《[数学]数学实验与数学建模.doc》由会员分享,可在线阅读,更多相关《[数学]数学实验与数学建模.doc(39页珍藏版)》请在三一文库上搜索。
1、 数 学 建 模 实 验 报 告 学号:201014100130 姓名:廖 日 娟 专业班级:信息与计算科学1班 任课老师:吴 霞 老 师 实验一 matlab概述,安装和简单计算一,实验目的:1,了解matlab的应用,学会安装matlab软件2,熟悉matlab的工作页面3,掌握matlab的基本概念,基本函数和基本赋值与运算二,实验环境或设备:WindowsXP, MATLAB软件三,实验属性:验证试验四,实验内容:步骤与结果1,采用不同命令求1.6180389的整数。 x=1.6180389; round(x)ans = 2 fix(x)ans = 1 floor(x)ans = 1
2、ceil(x)ans = 22,利用matlab计算下列简单算术运算:(1)2158.21+645835; (2)(3) (4) 2158.21+6458/35ans = 2.3427e+003 3.27845-2.5632+3*pians = 1.5937e+023 sin(48/180*pi)+cos(24/180*pi)-log(3.56)ans = 0.3869 tan(56/180*pi)+abs(3-5.2518)ans = 3.73443,求下列函数在指定点的函数值:(1) (2)(3) (4) x=7.23; 3*x5-6*x2+7*x-9ans = 5.8995e+004 x
3、=2.4; 3(2*x)-2(3*x)ans = 48.0328 x=pi/12; 3*sin(2*x)+5*tan(3*x)ans = 6.5000 x=3.25; 2*(log(3*x+8)2-5*log(x)ans = 10.65394,输入下列向量或矩阵:(1) (1 2 3 5 8 13 21 34 55); (2)(1 4 7 10 13 16 19)(3), (4), (5) (6) A1=1 2 3 5 8 13 21 34 55A1 = 1 2 3 5 8 13 21 34 55 A2=1:3:19A2 = 1 4 7 10 13 16 19 A3=7;2;5;4A3 = 7
4、 2 5 4 A4=2:2:8A4 = 2 4 6 8 A4ans = 2 4 6 8 A5=2 -1 3;3 1 -6;4 -2 9A5 = 2 -1 3 3 1 -6 4 -2 9 A6=1 1 1 1 ;2 3 4 5;4 9 16 25;8 27 64 125A6 = 1 1 1 1 2 3 4 5 4 9 16 25 8 27 64 1255,求上题中第(5),(6)两小题中矩阵的行列式值和逆矩阵。 A5=2 -1 3;3 1 -6;4 -2 9; det(A5)ans = 15 AN=inv(A5)AN = -0.2000 0.2000 0.2000 -3.4000 0.4000
5、1.4000 -0.6667 0 0.3333 A6=1 1 1 1 ;2 3 4 5;4 9 16 25;8 27 64 125; det(A6)ans = 12 AN=inv(A6)AN = 10.0000 -7.8333 2.0000 -0.1667 -20.0000 19.0000 -5.5000 0.5000 15.0000 -15.5000 5.0000 -0.5000 -4.0000 4.3333 -1.5000 0.1667实验总结通过本次试验,了解并掌握了matlab的基本命令和基本函数,同时也感觉到了matlab的强大的运算能力与实用性,我们应不断的运用它。 实验二 符号函
6、数及其微积分一,实验目的:掌握符号函数的计算,学会绘制二维图形,求符号函数的极限,导数,积分。二,实验环境或设备:WindowsXP, MATLAB软件三,实验属性:验证试验四,实验内容:步骤与结果1,求下列各组函数的复合函数:(1) f(x)=x3+3; g(x)=3*tan(3*x-2);求f(g(x); syms x y z u t f=x3+3;g=3*tan(3*x-2); compose(f,g) ans = 27*tan(3*x-2)3+3 compose(f,g,t) ans = 27*tan(3*t-2)3+3(2) f(x)=sqrt(3*x+2); g(x)=(sin(x
7、)2-1;求f(g(x); syms x y z f=sqrt(3*x+2);g=(sin(x)2-1; compose(f,g) ans = (3*sin(x)2-1)(1/2)(3) f(x)=3(x+1); g(x)=log(x2+1);求f(g(x); syms x y z f=3(x+1);g=log(x2+1); compose(f,g) ans = 3(log(x2+1)+1)2,求下列函数的反函数:(1):y=(log(x)2+2 finverse(log(x)2+2)Warning: finverse(log(x)2+2) is not unique. In sym.finv
8、erse at 43 ans = exp(-2+x)(1/2)(2):y=(3*x-1)/(2+3*x) finverse(3*x-1)/(2+3*x) ans = -1/3*(1+2*x)/(-1+x)3,按要求作下列函数的图象:(1)用plot命令作y=1/3*x3-2,的图像。fplot(1/3*x3-2,-2,2)(2)用plot命令作y=sin(x),的图像。 fplot(sin(x),0,2*pi)fplot(tan(x),-pi,pi)(3)在同一窗口用不同线型作y=2(x),的图像,并加标注; theta=0:0.01:2*pi; polar(theta,2*theta,-k)
