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1、I.一重积分A.用int积分int(sin(x),x,0,pi)ans=2B.trapz计算X=0:pi/100:pi;Y=sin(X);>>Z=trapz(X,Y)Z=1.999835503887444C.符号分析symsx;IS=int(sym('exp(-x*x)'),'x',0,1)vpa(IS)IS=(pi^(1/2)*erf(1))/2ans=0.74682413281242702539946743613185D.用quad或quadlfun=inline('exp(-x.*x)','x')a=quad(fun,0,1)b=quadl(fun,0,1)fun
2、=Inlinefunction:fun(x)=exp(-x.*x)a=0.7468b=0.7468F=@(x)exp(-x.*x);Q=quad(F,0,1)Ql=quadl(F,0,1)Q=0.7468Ql=0.7468I.多重积分A.用MUPAD工具箱计算F2=int(int(int(x^2+y^2+z^2,z=sqrt(x*y)..x^2*y),y=sqrt(x)..x^2),x=1..2)B.符号法symsxy;s=vpa(int(int(x^y,x,0,1),y,1,2))Warning:Explicitintegralcouldnotbefound.s=0.
3、69314718055994530941723212145818C.dblquad数值法F=@(x,y)y*sin(x)+x*cos(y);Q=dblquad(F,pi,2*pi,0,pi)Q=-9.8696D.其他不常用I.极限与导数A.极限symsxab;f=x*(1+a/x)^x*sin(b/x);L=limit(f,x,inf)L=b*exp(a)inf:为无穷B.单边极限symx;limit((exp(x^3)-1)/(1-cos(sqrt(x-sin(x)))),x,0,'right')ans=12C.多变量函数极限symsxya;f=exp(-1/(y^2
4、+x^2))*sin(x)^2..../x^2*(1+1/y^2)^(x+a^2*y^2);L=limit(limit(f,x,1/sqrt(y)),y,inf)L=exp(a^2)三个或三个以上的黑点表示“续行”I.微分A.函数的导数解symsx;f=sin(x)/(x^2+4*x+3);df1=diff(f)df4=diff(f,4)text(0.1,0.5,['$'latex(df4)'$'],'interpreter','latex','FontSize',10)df1=cos(x)/(x^2+4*x+3)-(sin(x)*(2*x+4))/(x^2+4*x+3
5、)^2df4=sin(x)/(x^2+4*x+3)+(12*sin(x))/(x^2+4*x+3)^2+(24*sin(x))/(x^2+4*x+3)^3-(24*cos(x)*(2*x+4)^3)/(x^2+4*x+3)^4-(12*sin(x)*(2*x+4)^2)/(x^2+4*x+3)^3-(48*sin(x)*(2*x+4)^2)/(x^2+4*x+3)^4+(24*sin(x)*(2*x+4)^4)/(x^2+4*x+3)^5+(4*cos(x)*(2*x+4))/(x^2+4*x+3)^2+(16*cos(x)*(2*x+4))/(x^2+4*x+3)^3
6、+(8*cos(x)*(8*x+16))/(x^2+4*x+3)^3-(6*sin(x)*(2*x+4)*(8*x+16))/(x^2+4*x+3)^4symsxy;z=(x^2-2*x)*exp(-x^2-y^2-x*y);zx=simple(diff(z,x))zy=diff(z,y)zx=(2*x+2*x*y-x^2*y+4*x^2-2*x^3-2)/exp(x^2+x*y+y^2)zy=((2*x-x^2)*(x+2*y))/exp(x^2+x*y+y^2)[x,y]=meshgrid(-3:.2:3,-2:.2:2);z=(x.^2-2*x).*exp(-x.
7、^2-y.^2-x.*y);surf(x,y,z),axis([-33-22-0.71.5])contour(x,y,z,30),holdonzx=-exp(-x.^2-y.^2-x.*y).*(-2*x+2+...2*x.^3+x.^2.*y-4*x.^2-2*x.*y);zy=-x.*(x-2).*(2*y+x).*exp(-x.^2-y.^2-x.*y);quiver(x,y,zx,zy)A.隐函数的偏导数symsxy;f=(x^2-2*x)*exp(-x^2-y^2-x*y);pretty(-simple(diff(f,x)/di
