Maple paketining asosiy maqsadi va

sin(Pi/3);	Enter tugmasi bosing va natija :
>cos(Pi/3)		Enter :	1/2
cos(Pi);		Enter :	-1
sin(Pi/3)+cos(Pi/2)+2*sin(Pi/12);		Enter :
cot(Pi/2);		Enter :	0
tan(Pi/3);		Enter :	3
x:=Pi/2:y:=sin(x)+cos(x);		Enter :	y := 1
exp(1.);		Enter :	2.718281828
ln(1);		Enter :	0
arcsin(1);		Enter :	1  2
arccos(1/2);		Enter :	1  3

1) cos(π/3)*sin(π/12)+tg(π/5) berilgan trigonometrik funksiyani hisoblang. 2*cos(Pi/3)*sin(Pi/15)+tan(Pi/5); Enter tugmasini bosing va natija:


Berilgan sonnnig faktorialini hisoblash uchun Maple dasturida factorial buyrug’i tanlanadi.

Masalan.

• 
  factorial(10); Enter tugmasini bosing natija: 3628800
  
• 
  factorial(23); Enter tugmasini bosing natija: 25852016738884976640000
  

Berilgan sonnnig kattasini hisoblash uchun Maple dasturida max buyrug’i tanlanadi.

• 
  max(44,47,-60); Enter tugmasini bosing natija: 47
  
• 
  max(414,-620,-60,548,-56); Enter tugmasini bosing natija: 548
  

>max(414*9,-620+5,-60-5,548*3,-56*5); ^{Enter tugmasini bosing natija:3726} Berilgan sonnnig eng kichigini hisoblash uchun Maple dasturida min buyrug’i tanlanadi.

• 
  min(44,47,-60); Enter tugmasini bosing natija: -60
  
• 
  min(414,-620,-60,548,-56); Enter tugmasini bosing natija: -620
  

>min(414*9,-620+5,-60-5,548*3,-56*5); ^{Enter tugmasini bosing natija:-615}

“Maple” dasturida oddiy tenglamalarni yechish.

Maple muhitida tenglamalarni yechish uchun universal buyruq solve(t,x) mavjud, bu yerda t – tenglama, x – tenglamadagi noma’lum o’zgaruvchi. Bu buyruqning bajarilishi natijasida chiqarish satrida ifoda paydo bo’ladi, bu ana shu tenglamaning yechimi hisoblanadi. Masalan:

• solve(a*x+b=c,x);

• 
  b  c
  

a

Agar tenglama bir nechta yechimga ega bo’lsa va undan keyingi hisoblashlarda foydalanish kerak bo’lsa, u holda solve buyrug’iga biror-bir nom name beriladi.. Tenglamaning qaysi yechimiga murojoat qilish kerak bo’lsa, uning nomi va kvadrat qavs ichida esa yechim nomeri yoziladi: name[k]. Masalan:

• x:=solve(x^2-a=0,x);

• 
  x[1];
  

x :=
a, 

• x[2];


Tenglamalar sistemasini yechish. Tenglamalar sistemasi ham xuddi shunday solve({t1,t2,…},{x1,x2,…}) buyrug’i yordami bilan yechiladi, faqat endi buyruq parametri sifatida birinchi figurali qavsda bir- biri bilan vergul bilan ajratilgan tenglamalar, ikkinchi figurali qavsda esa noma’lum o’zgaruvchilar ketma-ketligi yoziladi.

Masalan:

1. 
   Tenglamalar sistemasini yeching.
   

>eq:={x-y=1,x+y=3};

eq := {x - y = 1, x + y = 3}

• 
  s:=solve(eq,{x,y});
  

Enter tugmasini bosib natija:

s := {y = 1, x = 2}.

2. 
   Tenglamalar sistemasini yeching.
   

• 
  eq:={2*x-2*y=4,x+4*y=6};
  

eq := {x + 4 y = 6, 2 x - 2 y = 4}

• 
  s:=solve(eq,{x,y});
  

Enter tugmasini bosib natija:

s := {y = 4/5, x = 14/5}

3. 
   Tenglamalar sistemasini yeching.
   

“Maple” dasturida quyidagicha kiritiladi:

eq:={sqrt(x)-2*sqrt(y)=4,sqrt(x)+4*sqrt(y)=6};

• 
  s:=solve(eq,{x,y});
  

Enter tugmasini bosib natija:

s := {y = 1/9, x = 196/9}
Agar bizga keyingi hisoblashlarda tenglamalar sistemasining yechimidan foydalanish yoki ular ustida ba’zi arifmetik amallarni bajarish zarur bo’lsa, u holda solve buyrug’iga biror bir name nomini berish kerak bo’ladi. Keyin esa ta’minlash buyrug’i assign( name) bajariladi. Shundan keyin yechimlar ustida arifmetik amallarni bajarish mumkin.

Masalan:

• 
  s:=solve({a*x-y=1,5*x+a*y=1},{x,y});
  

• assign(s); simplify(x-y);

s := { y  ^{a  5} 

₂ , x
a  5
1  a _}
a²  5

₆ 1
a²  5
Tenglamalarning sonli yechimini topish. Agar transsentdent tenglamalar analitik yechimga ega bo’lmasa, u holda tenglamaning sonli yechimini topish uchunmaxsus buyruq fsolve(eq,x) dan foydalaniladi, bu yerda ham parametrlar solve buyrug’i kabi ko’rinishda bo’ladi.

Masalan:

• 
  x:=fsolve(cos(x)=x,x);
  

x:=.7390851332
Funksional tenglamalarni yechish. rsolve(t,f) buyrug’i yordamida
f butun funksiya uchun t rekurrent tenglamani yechish mumkin. f(n) funksiya uchun ba’zi bir boshlang’ich shartlarni berish mumkin, u holda berilgan rekurrent tenglamaning xususiy yechimi hosil bo’ladi

Masalan:

>eq:=5+f(n)=21*f(n)-f(n);

rsolve({eq,f(1)=0,f(2)=1},f);
eq := 5+f(n) = 20*f(n)
{f(2) = 1, f(1) = 0, f(n) = 5/19}

Natijada oshkor bo’lmagan ko’rinishdagi yechim paydo bo’ladi. Lekin Maple muhitida bunday yechimlar ustida ishlash imkoni ham mavjud. Funksional tenglamalarning oshkor bo’lmagan yechimlarini convert buyrug’i yordamida biror elementar funksiyaga almashtirib olish mumkin. Yuqorida keltirilgan misolni davom ettirgan holda , oshkor ko’rinishdagi yechimni olish mumkin:

• f:=convert(F(x),radical);

f := ³ 
2
Trigonometrik tenglamalarni yechish. Trigonometrik tenlamani echish uchun qo’llanilgan solve buyrug’i faqat bosh yechimlarni, ya’ni [0, 2] intervaldagi yechimlarni beradi. Barcha yechimlarni olish uchun oldindan EnvAllSolutions:=true qo’shimcha buyruqlarni kiritish kerak bo’ladi . Masalan:

• _EnvAllSolutions:=true:

• 
  solve(sin(x)=cos(x),x);
  

¹    _Z1~
4

Maple muhitida _Z~ belgi butun turdagi o’zgarmasni anglatadi, shuning uchun ushbu tenglama yechimining odatdagi ko’rinishi x:=π/4+πn bo’ladi, bu yerda n – butun son.