数学实验及建模作业

1、数学实验与建模作业实验1 MATLAB运算基础1. 先求下列表达式的值，然后显示MATLAB工作空间的使用情况并保存全部变量。(1) z1=2*sin(85/180*pi)/(1+exp(2)z1 = 0.2375 (2) ，其中 x=2,1+2*i;-0.45,5 ;z2=1/2*log(x+sqrt(1+x.*x)z2 = 0.7218 0.7347 + 0.5317i -0.2180 1.1562 (3) ，a=-3.0:0.1:3.0 ;z3=(exp(0.3*a)-exp(0.3*a)/2.*sin(a+0.3)z3 = Columns 1 through 13 0 0 0 0 0

2、0 0 0 0 0 0 0 0 Columns 14 through 26 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 27 through 39 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 40 through 52 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 53 through 61 0 0 0 0 0 0 0 0 0 (4) 其中for t=0:0.5:2.5if t=0 & t=1 & t=2 & t A=12,34,-4;34,7,87;3,65,7 ,B=1,3,-1;2,0,3;3,-2,7,I=1,0,0

3、;0,1,0;0,0,1A = 12 34 -4 34 7 87 3 65 7B = 1 3 -1 2 0 3 3 -2 7I = 1 0 0 0 1 0 0 0 1 ans11=A+6*Bans11 = 18 52 -10 46 7 10521 53 49 ans12=A-B+Ians12 = 12 31 -3 32 8 84 0 67 1 ans21=A*Bans21 = 68 44 62 309 -72 596 154 -5 241 ans22=A.*Bans22 = 12 102 4 68 0 261 9 -130 49 ans31=A3ans31 = 37226 233824 486

4、04 247370 149188 600766 78688 454142 118820 ans32=A.3ans32 = 1728 39304 -64 39304 343 658503 27 274625 343 ans41=A/Bans41 = 16.4000 -13.6000 7.6000 35.8000 -76.2000 50.2000 67.0000 -134.0000 68.0000 ans42=BAans42 = 109.4000 -131.2000 322.8000 -53.0000 85.0000 -171.0000 -61.6000 89.8000 -186.2000 ans

5、51=A,Bans51 = 12 34 -4 1 3 -1 34 7 87 2 0 3 3 65 7 3 -2 7 ans52=A(1,3,:);B2ans52 = 12 34 -4 3 65 7 4 5 1 11 0 1920 -5 403设有矩阵A和B，（1） 求他们的乘积C。（2） 求矩阵C的右下角3x2子矩阵赋给D。（3） 查看MATLAB 工作空间的使用情况。 A=1 2 3 4 5;6 7 8 9 10;11 12 13 14 15;16 17 18 19 20;21 22 23 24 25,B=3 0 16;17 -6 9;0 23 -4;9 7 0;4 13 11A = 1 2

6、 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25B = 3 0 16 17 -6 9 0 23 -4 9 7 0 4 13 11 C=A*BC = 93 150 77 258 335 237 423 520 397 588 705 557 753 890 717 D=C(3:5,2:3)D = 520 397 705 557 890 7174完成下列操作：（1） 求100，999之间能被21整除的数的个数。(2)建立一个字符串向量，删除其中的大写字母。（1）n=0;for i=100:999 if rem(i,21)=

7、0 n=n+1; endendnn =43 (2)ch=IamaStuDenTOk;k=find(ch=A&ch=Z);ch(k)=;chch =amatuenk实验2 选择结构程序设计1. 求下列分段函数的值x=input(请输入x的值：);if x=0 & x10 & x=2 & x=3y=x2-5*x+6elsey=x2-x-1end2输入一个百分制成绩，要求输出成绩等级A，B，C，D，E。其中90100分为A，8089分为B，7079分为C，6069分为D，60分以下为E。要求：（1） 分别用if语句和switch语句实现。（2） 输入百分制成绩后要判断该成绩的合理性，对不合理的成绩应

