# Maple V 講習班

1997年12月5日

## 了不起, Ramanujan!

> restart:
> Digits:=30;
> evalf(exp(Pi*163^(1/2)));

## 因式分解

> restart:
> u:=5/2*(x+y)*(p+q)-2*x*p;
> v:=2*q*y-(x+y)*(p+q);
> factor(2*u^2+3*u*v+5*v^2);

## 將cos(nx)表示為cos(x)的多項式

> for n to 10 do expand(cos(n*x)) od;

## 將cosn(x)表示為cos(kx)的線性結合

> for n to 10 do combine(2^(n-1)*cos(x)^n) od;

## xnex的不定積分

> for n to 6 do int(x^n*exp(x),x) od;

## ex/x 的逐次微分

> for n to 5 do diff(exp(x)/x,x\$n) od;

## lnnx 的不定積分

> for n to 5 do int(ln(x)^n,x) od;

## 1/lnnx 的不定積分

> for n to 6 do int(1/ln(x)^n,x) od;

## ex/xn 的不定積分

> for n to 6 do int(exp(x)/x^n,x) od;

## cos(x)/xn 的不定積分

> for n to 6 do int(cos(x)/x^n,x) od;

## 腎臟線

> restart:
> x:=cos(t);
> y:=sin(t);
> m:=[x+x*sin, y+x*cos, -Pi..Pi];
> t:=n*Pi/50;
> w:=evalf(m):
> plot([w\$n=1..100],color=black,axes=none);

## 參數曲線

> restart;
>w:=1+cos(t)/2:z:=t/6-sin(2*t)/12:x:=w*cos(z):y:=w*sin(z):
plot([x,y,t=0..12*Pi],axes=none);

## 極坐標曲線

> plot(cos(7*t/2)+1/4,t=0..4*Pi,coords=polar);
> plot(2-cos(3*t)-cos(31*3*t/32),t=0..64*Pi, coords=polar,numpoints=1000);
>plot(2-cos(7*t)-cos(31*7*t/32),t=0..64*Pi,coords=polar,numpoints=1000);
> plot(100+t+15*cos(3.05*t), t = 0 .. 200, coords = polar, axes = none);

以上檔案出現於:

workshop.html
elementary/ele.html