數(shù)學(xué)實(shí)驗(yàn)與建模作業(yè)

1、數(shù)學(xué)實(shí)驗(yàn)與建模作業(yè)實(shí)驗(yàn)1 MATLAB運(yùn)算基礎(chǔ)1. 先求下列表達(dá)式的值，然后顯示MATLAB工作空間的使用情況并保存全部變量。(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 48604 7868

4、8 ans32=A.3ans32 = 1728 39304 -64 39304 343 27 343 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 ans51=A,Bans51 = 12 34 -4 1 3 -1 34 7 87 2 0 3 3 65 7 3 -2

5、7 ans52=A(1,3,:);B2ans52 = 12 34 -4 3 65 7 4 5 1 11 0 1920 -5 403設(shè)有矩陣A和B，（1） 求他們的乘積C。（2） 求矩陣C的右下角3x2子矩陣賦給D。（3） 查看MATLAB 工作空間的使用情況。 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 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

6、 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之間能被21整除的數(shù)的個(gè)數(shù)。(2)建立一個(gè)字符串向量，刪除其中的大寫字母。（1）n=0;for i=100:999 if rem(i,21)=0 n=n+1; endendnn =43 (2)ch=IamaStuDenTOk;k=find(ch=A&ch

7、=Z);ch(k)=;chch =amatuenk實(shí)驗(yàn)2 選擇結(jié)構(gòu)程序設(shè)計(jì)1. 求下列分段函數(shù)的值x=input(請(qǐng)輸入x的值：);if x=0 & x10 & x=2 & x=3y=x2-5*x+6elsey=x2-x-1end2輸入一個(gè)百分制成績(jī)，要求輸出成績(jī)等級(jí)A，B，C，D，E。其中90100分為A，8089分為B，7079分為C，6069分為D，60分以下為E。要求：（1） 分別用if語(yǔ)句和switch語(yǔ)句實(shí)現(xiàn)。（2） 輸入百分制成績(jī)后要判斷該成績(jī)的合理性，對(duì)不合理的成績(jī)應(yīng)輸出錯(cuò)誤成績(jī)。if語(yǔ)句實(shí)現(xiàn)如下：x=input(請(qǐng)輸入百分制成績(jī)：);if x=fix(x)|x100disp(

8、輸入錯(cuò)誤！)elseif x=90 & x=80 & x=70 & x=60 & x=69disp(D)elsedisp(E)endswitch語(yǔ)句實(shí)現(xiàn)如下：x=input(請(qǐng)輸入百分制成績(jī)：);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)otherwise disp(輸入錯(cuò)誤！)end3假定某地區(qū)電話收費(fèi)標(biāo)準(zhǔn)為：通話時(shí)間3分鐘以下，收費(fèi)0.5元；3分

9、鐘以上，則每超過(guò)分鐘加收0.15元；通話時(shí)間在7：0022：00之間者，按上述標(biāo)準(zhǔn)全價(jià)收費(fèi)，在其他通話時(shí)間者，按上述標(biāo)準(zhǔn)半價(jià)收費(fèi)。計(jì)算某人在t1到t2通話時(shí)間，應(yīng)繳多少電話費(fèi)t1=input(請(qǐng)輸入通話開(kāi)始時(shí)間： );t2=input(請(qǐng)輸入通話結(jié)束時(shí)間 ：);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 num2cell(0:3) if t1*60=7 & t1*60=7 & t1=7 & t1*60=7 & t15disp(輸

10、入數(shù)太大！);disp(m(5,:);elsedisp(m(n,:)；end實(shí)驗(yàn)三 循環(huán)結(jié)構(gòu)程序設(shè)計(jì)1.根據(jù)，求的近似值。當(dāng)n分別取100、1000、1000時(shí)，結(jié)果是多少？ m=0;for n=1:100m=m+1./(n2);endpia=sqrt(m*6)pia =3.1321n=1000時(shí)pia =3.1406n=10000時(shí)pia = 3.14152根據(jù),求：（1）y3時(shí)的最大值。（2）與（1）的n值對(duì)應(yīng)的y 值 y=1;n=1;while y0 x=x+1; end if f(j)=0 y=y+1; end if f(j)0 z=z+1; endendxyzmx = 4.3776e

11、+011mn = -8.9941e+011s = -7.4275e+011x = 49y = 2z =49試驗(yàn)四 函數(shù)與文件1、一個(gè)自然數(shù)是素?cái)?shù)，且它的各位數(shù)字位置經(jīng)過(guò)任意對(duì)換后仍為素?cái)?shù)，則稱為絕對(duì)素?cái)?shù)。試求所有的兩位絕對(duì)素?cái)?shù)。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=fix(sqrt(n) n endend for n=11:2:99is_prime(n);endn = 11n

12、 = 13n = 17n = 19n = 31n = 37n = 71n = 73n = 79n = 97實(shí)驗(yàn)五 高層繪圖操作1.畫出空間曲線在范圍內(nèi)的圖形，并畫出相應(yīng)的等高線。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(x);z=10*sin(sqrt(x.2+y.2)./sqrt(1+x.2+y.2);contour3(x,y,