8、输出错误成绩。if语句实现如下：x=input(请输入百分制成绩：);if x=fix(x)|x100disp(输入错误！)elseif x=90 & x=80 & x=70 & x=60 & x=69disp(D)elsedisp(E)endswitch语句实现如下：x=input(请输入百分制成绩：);switch (x)case num2cell(90:100)disp(A)case num2cell(80:90)disp(B)case num2cell(70:80)disp(C)case num2cell(60:70)disp(D)case num2cell(0:60)disp(E)o

9、therwise disp(输入错误！)end3假定某地区电话收费标准为：通话时间3分钟以下，收费0.5元；3分钟以上，则每超过分钟加收0.15元；通话时间在7：0022：00之间者，按上述标准全价收费，在其他通话时间者，按上述标准半价收费。计算某人在t1到t2通话时间，应缴多少电话费t1=input(请输入通话开始时间： );t2=input(请输入通话结束时间 ：);if (t1=24)|(t2=24) if t2t1 dt=t2-t1; else dt=t2+24-t1; end; if dt*60 = fix(dt*60) switch (fix(dt*60) case num2cel

10、l(0:3) if t1*60=7 & t1*60=7 & t1=7 & t1*60=7 & t15disp(输入数太大！);disp(m(5,:);elsedisp(m(n,:)；end实验三 循环结构程序设计1.根据，求的近似值。当n分别取100、1000、1000时，结果是多少？ m=0;for n=1:100m=m+1./(n2);endpia=sqrt(m*6)pia =3.1321n=1000时pia =3.1406n=10000时pia = 3.14152根据,求：（1）y3时的最大值。（2）与（1）的n值对应的y 值 y=1;n=1;while y0 x=x+1; end if

11、 f(j)=0 y=y+1; end if f(j)0 z=z+1; endendxyzmx = 4.3776e+011mn = -8.9941e+011s = -7.4275e+011x = 49y = 2z =49试验四 函数与文件1、一个自然数是素数，且它的各位数字位置经过任意对换后仍为素数，则称为绝对素数。试求所有的两位绝对素数。function r=is_prime(n) x=fix(n/10);y=n-10*x;m=10*y+x;for i=2:fix(sqrt(n) if rem(n,i) =0 break; end if rem(m,i) =0 break; end if i=

12、fix(sqrt(n) n endend for n=11:2:99is_prime(n);endn = 11n = 13n = 17n = 19n = 31n = 37n = 71n = 73n = 79n = 97实验五 高层绘图操作1.画出空间曲线在范围内的图形，并画出相应的等高线。x=-30: 0.5:30;x,y=meshgrid(x);z=10*sin(sqrt(x.2+y.2)./sqrt(1+x.2+y.2);mesh(x,y,z);xlabel(x-axis),ylabel(y-axis),zlabel(z-axis); x=-30: 0.5:30;x,y=meshgrid(

13、x);z=10*sin(sqrt(x.2+y.2)./sqrt(1+x.2+y.2);contour3(x,y,z,30)xlabel(x-axis),ylabel(y-axis),zlabel(z-axis);2.根据给定的参数方程，绘制下列曲面的图形。a) 椭球面b) 椭圆抛物面c) 单叶双曲面d) 双曲抛物面e) 旋转面f) 圆锥面g) 环面h) 正螺面 a) ezmesh(3*cos(u)*sin(v),2*cos(u)*cos(v),sin(u),0,2*pi,0,2*pi)b) ezmesh(3*u*sin(v),2*u*cos(v),4*u2,-5,5,0,2*pi)c) ezm

14、esh(3*sec(u)*sin(v),2*sec(u)*cos(v),4*tan(u),-pi*4/9,pi*4/9,0,2*pi)d) ezmesh(u,v,(u2-v2)/3,-10,10,-10,10)e) ezmesh(log(u)*sin(v),log(u)*cos(v),u,0.1,10,0,2*pi)f) ezmesh(u*sin(v),u*cos(v),u,-10,10,0,2*pi)g)ezmesh(3+0.4*cos(u)*cos(v),(3+0.4*cos(u)*sin(v),0.4*sin(v),0,2*pi,0,2*pi) h) ezmesh(u*sin(v),u*

