9.积分和微分运算
概述:
1 定积分概念
2 利用梯形求面积
1 clear all; 2 X1=[1 2 3 4 5 6 7] 3 z1=trapz(X1) 4 X2=[1 2 3;3 6 8;2 5 9] 5 z2=trapz(X2) 6 z3=trapz(X2,2) 7 x=[1 2 3] 8 z4=trapz(x,X2)
3 利用矩形求面积
1 clear all; 2 X1=[1 2 3 4 5 6 7] 3 z1=cumsum(X1) 4 X2=[1 2 3;3 6 8;2 5 9] 5 z2=cumsum(X2) 6 z3=cumsum(X2,1) 7 z4=cumsum(X2,2) 8 z5=cumsum(X2,3)
1 clear all; 2 x=0:0.01:5*pi; 3 y=cos(x./2)'; 4 z=cumsum(y)*0.01; 5 z1=z(end) 6 z2=trapz(x,y) 7 figure; 8 plot(x,y,'r-'); 9 hold on; 10 plot(x,z,'b:') 11 legend('被积函数','积分曲线');
4 单变量数值积分求解
1 function y=myfun1(x) 2 y=1./(sin(x)+exp(-x.^2));
1 clear all; 2 syms x; 3 f=inline('1./(sin(x)+exp(-x.^2))') 4 y=quad(f,0,1.3) 5 y1=quad(@myfun1,0,1.3) 6 y2=quad(@myfun1,0,1.3,1.e-10)
1 clear all; 2 syms x; 3 f=inline('1./(sin(x)+exp(-x.^2))','x'); 4 y=quadl(f,0,1.3) 5 y1=quadl(f,0,1.3,1.e-20)
5 双重积分求解
1 function z= integrnd(x,y) 2 z=y*sin(x)+x*cos(y);
1 clear all; 2 syms x; 3 f=inline('x*cos(y)+y*sin(x)','x','y'); 4 y=dblquad(f,pi,2*pi,0,pi) 5 y1=dblquad(@integrnd,pi,2*pi,0,pi) 6 y2=dblquad(@(x,y) x*cos(y)+y*sin(x),pi,2*pi,0,pi)
6 三重积分求解
1 clear all; 2 f=inline('z*cos(x)+y*sin(x)','x','y','z'); 3 q=triplequad(f,0,pi,0,1,-1,1) 4 %采用匿名函数的形式 5 q1=triplequad(@(x,y,z) (y*sin(x)+z*cos(x)),0,pi,0,1,-1,1) 6 q2=triplequad(@(x,y,z) (y*sin(x)+z*cos(x)),0,pi,0,1,-1,1,1.e-10) 7 q3=triplequad(@(x,y,z) (y*sin(x)+z*cos(x)),0,pi,0,1,-1,1,1.e-10,@quad)
7 常微分方程
1 clear all; 2 f1=dsolve('Dy-y=sin(x)') 3 f2=dsolve('Dy-y=sin(x)','x')
求微分方程的特解
1 clear all; 2 dsolve('Dy=a*y','y(0)=b')
求微分方程的解
1 clear all; 2 dsolve('D2y+2*Dy+exp(x)=0','x')
