《微分積分》word版

1、.I. 一重積分A. 用int積分intsinx,x,0,pi ans =2 B. trapz 計(jì)算X = 0:pi/100:pi;Y = sinX;>> Z = trapzX,YZ = 1.999835503887444C. 符號(hào)分析syms x;IS=intsym'exp-x*x','x',0,1vpaIS IS =pi1/2*erf1/2ans =0.74682413281242702539946743613185 D. 用quad或quadlfun=inline'exp-x.*x','x'a=quadfun,0

2、,1b=quadlfun,0,1 fun = Inline function: funx = exp-x.*xa = 0.7468b = 0.7468 F = x exp-x.*x;Q = quadF,0,1Ql = quadlF,0,1 Q = 0.7468Ql = 0.7468 II. 多重積分A. 用MUPAD工具箱計(jì)算F2=intintintx2+y2+z2,z=sqrtx*y.x2*y,y=sqrtx.x2,x=1.2B. 符號(hào)法syms x y;s=vpaintintxy,x,0,1,y,1,2 Warning: Explicit integral could not be fou

3、nd.s =0.69314718055994530941723212145818 C. dblquad 數(shù)值法F = x,y y*sinx+x*cosy;Q = dblquadF,pi,2*pi,0,pi Q = -9.8696 D. 其他不常用III. 極限與導(dǎo)數(shù)A. 極限syms x a b;f=x*1+a/xx*sinb/x;L=limitf,x,inf L =b*expa inf:為無(wú)窮B. 單邊極限sym x;limitexpx3-1/1-cossqrtx-sinx,x,0,'right' ans =12 C. 多變量函數(shù)極限syms x y a;f=exp-1/y2

4、+x2*sinx2./x2*1+1/y2x+a2*y2;L=limitlimitf,x,1/sqrty,y,inf L =expa2 三個(gè)或三個(gè)以上的黑點(diǎn)表示“續(xù)行IV. 微分A. 函數(shù)的導(dǎo)數(shù)解syms x;f=sinx/x2+4*x+3;df1=difffdf4=diff f,4 text0.1,0.5, '$' latexdf4 '$','interpreter','latex','FontSize',10df1 =cosx/x2 + 4*x + 3 - sinx*2*x + 4/x2 + 4*x + 32df

5、4 =sinx/x2 + 4*x + 3 + 12*sinx/x2 + 4*x + 32 + 24*sinx/x2 + 4*x + 33 - 24*cosx*2*x + 43/x2 + 4*x + 34 - 12*sinx*2*x + 42/x2 + 4*x + 33 - 48*sinx*2*x + 42/x2 + 4*x + 34 + 24*sinx*2*x + 44/x2 + 4*x + 35 + 4*cosx*2*x + 4/x2 + 4*x + 32 + 16*cosx*2*x + 4/x2 + 4*x + 33 + 8*cosx*8*x + 16/x2 + 4*x + 33 - 6*

6、sinx*2*x + 4*8*x + 16/x2 + 4*x + 34 syms x y;z=x2-2*x*exp-x2-y2-x*y;zx=simplediffz,xzy=diffz,y zx =2*x + 2*x*y - x2*y + 4*x2 - 2*x3 - 2/expx2 + x*y + y2zy =2*x - x2*x + 2*y/expx2 + x*y + y2 x,y=meshgrid-3:.2:3,-2:.2:2;z=x.2-2*x.*exp-x.2-y.2-x.*y;surfx,y,z, axis-3 3 -2 2 -0.7 1.5 contourx,y,z,30, hold onzx=-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;quiverx,y,zx,zy B. 隱函數(shù)的偏導(dǎo)數(shù)syms x y;f=x2-2*x*exp-x2-y2-x*y;pretty-simpledifff, x/dif