15、cos(v),4*v,-10,10,0,2*pi)3.已知，完成下列操作：（1） 在同一坐标系下用不同颜色和线形绘制3条曲线。（2） 以子图形式绘制3条曲线。（3） 分别用条形图、阶梯图、杆图和填充图绘制3条曲线。 （1）x=linspace(-10,10,100);y1=x.2;y2=cos(2*x);y3=y1.*y2;hold on;plot(x,y1,r-);plot(x,y2,g-);plot(x,y3,b.-);hold off （2）x=linspace(-10,10,100);y1=x.2;y2=cos(2*x);y3=y1.*y2;subplot(1,3,1);plot(x,

16、y1,r-);subplot(1,3,2);plot(x,y2,g-);subplot(1,3,3);plot(x,y3,b.-);（3）x=linspace(-10,10,100);y1=x.2;y2=cos(2*x);y3=y1.*y2;subplot(3,1,1);bar(x,y1,r);subplot(3,1,2);stairs(x,y2,g);subplot(3,1,3);stem(x,y3,b);hold off; 4绘制极坐标曲线，并分析参数对曲线形状的影响。a=input(a=);b=input(b=);n=input(n=);theta=0:pi/180:2*pi;rho=a

17、*sin(b+n*theta);polar(theta,rho);a=3b=0n=3a=3b=pin=3a=3b=pin=1a=1b=pin=35.绘制函数的曲面图和等高线。（1）（2）(1)x=linspace(-10,10,100);x,y=meshgrid(x);z=(x.2-2*x).*exp(-x.2-y.2-x.*y);mesh(x,y,z)x=linspace(-10,10,100);x,y=meshgrid(x);z=(x.2-2*x).*exp(-x.2-y.2-x.*y);contour3(x,y,z)(2)x=linspace(-5,5,100);x,y=meshgrid

18、(x);z=1./sqrt(x-1).2+y.2)-1./sqrt(x+1).2+y.2);mesh(x,y,z)x=linspace(-5,5,100);x,y=meshgrid(x);z=1./sqrt(x-1).2+y.2)-1./sqrt(x+1).2+y.2);contour3(x,y,z)实验六 数据处理与多项式计算1、 将100个学生5门功课的成绩存入矩阵P中，进行如下处理：（1） 分别求5门课的最高分、最低分和相应学生的学号。（2） 分别求5门课的平均分和标准方差。（3） 5门课总分的最高分、最低分及相应学生学号。（4） 将5门课总分按从大到小的顺序存入zcj中，相应学生学号存

19、入xsxh。P=input(请将100个学生5门功课的成绩构成一个100行5列矩阵输入：)Max,I=max(P)MIin,J=min(P)Average=mean(P)STD=std(P)fx=sum(P,2);ZFMax,U=max(fx)ZFMin,V=min(fx)zcj,xsxh=sort(-fx);ZCJ=-zcjxsxh请将100个学生5门功课的成绩构成一个100行5列矩阵输入：100*rand(100,5)P = 95.0129 58.2792 43.9791 36.0311 28.5939 23.1139 42.3496 34.0048 54.8513 39.4128 60.

20、6843 51.5512 31.4217 26.1770 50.3014 48.5982 33.3951 36.5078 59.7345 72.1980 89.1299 43.2907 39.3240 4.9278 30.6209 76.2097 22.5950 59.1525 57.1057 11.2164 45.6468 57.9807 11.9747 70.0857 44.3290 1.8504 76.0365 3.8129 96.2288 46.6763 82.1407 52.9823 45.8598 75.0518 1.4669 44.4703 64.0526 86.9867 73.

