lingo微积分.ppt

1、 syms x; f=cos(x2); diff(f) ans = -2*sin(x2)*x syms x; diff(cos(x2) ans = -2*sin(x2)*x syms a x; diff(a*cos(x2) ans = -2*a*sin(x2)*x,导数, syms x f=log(x); diff(f) ans = 1/x, syms x f=log(x); diff(f,2) %二阶导数 ans = -1/x2, syms x y z=3*x3*y2+sin(x*y); diff(z,x,3) %三阶导数 ans = 18*y2-cos(x*y)*y3, syms x; f

2、=cos(x); diff(f,3) %三阶导数 ans = sin(x) syms x y z=3*x3*y2+sin(x*y); zx=diff(z,x); zxy=diff(zx,y) %二阶交叉偏导数 zxy = 18*x2*y-sin(x*y)*x*y+cos(x*y), syms x y; f=x*y/(x.2+y.2); diff(f,x)%对x的一阶偏导数 ans = y/(x2+y2)-2*x2*y/(x2+y2)2 diff(f,y)%对y的一阶偏导数 ans = x/(x2+y2)-2*x*y2/(x2+y2)2 diff(f,x,2) % 对x的二阶偏导数 ans =

3、-6*y/(x2+y2)2*x+8*x3*y/(x2+y2)3 diff(diff(f,x),y) % 对x，y的二阶偏导数 ans = 1/(x2+y2)-2*y2/(x2+y2)2-2*x2/(x2+y2)2+8*x2*y2/(x2+y2)3,隐函数求导 syms x y; f=x*y-exp(x)+exp(y); -diff(f,x)/diff(f,y) ans = (-y+exp(x)/(x+exp(y), syms x y; f=x2+y2-x*y; -diff(f,x)/diff(f,y) ans = (-2*x+y)/(2*y-x), syms x y z; f=x2+y2+z2

4、-4*z; -diff(f,x)/diff(f,z) ans = -2*x/(2*z-4),参数方程求导 syms t a b; x=a*cos(t);y=b*sin(t); f=diff(y,t)/diff(x,t) f = -b*cos(t)/a/sin(t) simple(f) ans = -b/a/tan(t), syms t x=t*sin(t); y=t*(1-cos(t); dx=diff(x,t); dy=diff(y,t); dy/dx ans = (1-cos(t)+t*sin(t)/(sin(t)+t*cos(t), f=inline(sqrt(x.3+2*x.2-x+1

5、2)+(x+5).(1/6)+5*x+2); g=inline(3*x.2+4*x-1)./sqrt(x.3+2*x.2-x+12)/2+1/6./(x+5).(5/6)+5); x=-3:0.01:3; p=polyfit(x,f(x),5); %拟合f(x) dp=polyder(p); %对拟合多项式p求导数 dpx=polyval(dp,x); %求dp的函数值 dx=diff(f(x,3.01)/0.01; %直接对f求数值导数 gx=g(x); %求f的导函数g的导数值 plot(x,dpx,x,dx,.,x,gx,-),不定积分 syms x; f=cos(x); int(f)

6、ans = sin(x), syms x f=1/x2; int(f) ans = -1/x, syms x int(-2*x/(1+x2)2) ans = 1/(1+x2),定积分 syms x; f=cos(x); int(f,0,pi/2) ans = 1, syms x f=sqrt(x2+3); int(f,x,-1,1) ans = 2+3/2*log(3), syms x; f=sin(x); int(f) ans = -cos(x) int(f,x,-pi/2,pi/2) ans = 0, I=quadl(x.*sin(x)./(1+cos(x).*cos(x),0,pi) I

7、 = 2.4674, X=1:0.01:2.5; Y=exp(-X); trapz(X,Y) ans = 0.2858,广义积分 syms x f=1/(x3); int(f,x,1,inf) ans = 1/2,二重积分 x= 0:pi/100:pi; y = sin(X); z = trapz(x,y) z = 1.9998, syms x y f = (x,y)exp(-x.2/3).*sin(x.2+2*y); I=dblquad(f,-1,1,-1,1) I = 0.4658, syms x y; f=x*sin(x); int(int(f,x,y,sqrt(y),y,0,1) ans = 5*sin(1)-4*cos(1)-2, syms x y; z=abs(y-x2); in