MATLAB R2010a

第二章[2—1、2、3、4、5、6、7、8、9、10、11、12、23、24、25] %分段函数的写法 syms y x

z=int(x*y,x,0,1);

g = evalin(symengine,[' piecewise([y > 1/2,' char(z) '], [y <= 1/2, 1])']) G=int(g,y) g =

piecewise([1/2 < y, y/2], [y <= 1/2, 1]) G =

piecewise([1/2 < y, y^2/4], [y <= 1/2, y])

%习题2-1

class(vpa(sym(3/7+0.1),4))

%习题2-2

findsym(sym('sin(w*t)'),1) findsym(sym('a*exp(-X)'),1) findsym(sym('z*exp(j*th)'),1)

%习题2-3

syms x a positive

x_1=solve('x^3-44.5') syms x unreal

x_2=solve('x^2-a*x+a^2') syms a unreal

x_2=solve('x^2-a*x+a^2')

x_3=solve('x^2-a*x-a^2')

syms x real

evalin(symengine,'anames(Properties)') evalin(symengine,'getprop(x)')

%习题2-4

7/3, pi/3 , pi*3^(1/3)

a = pi*3^(1/3) ,

b = sym( pi*3^(1/3) ), c = sym( pi*3^(1/3),'d'),

d = sym( 'pi*3^(1/3) ' )

vpa(abs(a-d)) , vpa(abs(b-d)) , vpa(abs(c-d))

%习题2-5

syms a11 a12 a13 a21 a22 a23 a31 a32 a33 A = [a11 a12 a13;a21 a22 a23;a31 a32 a33] a=det(A) B=inv(A)

C=subexpr(B)

[RS,w]=subexpr(B,'w')

%习题2-6

syms k

syms a positive

% fk =a^k * heaviside(k) fk =a^k

s=symsum(fk,k,0,inf)

%习题2-7

clear all syms k

syms x positive

fk =2/(2*k+1)*(((x-1)/(x+1))^(2*k+1)) s=symsum(fk,k,0,inf) s1=simple(s)

%习题2-8

clear all, syms t y=abs(sin(t))

df=diff(y),class(df)

df1=limit(df,t,0,'left') df2=subs(df,'t',sym(pi/2))

%习题2-9

clear all, syms x;

f=exp(-abs(x)).*abs(sin(x));

fint=int(f,x,-5*pi,1.7*pi), digits(64), vpa(fint) class(fint)

%习题2-10

clear all,syms x y,f=x.^2+y.^2,

fint=(int(int(f,y,1,x.^2),x,1,2)), double(fint)

%习题2-11

clear all, syms t x; f=sin(t)/t, yx=int(f,t,0,x), ezplot(yx,[0 2*pi]) fint=subs(yx,x,4.5),%或yxd=int(f,t,0,4.5),fint=double(yxd) hold on, plot(4.5,fint,'*r')

%习题2-12

% clear all, syms x n; f=(sin(x))^n; yn=int(f,'x',0,pi/2), class(yn)

clear all, syms x n; syms n positive ; f=(sin(x))^n; yn=int(f,'x',0,pi/2), class(yn)

% y(1/3)=?

yn1=subs(yn,'n',sym(1/3)),vpa(yn1) %或yn=limit(yn,n,1/3),vpa(yn)

%或yy=int(sin(x).^(1/3),x,0,pi/2) ,vpa(yy)

%习题2-23

clear, syms x y S

S = dsolve('Dy*y/5+x/4=0','x')

ezplot(subs(S(1),'C3',1),[-2,2 -2,2],1), hold on ezplot(subs(S(2),'C3',1),[-2,2 -2,2],1)

%解为 S =

% 2^(1/2)*(C3 - (5*x^2)/8)^(1/2) % -2^(1/2)*(C3 - (5*x^2)/8)^(1/2)

ezplot(subs(S(1),'C3',1),[-2,2 -2,2],1), hold on

ezplot(subs(S(2),'C3',1),[-2,2 -2,2],1) % 用此两条指令绘圆，在 y=0处有间隙

ezplot(subs(y^2-(S(1))^2, 'C3', 1),[-2,2 -2,2],2) %用椭圆方程绘图不产生间隙

colormap([0 0 1]) %用ezplot(fun)绘图时，如果fun中只有一个参数，绘图的颜色是蓝色；如果fun中有两个参数，绘图的颜色是绿色，此指令设置图形颜色为蓝。 grid on

S1=subs(S(1),'C3',1)

subs(S1,{x},{1.6^(1/2)}) y=double(solve(S1))

t=linspace(y(2),y(1),100) S2=subs(S(2),'C3',1) figure

plot(t,subs(S1,x,t)), hold on plot(t,subs(S2,x,t)) axis([-2,2 -2,2])

%习题2-24

x=dsolve('Dx=a*t^2+b*t','x(0)=2','t')

%习题2-25

[f,g]=dsolve('Df=3*f+4*g','Dg=-4*f+3*g','f(0)=0','g(0)=1','x')

第三章[3—1、2、3、4、5、6、7、8]

%习题3-1

a=0:2*pi/9:2*pi

b=linspace(0,2*pi,10)

%习题3-2

rand( 'twister',0), A=rand(3,5)

[I1,J1]=find(A>0.5)

subindex_A=sub2ind(size(A),I1,J1)

subindex_A=find(A>0.5)

[I,J]=ind2sub(size(A),subindex_A) index_A=[I J]

2_2

rand('twister',0),A=rand(3,5),B=A>0.5,C=find(B) [ci,cj]=ind2sub(size(A),C) %此法太繁 [Ci,Cj]=find(B)