21、9993 66.4052 61.5432 20.9069 93.4237 43.1873 72.4062 79.1937 37.9818 26.4449 63.4266 28.1634 92.1813 78.3329 16.0300 80.3026 26.1819 73.8207 68.0846 87.2855 8.3881 70.8471 17.6266 46.1095 23.7880 94.5463 78.3859 40.5706 56.7829 64.5831 91.5942 98.6158 93.5470 79.4211 96.6887 60.1987 47.3343 91.6904

22、5.9183 66.4931 25.3561 90.2819 41.0270 60.2869 87.0381 87.3451 45.1059 89.3650 5.0269 0.9927 51.3401 80.4517 5.7891 41.5375 13.7010 73.2651 82.8864 35.2868 30.4999 81.8756 42.2227 16.6270 81.3166 87.4367 43.0166 96.1370 39.3906 0.9861 1.5009 89.0322 7.2059 52.0757 13.8891 76.7950 73.4908 55.3408 71.

23、8124 20.2765 97.0845 68.7324 29.1984 56.9190 19.8722 99.0083 34.6112 85.7964 46.0806 60.3792 78.8862 16.6035 33.5755 44.5307 27.2188 43.8659 15.5613 68.0204 8.7745 19.8814 49.8311 19.1116 5.3444 44.3483 1.5274 21.3963 42.2452 35.6656 36.6300 74.6786 64.3492 85.5976 49.8305 30.2534 44.5096 32.0036 49

24、.0250 43.4441 85.1845 93.1815 96.0099 81.5935 56.2458 75.9479 46.5994 72.6632 46.0770 61.6621 94.9759 41.8649 41.1953 45.7354 11.3340 55.7939 84.6221 74.4566 45.0689 89.8252 1.4233 52.5152 26.7947 41.2219 75.4551 59.6177 20.2647 43.9924 90.1610 79.1123 81.6206 67.2137 93.3380 0.5584 81.4952 97.7092

25、83.8118 68.3332 29.7406 67.0004 22.1908 1.9640 21.2560 4.9162 20.0876 70.3684 68.1277 83.9238 69.3180 27.3088 52.2061 37.9481 62.8785 65.0106 62.6235 93.2897 83.1796 13.3773 98.2988 53.6852 71.3354 50.2813 20.7133 55.2673 5.9504 22.8039 70.9471 60.7199 40.0074 8.8962 44.9642 42.8892 62.9888 19.8789

26、27.1308 17.2200 30.4617 37.0477 62.5201 40.9072 96.8820 18.9654 57.5148 73.3363 47.4041 35.5716 19.3431 45.1425 37.5885 90.8989 4.9047 68.2223 4.3895 0.9876 59.6247 75.5339 30.2764 2.7185 41.9858 32.8955 89.4813 54.1674 31.2685 75.3670 47.8194 28.6150 15.0873 1.2863 79.3872 59.7171 25.1201 69.7898 3

27、8.3967 91.9957 16.1449 93.2736 37.8373 68.3116 84.4722 82.9474 13.0982 86.0012 9.2842 36.7753 95.6122 94.0820 85.3655 3.5338 62.0801 59.5548 70.1853 59.3563 61.2395 73.1277 2.8748 84.7676 49.6552 60.8540 19.3893 81.2118 20.9272 89.9769 1.5760 90.4812 61.0114 45.5092 82.1629 1.6355 56.9206 70.1493 8.

28、1074 64.4910 19.0075 63.1790 9.2196 85.1122 81.7974 58.6918 23.4413 42.4889 56.2049 66.0228 5.7581 54.8782 37.5577 31.9296 34.1971 36.7568 93.1583 16.6154 37.4899 28.9726 63.1451 33.5197 83.3151 86.7796 34.1194 71.7634 65.5531 83.8640 37.2176 53.4079 69.2669 39.1904 45.1614 7.3690 72.7113 8.4079 62.

