Maple paketining asosiy maqsadi va uning imkoniyatlari

>eq:=(1+sin(2*x)+cos(2*x))/(1+sin(2*x)-cos(2*x)):
> convert(eq, tan):
> eq=normal(“);
.

4. 
   Maple muhitida trigonometric funksiyalar va ular bilan amallar
   

1. Matematik funksiyalar. Maple da ko’plab matematik, shu jumladan logarifmik, eksponensional, trigonometrik, teskari trigonometrik, giperbolik va boshqa funksiyalar ishlatiladi (standart funksiyalar jadvaliga qarang). Ularning hammasi bir argumentli. U butun, rasional, haqiqiy va kompleks bo’lishi mumkin.
Funksiyalarda argumentlar qavs ichiga olinadi.
“Maple” dasturida trigonometrik finksiyalarning yozilishi

sinx	sin(x)	chx	cosh(x)
cosx	cos(x)	thx	tanh(x)
tgx	tan(x)	cthx	coth(x)
ctgx	cot(x)	secx	sec(x)

Masalan:

> 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 :	
> arccos(1/2);	Enter :	

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. _x:=solve(x^2-a=0,x);___x_:=_a_,__a_>_x[1];___a_>_x[2];'>Masalan:_>_solve(a*x+b=c,x);'>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 := a,  a
> x[1];

a
> x[2];

 a
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});
a5 1a
s := {ya2 5, xa2_5 }

> assign(s); simplify(x-y);
1

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