实验十一级数与方程符号求解

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1、实验十一级数与方程符号求解一、实验目的1、掌握级数求和的方法2、掌握将函数展开为泰勒级数的方法3、掌握微分方程符号求解的方法4、掌握代数方程符号求解的方法二、实验内容1、级数符号求和10（1）计算S=Z>>n=sym(’n’)；s=symsum(l/(2*n~l),1,10)31037876/14549535oo(2)求级数的和函数，并求艺二n=l"=15>>n=sym(，n，):x=sym(’x’)；s二symsum(n本n本x"(n一1)，n,1，inf)>>sl=symsum(n*n/5^n,n,1,inf)15/32

2、2、将1m在;v=l处按5次多项式展开为泰勒级数。>>x=sym(’x’)；taylor(log(x),6,1)ans=x-l-l/2*(x-l)"2+l/3*(x-l)"3-l/4*(x-l)"4+1/5*(x_l厂53、求下列方程的符号解。⑴ln(l+x)-51+sinx=2(2)r+9a/x+1—1—0(3)3x^v+5sina:-78.5=0(4)

3、V%2+夕2-100=0[3^+5^-8=0(1)〉〉x=solve(’log(l+x)-5/(l+sin(x)-2)’，’x’)-3.92225019662164012

4、68562035062927-1.5308457578423990317770669453365*i(2)〉〉x=solve(’x*x+9*sqrt(x+l)-l’，’x’)-1+(1/12*(972+12*6465"(1/2)厂(1/3)+2/(972+12*6465"(1/2))^(1/3)+l/2*i*3"(1/2)*(-1/6*(972+12*6465"(1/2)厂(1/3)+4/(972+12*6465"(1/2))"(1/3))厂2-1+(1/12*(972+12*6465"(1/2)V(1/3)+2/(972+

5、12*6465"(1/2)V(1/3)-l/2*i*3"(1/2)*(-1/6*(972+12*6465"(1/2)厂(1/3)+4/(972+12*646571/2))71/3))厂2-1(2)>>x=solve(’3*x*exp(x)+5*sin(x)-78.5’，’x’)1.1438132465904248768705131138349-3.5140576459458125696291745801210*i(3)>>[xy]=solve(’sqrt(x*x+y*y)-100’，’3*x+5*y-8’，’x，y’)12/

6、17-10/17*2124671/2)12/17+10/17*21246^(1/2)20/17+6/17*21246"(1/2)20/17-6/17*2124671/2)4、求微分方程初值问题的符号解，并与数值解进行比较。^2+4^+29^0dx一dx^(0)=0^'(0)=15>>functiondy=vdp29(t,y)dy=zeros(2,1);dy⑴二y⑵;dy(2)=-4*y(2)-29*y(l);[ty]=ode45(’vdp29’，[010],[0,15])00.00000.00000.00000.00000.

7、00000.00000.00010.00010.00020.00030.00040.00080.00130.00170.00210.00420.00630.00840.01050.02090.03140.04190.05230.08920.12600.16280.19960.23770.27570.31380.35180.42690.46440.50190.53970.57750.61530.65310.69080.72840.76600.80370.84160.87950.91740.95530.99281.03031.0

8、6781.10521.14301.18071.29391.33151.36911.40671.44451.48241.52031.55811.59611.63411.67211.7101L74781.78551.82321.86091.89851.93601.97362.01121.08682.12462.16251.20071.23891.27721.31541.35311.39071.42842.46612.50362.54112.57862.61612.65392.69172.72952.76722.80542.843

9、52.91982.95742.99503.03263.07032.10772.14522.18262.22012.25782.29552.33332.37101.40911.44711.48521.52321.56081.59841.63601.67353.74923.78713.8249