1、實驗十一 級數(shù)與方程符號求解一、實驗?zāi)康?、掌握級數(shù)求和的方法2、掌握將函數(shù)展開為泰勒級數(shù)的方法3、掌握微分方程符號求解的方法4、掌握代數(shù)方程符號求解的方法二、實驗內(nèi)容1、級數(shù)符號求和（1）計算 n=sym(n);s=symsum(1/(2*n-1),1,10) s = 31037876/14549535（2）求級數(shù)的和函數(shù)，并求之和。 n=sym(n);x=sym(x);s=symsum(n*n*x(n-1),n,1,inf) s = (-x-1)/(x-1)3 s1=symsum(n*n/5n,n,1,inf) s1 = 15/322、將在處按5次多項式展開為泰勒級數(shù)。 x=sym(x);

2、taylor(log(x),6,1) ans = x-1-1/2*(x-1)2+1/3*(x-1)3-1/4*(x-1)4+1/5*(x-1)53、求下列方程的符號解。(1) x=solve(log(1+x)-5/(1+sin(x)-2),x) x = -3.9222501966216401268562035062927-1.5308457578423990317770669453365*i(2) x=solve(x*x+9*sqrt(x+1)-1,x) x = -1+(1/12*(972+12*6465(1/2)(1/3)+2/(972+12*6465(1/2)(1/3)+1/2*i*3(1

3、/2)*(-1/6*(972+12*6465(1/2)(1/3)+4/(972+12*6465(1/2)(1/3)2 -1+(1/12*(972+12*6465(1/2)(1/3)+2/(972+12*6465(1/2)(1/3)-1/2*i*3(1/2)*(-1/6*(972+12*6465(1/2)(1/3)+4/(972+12*6465(1/2)(1/3)2 -1(3) x=solve(3*x*exp(x)+5*sin(x)-78.5,x) x = 1.1438132465904248768705131138349-3.5140576459458125696291745801210*i(

4、4) x y=solve(sqrt(x*x+y*y)-100,3*x+5*y-8,x,y) x = 12/17-10/17*21246(1/2) 12/17+10/17*21246(1/2) y = 20/17+6/17*21246(1/2) 20/17-6/17*21246(1/2)4、求微分方程初值問題的符號解，并與數(shù)值解進(jìn)行比較。 function dy=vdp29(t,y) dy=zeros(2,1); dy(1)=y(2);dy(2)=-4*y(2)-29*y(1);t y=ode45(vdp29,0 10,0,15)t = 0 0.0000 0.0000 0.0000 0.0000

5、 0.0000 0.0000 0.0001 0.0001 0.0002 0.0002 0.0003 0.0004 0.0008 0.0013 0.0017 0.0021 0.0042 0.0063 0.0084 0.0105 0.0209 0.0314 0.0419 0.0523 0.0892 0.1260 0.1628 0.1996 0.2377 0.2757 0.3138 0.3518 0.3893 0.4269 0.4644 0.5019 0.5397 0.5775 0.6153 0.6531 0.6908 0.7284 0.7660 0.8037 0.8416 0.8795 0.917

6、4 0.9553 0.9928 1.0303 1.0678 1.1052 1.1430 1.1807 1.2185 1.2563 1.2939 1.3315 1.3691 1.4067 1.4445 1.4824 1.5203 1.5581 1.5961 1.6341 1.6721 1.7101 1.7478 1.7855 1.8232 1.8609 1.8985 1.9360 1.9736 2.0112 2.0490 2.0868 2.1246 2.1625 2.2007 2.2389 2.2772 2.3154 2.3531 2.3907 2.4284 2.4661 2.5036 2.54

7、11 2.5786 2.6161 2.6539 2.6917 2.7295 2.7672 2.8054 2.8435 2.8816 2.9198 2.9574 2.9950 3.0326 3.0703 3.1077 3.1452 3.1826 3.2201 3.2578 3.2955 3.3333 3.3710 3.4091 3.4471 3.4852 3.5232 3.5608 3.5984 3.6360 3.6735 3.7114 3.7492 3.7871 3.8249 3.8626 3.9003 3.9380 3.9757 4.0137 4.0517 4.0896 4.1276 4.1

8、659 4.2043 4.2426 4.2809 4.3201 4.3594 4.3986 4.4378 4.4754 4.5131 4.5507 4.5883 4.6263 4.6642 4.7022 4.7401 4.7870 4.8339 4.8808 4.9276 4.9694 5.0111 5.0529 5.0946 5.1336 5.1725 5.2114 5.2503 5.2947 5.3390 5.3834 5.4277 5.4909 5.5542 5.6174 5.6806 5.7319 5.7832 5.8344 5.8857 5.9390 5.9923 6.0456 6.