29、7315 95.6601 19.9838 30.9290 45.4355 69.9080 14.7153 4.9493 83.8496 44.1828 39.7184 86.9933 56.6710 56.8072 35.3250 41.3629 76.9436 12.1925 37.0414 15.3606 65.5213 44.4162 52.2112 70.2740 67.5645 83.7585 62.0620 11.7060 54.6571 69.9213 37.1608 95.1689 76.9918 44.4880 72.7509 42.5253 64.0010 37.5056

30、69.4567 47.8384 59.4663 24.7328 82.3387 62.1310 55.4842 56.5739 35.2702 4.6636 79.4821 12.1047 71.6542 18.7860 59.7913 95.6843 45.0754 51.1311 49.0644 94.9150 52.2590 71.5883 77.6401 40.9274 28.8798 88.0142 89.2842 48.9345 46.3526 88.8833 17.2956 27.3102 18.5904 61.0944 10.1585 97.9747 25.4769 70.06

31、35 7.1168 6.5315 27.1447 86.5603 98.2709 31.4280 23.4300 25.2329 23.2350 80.6638 60.8384 93.3098 87.5742 80.4872 70.3568 17.5020 6.3128 73.7306 90.8398 48.4964 62.1027 26.4218 13.6519 23.1894 11.4613 24.5960 99.9532 1.1757 23.9313 66.4856 58.7358 21.1988 89.3898 4.9754 36.5374 50.6053 49.8410 19.913

32、8 7.8384 14.0044 46.4779 29.0488 29.8723 64.0815 56.6773 54.1419 67.2754 66.1443 19.0887 82.3008 94.2327 95.7991 28.4409 84.3869 67.3949 34.1759 76.6552 46.9224 17.3900 99.9447 40.1804 66.6124 6.4781 17.0793 96.1636 30.7688 13.0945 98.8335 99.4295 5.8862 41.1568 9.5413Max = 98.8335 99.4295 99.9447 9

33、6.2288 99.9532I = 100 100 98 8 91MIin = 0.9861 1.2863 0.5584 2.8748 1.4233J = 24 55 40 60 37Average = 52.8568 46.5241 53.1197 51.4998 49.6100STD = 28.1762 27.8987 27.1515 26.3283 29.8811ZFMax = 402.9786U = 34ZFMin = 117.2834V = 94ZCJ = 402.9786 377.1898 361.4687 357.5655 352.1466 347.2976 340.3146 3

34、35.9142 335.8704 333.9000 321.9776 321.7549 321.7504 320.8030 319.8763 315.1510 311.4151 309.6008 308.4261 304.7092 301.5912 300.8845 295.7322 295.3961 295.3650 293.0287 292.5175 291.4673 291.3281 291.0537 288.5547 286.6667 285.3686 283.8330 283.2800 281.3660 280.7196 279.7398 272.2107 272.0485 271.

35、2946 271.0768 271.0500 267.8188 266.8340 262.6244 262.2329 261.8962 261.2708 260.4563 259.4946 257.5015 255.6047 254.8474 254.1667 250.4337 241.8184 241.0094 237.2373 235.2104 233.9751 232.7922 232.0375 231.3490 230.0168 227.1763 226.2793 225.5348 224.6048 222.6313 220.1356 218.9756 218.2175 217.179

36、1 214.5506 214.3957 214.1229 208.7581 207.2932 207.1635 206.5119 197.8778 197.3575 196.1464 195.9236 193.7323 180.5979 172.8517 171.5271 170.1077 165.9372 163.5843 163.4407 155.0162 150.8009 138.5170 137.4644 134.4492 118.5922 117.2834xsxh = 34 17 84 96 16 23 40 10 82 77 35 58 44 19 45 39 73 56 14 3

37、2 90 43 68 37 76 13 69 11 25 97 62 57 27 79 88 60 59 18 26 95 83 41 98 49 87 65 89 1 78 15 71 9 38 100 33 4 81 64 54 12 28 50 61 93 7 20 6 47 8 74 3 63 67 21 75 70 80 52 5 86 22 51 53 66 36 2 55 91 92 48 72 99 29 46 24 30 31 85 42 942、某气象观测站测得某日6：0018：00之间每隔2小时室外温度如下表所示：时间h681012141618室外温度t118020022025.030.028.024.0室外温度t215.019.024.028.034.032.030.0试用三次样条差值分别求出该日室内外6：3017：30时之间每隔两小时各点的近似温度。Time=6:2:18;H=6.5:2:17.5;t1=18.0,20.0,22.0,25.0,30.0,28.0,24.0;t2=15.0,19.0,24.0,28.0,34.0,32.0,30.0;T1