter (nevyhodnoti radek, radky musi matematicky "navazovat")) b) Text (cerveny text) ; ; 10 Hlaseni chyb (4.6.3) (4.6.4) Error, unable to match delimiters sin(x

6 ... zadna chybova hlaska, ale taky zadny vystup v Maple 16 jeste byla chybova hlaska: Warning, premature end of input, use <Shift + <Enter to avoid this message. sin(x; Error, `;` unexpected Error, unable to match delimiters Operace s vyrazy (classic mod) - zjednodusi vyraz v1 := ((3-2*sqrt(2))/(3*sqrt(2)-4))^2; ( ) simplify(v1); 1 2 v2 := (sqrt(a)*a^(1/3)/(a*sqrt(a))^(1/3))^(-1); simplify(v2); simplify(v2, symbolic); # nebere v potaz podmínky 1 ( ) ( ) ( ) ( ) v3 := (a^2+1)^(1/2)/(a*(1+1/a^2)^(1/2)); #výsledek a /a ( ) simplify(v3); ( ) simplify(v3, symbolic); # tento vysledek neni spravne 1 ( ) simplify(v3, assume = negative); ( )

:= ((3-2*sqrt(2))/(3*sqrt(2)-4))^2; (4.8.1.

7 ( ) simplify(v3, assume = positive); ( ) - roznasobi soucin v1 := (2*x+1)*(x-3); simplify(v1); expand(v1); v2 := (x+1)^3; v3 := expand(v2); ( ) ( ) ( ) - rozlozi na soucin cinitelu v3; simplify(v3); factor(v3); combine - slouci vyrazy stejneho typu ( ) ( ) ( ) v := sqrt(2)*sqrt(3); simplify(v); combine(v); ( ) ( ) ( ) convert - ukazeme si jenom prevod na parcialni zlomky v := 1/(x^2-1); convert(v, parfrac); ( ) w := a/(x^2-1);

$8.3.1) (4.8.3.2) (4.8.3.3) v := sqrt(2)*sqrt(3); simplify(v); combine(v); (4.8.4.1) (4.8.4.2) (4.8.4.3) convert - ukazeme si jenom prevod na parcialni zlomky v := 1/(x^2-1); convert(v, parfrac); (4.$

8 convert(w, parfrac, x); ( ) z := [a+b-2*b]/(a-b); simplify(z); ( ) ( ) Deleni polynomu - zjisti, zda jsou polynomy delitelne beze zbytku delenec := x^3-1; delitel:=x-1; divide(delenec, delitel); true divide(delenec, delitel, 'podil'); true podil; p := x^2+x+1; divide(p, delitel, 'q'); false q; q ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) - vydeli dva polynomy a zbytek ulozi do promenne je jako nahore v casti pro divide, i.e. q := x-1; quo(p, q, x); quo(p, q, x, 'zbytek'); ( ) ( ) ( )

2) Deleni polynomu - zjisti, zda jsou polynomy delitelne beze zbytku delenec := x^3-1; delitel:=x-1; divide(delenec, delitel); true

9 zbytek; 3 p/q = quo(p, q, x, 'zbytek')+zbytek/q; ( ) ( ) ( ) - zbytek po deleni dvou polynomu rem(p, q, x); 3 p/q = quo(p, q, x)+rem(p, q, x)/q; ( ) ( )

8.3) (4.8.8.4) (4.8.8.5) - zbytek po deleni

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