1. Maple paketining asosiy maqsadi va uning imkoniyatlari. Maple tizimida o’zgaruvchilar. Tenglamalarni yechish

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.
Masalan:
> x:=fsolve(cos(x)=x,x);
x:=.7390851332
3.Berilgan misollarni yechish:
1)Quyidagi tenglamani Maple tizimida yeching(26-misol):

Javob:
>fsolve({x^2*y^3 = 16, x^3*y^2 = 2}, {x, y});
{x = 0.5000000000, y = 4.000000000}
2)Quyidagi ifodani Maple tizimida yozing va qiymatini toping(26-misol):
, ,
bu yerda = 0.22; = -6.72; = 10.05; = 0.35
Javob:
> assign([x = 0.22, y = -6.72, u = 10.05, v =0.35]); x, y, u, v;
0.22, -6.72, 10.05, 0.35
> f := (2/3+y^2)*(x+(1/2)*y)/(y^2+1/(y^2+1));
-3.184827441
>g := sqrt(sin(arctan(u))^2)+sqrt(abs(cos(v)));
1.964298505
3)Quyidagi aniq integrallarni Maple tizimida hisoblang va integral ostidagi funksiyaning 1-chi hamda 2-chi tartibli hosilalarini toping(26-misol):

Javob:
//integralni hisoblash

>evalf(int((x+5)/(tan(x)-2),x=1.4..2.2),6);
-0.673585
//1-tartibli hosilasini topish
>diff((x+5)/(tan(x)-2),x);

//2-tartibli hosilasini topish
>diff((x+5)/(tan(x)-2),x$2);

4)Chegaraviy masala Maple tizimi bilan sonli yechilsin va yechim grafigi qurilsin(26-misol):
y”-(4x²+1)y=-2.2xcosx
y(0)=0.5, y(1)=2.4
Javob:
>de := diff(y(x),x$2)-(4*x*x+1)*y(x)=-2.2*x*cos(x);
>cond := y(0)=0.5, y(1)=2.4;
>dsolve({de,cond},y(x));