一、试编写Maple 程序。
1．> restart:
> f:=unapply(exp(a*x)*cos(b*x),x);
:= f → x e
()
a x ()cos
b x
2．> restart:
> f:=x^3+3*x^2*y+3*x*y^2+y^3: > f:=factor(f);
:= f () + y x 3
3．> restart:
> f:=(x+y)*(x^2-4*x)^2: > f:=expand(f);
:= f - + + - + x 58x 416x 3y x 48y x 316y x 2
4．> restart:
> eq1:=x^2-3*x+2=0: > solve({eq1},{x});
,{} = x 2{} = x 1
5．> restart:
> eq1:=(1-0.61*x)/x=0: > solve({eq1},{x});
{} = x 1.639344262
二、试编写计算下列各式的Maple 程序。
6．> restart:
> f:=(x-6)*(x-9): > limit(f,x=6);
7．> restart:
> y:=x^(4/5)+sin(sqrt(x)): > diff(y,x);
-32
x 2
()
+ x 312
x 3
8．> restart:
> with(student): > f:=2*sqrt(1-x^2):
> area:=middlesum(f,x=-1..1,100): > area:=evalf(area,4);
:= area 3.138
9．> restart:
> f:=sqrt(x)/(sqrt(x)+x^2+x^3): > f:=series(f,x=3.,7);
f .04591.03284() - x 3..01619() - x 3.2.006732() - x 3.3.002510()
- x 3.4
- + - + := .0008577() - x 3.5.0002727() - x 3.6()
O () - x 3.7 - + +
三、试编写计算下列各式Maple 程序
10．> restart:
> with(linalg):
> B:=matrix(2,2,[[1,3],[1,0]]): > inverse(B);
????????
????0
113-13 11 . > restart:
> with(linalg):
> A:=matrix(3,3,[3,2,4,5,7,3,1,6,0]): > B:=vector([-6,2,0]): > X:=linsolve(A,B);
:= X ????????
,,39-13-85
12. > restart:
> with(linalg):
> A:=matrix(3,3,[3,0,2,4,3,0,0,1,2]):
> det(A);
26
13．> restart:
> with(linalg):
> C:=matrix(3,3,[0,30,81,-30,0,-5,-81,5,0]):
> eigenvals(C); ,,0I 7486-I 7486四、 14．
> restart:
> with(plots):
> f:=(x+3)/(x^2+1): > plot({f},x=-10..10);
15 > restart:
> with(plots):
> f:=sin(x+y):
> plot3d({f},x=-Pi..Pi,y=-Pi..Pi);
16．> restart:
> with(plots):
> f:=4*x^3-6*x^2+12*x-7: > g:=12*x^2-12*x+12: >
tu1:=plot({f},x=-10..10,view=[-10..10,-100..100]):
>
tu2:=plot({g},x=-10..10,view=[-10..10,-100..100]):
> display({tu1,tu2});
17．> restart:
> with(plots):
> x:=cosh(p)*cos(t): > y:=cosh(p)*sin(t): > z:=p:
> plot3d({x,y,z},p=-2..2,t=0..2*Pi);
五
18. > restart:
> deq1:=diff(y(x),x)-y(x)=2*exp(4*x): > dsolve({deq1},{y(x)});
{} = ()y x ?? ???? + 23e ()3x _C1e x
19. > restart:
> deq1:=diff(y(x),x$2)-exp(x)*y(x)=0: > dsolve({deq1},{y(x)},series);
()y x ()y 0()()D y 0x 12()y 0x 2?? ??
?? + 16()()D y 016()y 0x 3 + + + + = ?? ???? + 1()()D y 01()y 0x 4?? ??
?? + 1()()D y 01()y 0x 5()O x 6 + +
20. > restart:
> with(inttrans):
> deq1:=10*diff(x(t),t$2)+5*diff(x(t),t)+500*x(t) > =Dirac(t-1)+Dirac(t-6): > eq2:=laplace(deq1,t,s):
> eq3:=subs(x(0)=2,D(x)(0)=2,eq2): > solve({eq3},{laplace(x(t),t,s)}): > SOL1:=invlaplace(%,s,t): > x:=subs(SOL1,x(t)); x 2e ()-/14t ?? ????cos 14799t 10799799e ()-/14t ?? ??
??
sin 14799t + := 23995()Heaviside - t 1799e ()- + /14t /14?? ????sin 14799() - t 1 + 23995()Heaviside - t 6799e ()- + /14t /32?? ????sin
1
4799() - t 6 + > plot({x},t=0..3,numpoints=300);