9、0989 6.1636 6.2283 6.2930 6.3577 6.4224 6.4871 6.5519 6.6166 6.6869 6.7572 6.8276 6.8979 6.9949 7.0919 7.1889 7.2859 7.3678 7.4498 7.5317 7.6136 7.7317 7.8499 7.9680 8.0861 8.1968 8.3075 8.4183 8.5290 8.6726 8.8163 8.9599 9.1036 9.3004 9.4971 9.6939 9.8907 9.9180 9.9453 9.9727 10.0000y = 0 15.0000 0

10、.0001 14.9998 0.0001 14.9996 0.0002 14.9994 0.0002 14.9992 0.0005 14.9982 0.0007 14.9972 0.0010 14.9962 0.0012 14.9952 0.0025 14.9902 0.0037 14.9851 0.0050 14.9801 0.0062 14.9751 0.0125 14.9499 0.0187 14.9247 0.0250 14.8995 0.0312 14.8742 0.0622 14.7473 0.0930 14.6197 0.1234 14.4912 0.1536 14.3620 0

11、.3005 13.7054 0.4405 13.0330 0.5733 12.3476 0.6989 11.6520 1.0822 9.1573 1.3736 6.6709 1.5749 4.2848 1.6912 2.0697 1.7299 0.0192 1.6960 -1.7426 1.6014 -3.1866 1.4581 -4.3028 1.2807 -5.0868 1.0796 -5.5694 0.8662 -5.7745 0.6497 -5.7327 0.4371 -5.4768 0.2376 -5.0471 0.0572 -4.4854 -0.1000 -3.8308 -0.23

12、10 -3.1229 -0.3350 -2.3954 -0.4116 -1.6795 -0.4618 -0.9999 -0.4876 -0.3723 -0.4909 0.1813 -0.4749 0.6495 -0.4429 1.0267 -0.3988 1.3087 -0.3458 1.5022 -0.2872 1.6122 -0.2260 1.6461 -0.1643 1.6126 -0.1049 1.5221 -0.0499 1.3864 -0.0007 1.2168 0.0415 1.0249 0.0762 0.8209 0.1032 0.6146 0.1225 0.4138 0.13

13、45 0.2238 0.1397 0.0519 0.1387 -0.0976 0.1326 -0.2223 0.1222 -0.3214 0.1085 -0.3940 0.0926 -0.4412 0.0753 -0.4646 0.0577 -0.4668 0.0403 -0.4508 0.0239 -0.4200 0.0088 -0.3775 -0.0044 -0.3267 -0.0157 -0.2706 -0.0247 -0.2121 -0.0316 -0.1538 -0.0363 -0.0974 -0.0390 -0.0451 -0.0398 0.0015 -0.0390 0.0415

14、-0.0367 0.0746 -0.0334 0.1001 -0.0292 0.1181 -0.0244 0.1289 -0.0195 0.1331 -0.0145 0.1316 -0.0096 0.1254 -0.0051 0.1152 -0.0010 0.1021 0.0025 0.0870 0.0055 0.0708 0.0078 0.0541 0.0096 0.0376 0.0107 0.0219 0.0112 0.0077 0.0113 -0.0049 0.0109 -0.0156 0.0101 -0.0242 0.0091 -0.0306 0.0078 -0.0350 0.0065

15、 -0.0373 0.0050 -0.0379 0.0036 -0.0369 0.0023 -0.0347 0.0010 -0.0315 -0.0001 -0.0276 -0.0010 -0.0232 -0.0018 -0.0185 -0.0024 -0.0137 -0.0029 -0.0091 -0.0031 -0.0048 -0.0032 -0.0009 -0.0032 0.0025 -0.0030 0.0054 -0.0028 0.0076 -0.0025 0.0092 -0.0021 0.0102 -0.0017 0.0107 -0.0013 0.0107 -0.0009 0.0103

16、 -0.0005 0.0096 -0.0002 0.0086 0.0001 0.0074 0.0004 0.0061 0.0006 0.0047 0.0007 0.0034 0.0008 0.0021 0.0009 0.0009 0.0009 -0.0001 0.0009 -0.0010 0.0008 -0.0018 0.0008 -0.0023 0.0007 -0.0027 0.0006 -0.0030 0.0004 -0.0031 0.0003 -0.0030 0.0002 -0.0029 0.0001 -0.0026 0.0000 -0.0023 -0.0001 -0.0019 -0.0

17、001 -0.0015 -0.0002 -0.0011 -0.0002 -0.0008 -0.0003 -0.0004 -0.0003 -0.0001 -0.0003 0.0002 -0.0002 0.0004 -0.0002 0.0006 -0.0002 0.0008 -0.0002 0.0008 -0.0001 0.0009 -0.0001 0.0008 -0.0000 0.0008 -0.0000 0.0007 0.0000 0.0006 0.0000 0.0005 0.0001 0.0003 0.0001 0.0002 0.0001 0.0001 0.0001 0.0000 0.000

18、1 -0.0001 0.0001 -0.0001 0.0001 -0.0002 0.0001 -0.0002 0.0000 -0.0002 0.0000 -0.0002 0.0000 -0.0002 -0.0000 -0.0002 -0.0000 -0.0001 -0.0000 -0.0001 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0001 -0.0000 0.0001 -0.0000 0.0001 -0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000