13、z,30)xlabel(x-axis),ylabel(y-axis),zlabel(z-axis);2.根據(jù)給定的參數(shù)方程，繪制下列曲面的圖形。a) 橢球面b) 橢圓拋物面c) 單葉雙曲面d) 雙曲拋物面e) 旋轉(zhuǎn)面f) 圓錐面g) 環(huán)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) ezmesh(3*sec(u)*sin(v),2*sec(u)*cos(v),4*tan(u),-pi*4/9,pi*

14、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*cos(v),4*v,-10,10,0,2*pi)3.已知，完成下列操作：（1） 在同一坐標(biāo)系下用不同顏色和線形

15、繪制3條曲線。（2） 以子圖形式繪制3條曲線。（3） 分別用條形圖、階梯圖、桿圖和填充圖繪制3條曲線。 （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,y1,r-);subplot(1,3,2);plot(x,y2,g-);subplot(1,3,3);plot(

16、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繪制極坐標(biāo)曲線，并分析參數(shù)對(duì)曲線形狀的影響。a=input(a=);b=input(b=);n=input(n=);theta=0:pi/180:2*pi;rho=a*sin(b+n*theta);polar(theta,rho);a=3b=0n=3a=3b=pin=3a=3b

17、=pin=1a=1b=pin=35.繪制函數(shù)的曲面圖和等高線。（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(x);z=1./sqrt(x-1).2+y.2)-1./sqrt(x+1).2+y.2);mesh(x,y,z

18、)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)實(shí)驗(yàn)六 數(shù)據(jù)處理與多項(xiàng)式計(jì)算1、 將100個(gè)學(xué)生5門功課的成績(jī)存入矩陣P中，進(jìn)行如下處理：（1） 分別求5門課的最高分、最低分和相應(yīng)學(xué)生的學(xué)號(hào)。（2） 分別求5門課的平均分和標(biāo)準(zhǔn)方差。（3） 5門課總分的最高分、最低分及相應(yīng)學(xué)生學(xué)號(hào)。（4） 將5門課總分按從大到小的順序存入zcj中，相應(yīng)學(xué)生學(xué)號(hào)存入xsxh。P=input(請(qǐng)將100個(gè)學(xué)生5門功課的成績(jī)構(gòu)成一個(gè)100行5列矩陣輸入：)Max,I=max(P

19、)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請(qǐng)將100個(gè)學(xué)生5門功課的成績(jī)構(gòu)成一個(gè)100行5列矩陣輸入：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 60.6843 51.5512 31.4217 26.1770 50.3014 48.5982 33.3951 36.

20、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 73.9993 66.4052 61.5432 20.9069 93.4237 43.1873 72.4062 79.

21、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 5.9183 66.4931 25.3561 90.2819 41.0270 60.2869 87.0381 8

22、7.3451 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 71.8124 20.2765 97.0845 68.7324 29.1984 56.9190 19.8722 99.

23、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 49.0250 43.4441 85.1845 93.1815 96.0099 81.5935 56.2458 75

24、.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 83.8118 68.3332 29.7406 67.0004 22.1908 1.9640 21.2560 4

25、.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 27.1308 17.2200 30.4617 37.0477 62.5201 40.9072 96.8820

26、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 38.3967 91.9957 16.1449 93.2736 37.8373 68.3116 84.4722 8

27、2.9474 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 8.1074 64.4910 19.0075 63.1790 9.2196 85.1122 81.7974 58.6

28、918 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 62.7315 95.6601 19.9838 30.9290 45.4355 69.9080 14.7153 4.9

29、493 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 69.4567 47.8384 59.4663 24.7328 82.3387 62.1310 55.4842

30、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 70.0635 7.1168 6.5315 27.1447 86.5603 98.2709 31.4280 23.4300

31、 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 19.9138 7.8384 14.0044 46.4779 29.0488 29.8723 64.0815 56.6773

32、 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 96.2288 99.9532I = 100 100 98 8 91MIin = 0.9861 1.2863 0.

33、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 335.9142 335.8704 333.9000 321.9776 321.7549 321.7504 320

34、.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 271.2946 271.0768 271.0500 267.8188 266.8340 262.6244 262.23

35、29 261.8962 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 217.1791 214.5506 214.3957 214.1229 208.7581 207.2932 207.1635

36、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 32 90 43 68 37 76 13 69 11 25 97 62 57 27 79 88 60 59 18

37、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、某氣象觀測(cè)站測(cè)得某日6：0018：00之間每隔2小時(shí)室外溫度如下表所示：時(shí)間h681012141618室外溫度t118020022025.030.028.024.0室外溫度t215.019.024.028.034.032.030.0試用三次樣條差值分別求出該日室內(nèi)外6：3017：30時(shí)之間每隔兩小時(shí)各點(diǎn)的近似溫度。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=interp1(Time,t1,H,s