R语言计算微积分例题及代码(最新整理)

1、计算向量、矩阵差分 x=1:5 x diff(x) 1 1 1 1 1 y=1:12 z=matrix(y,3,4,t) z diff(z),1 ,2 ,3 ,41,44442,4444 diff(x,diff=2) 1 0 0 0#求一元函数导数f=expression(5*x)/(1+x2) d(f,x)f=expression(2*x2) d(f,x)#求二元函数偏导数及梯度f=deriv(zx2+y2+x*y,c(x,y),func=t, hessian=f) ff(1,2)例 1 梯形积分1e-x2 dx-1trape=function(fun,a,b,tol=1e-6) n=1;h

2、=b-a t=h/2*(fun(a)+fun(b)repeat h=h/2;x=a+(2*1:n-1)*h i=t/2+h*sum(fun(x) if(abs(i-t)tol) break n=2*n;t=iisource(trape.r) f=function(x) exp(-x2) trape(f,-1,1)高精度积分f=function(x) exp(-x2) integrate(f,-1,1)2 1xy44例 2 简单二重积分-2 -1 (1-)dxdylibrary(cubature) f-function(x) 1-x1/4-x2/3adaptintegrate(f, c(-2,

3、-1), c(2, 1), maxeval=10000)例 3直接求和计算n=5;h=seq(0.1,0.9,by=0.2)fun=function(h)(2-(exp(2*h)+exp(-2*h)/5) r=fun(h)r w=pi*1/n*sum(r2) w转化为定积分f=function(h)(2-(exp(2*h)+exp(-2*h)/5)2 i=pi*integrate(f,0,1)as.character(i) i=as.numeric(i1) w=i*piw例 4 r-5 b-0.1 g-9.81z1-0.5-r z2-rn-100h-(z2-z1)/n #z=z1:h:z2f-

4、function(z)(r2-z2)/(b2*sqrt(2*g*(z+r) i=integrate(f,z1,z2)ias.character(i) i=as.numeric(i1) t=i/60/60t“”“”at the end, xiao bian gives you a passage. minand once said, people who learn to learn are very happy people. in every wonderful life, learning is an eternal theme. as a professional clerical an

5、d teaching position, i understand the importance of continuous learning, life is diligent, nothing can be gained, only continuous learning can achieve better self. only by constantly learning and mastering the latest relevant knowledge, can employees from all walks of life keep up with the pace of enterprise development and innovate to meet the needs of the market. this document is also edited by my studio professionals,