9、(4)用polar命令作的极限坐标图像 theta=0:0.01:pi;polar(theta,2*(cos(theta),-k)4. 求下列极限:(1); syms x y limit(sqrt(5-x)-sqrt(x+1)/(x2-4),x,2) ans = -1/12*3(1/2) syms x y limit(sin(x)*(log(x),x,0,right) ans = 0 syms x y limit(x2*(1-cos(1/x),x,inf) ans = 1/2 limit(sin(2*x)/(sqrt(x+1)-1)+cos(x),x,0) ans = 55,求下列函数的导数:
10、 syms x y a t diff(x/(x-sqrt(a2+x2),x) ans = 1/(x-(a2+x2)(1/2)-x/(x-(a2+x2)(1/2)2*(1-1/(a2+x2)(1/2)*x) y=log(sqrt(1+sin(x)/(1-sin(x); diff(y,x) ans = 1/2/(1+sin(x)*(1-sin(x)*(cos(x)/(1-sin(x)+(1+sin(x)/(1-sin(x)2*cos(x) y=atan(1-x2); diff(y,x) ans = -2*x/(1+(-1+x2)2) diff(-2*x/(1+(-1+x2)2),x) ans =
11、-2/(1+(-1+x2)2)+8*x2/(1+(-1+x2)2)2*(-1+x2) y=asin(sqrt(1-x4); diff(y,x) ans = -2/(1-x4)(1/2)*x3/(x4)(1/2) diff(-2/(1-x4)(1/2)*x3/(x4)(1/2),x) ans =-4/(1-x4)(3/2)*x6/(x4)(1/2)-6/(1-x4)(1/2)*x2/(x4)(1/2)+4/(1-x4)(1/2)*x6/(x4)(3/2)diff(-4/(1-x4)(3/2)*x6/(x4)(1/2)-6/(1-x4)(1/2)*x2/(x4)(1/2)+4/(1-x4)(1/2
12、)*x6/(x4)(3/2),x) ans =-24/(1-x4)(5/2)*x9/(x4)(1/2)-36/(1-x4)(3/2)*x5/(x4)(1/2)+16/(1-x4)(3/2)*x9/(x4)(3/2)-12/(1-x4)(1/2)*x/(x4)(1/2)+36/(1-x4)(1/2)*x5/(x4)(3/2)-24/(1-x4)(1/2)*x9/(x4)(5/2) syms x y s s=x3+y3-2*x*y; -diff(s,x)/diff(s,y)ans = (-3*x2+2*y)/(3*y2-2*x) y=sin(2(x2+3*x-2); diff(y,x) ans =
13、 cos(2(x2+3*x-2)*2(x2+3*x-2)*(2*x+3)*log(2)6,求下列不定积分: syms x y s z y=x2*log(x); int(y) ans = 1/3*x3*log(x)-1/9*x3 y=exp(2*x)*sin(x); int(y) ans = -1/5*exp(2*x)*cos(x)+2/5*exp(2*x)*sin(x) y=x3/(sqrt(2-x2); int(y) ans = -1/3*x2*(2-x2)(1/2)-4/3*(2-x2)(1/2) y=(sin(4*x)4; int(y) ans = -1/16*sin(4*x)3*cos
14、(4*x)-3/32*cos(4*x)*sin(4*x)+3/8*x y=sqrt(x2-2*x+5); int(y) ans = 1/4*(2*x-2)*(x2-2*x+5)(1/2)+2*asinh(1/2*x-1/2) y=(1/(1+x2)-1/(1+x)2)*atan(x); int(y) ans =-1/4*log(-i*x-i)+1/4*i*log(-i*x-i)+1/4*i*log(1+i*x)/(i*x+i)-1/4*log(1+i*x)/(i*x+i)*x+1/4*log(2)*log(1/4*x2+1/4)-1/4*i*log(1-i*x)/(-i*x-i)*x-1/4*
15、dilog(1/2+1/2*i*x)+1/4*log(1+i*x)/(i*x+i)+1/4*i*log(1+i*x)/(i*x+i)*x-1/8*log(1+i*x)2-1/4*log(i*x+i)-1/4*i*log(i*x+i)-1/4*i*log(1-i*x)/(-i*x-i)-1/4*log(1-i*x)/(-i*x-i)*x-1/4*dilog(1/2-1/2*i*x)-1/8*log(1-i*x)2+1/4*log(1-i*x)/(-i*x-i)7,求下列定积分: syms x y z y=sqrt(1+cos(2*x); int(y,0,3/4*pi) ans = -1+2*2(
16、1/2) y=1/(x*sqrt(2*x4+2*x2+1); int(y,1/2,1) ans =-1/2*Re(atanh(5(1/2)+1/4*log(3*5(1/2)-5)-1/4*log(3*5(1/2)+5)+1/2*Re(atanh(1/4*26(1/2)-1/4*log(3*26(1/2)-13)+1/4*log(3*26(1/2)+13) y=(cos(x)3*sin(x); int(y,0,pi/2) ans = 1/4 y=x2*exp(-x); int(y,0,inf) ans = 2 y=x3/(x2-3*x+2); int(y,0,1/2) ans = 13/8+8*
17、log(3)-15*log(2)实验结果:通过本次实验,了解并掌握了符号函数的计算,学会了使用matlab求符号函数的极限,导数和积分,同时也深刻认识到matlab能让我们更好的去学习数学,应用数学。 实验三 多元函数及其积分一,实验目的:掌握用polt3,mesh,surf,bar3,pie3等函数的绘制三维图形,学会求多元函数的偏导数。高阶偏导数以及重积分等的使用命令和 一元函数的微积分。二,实验环境或设备:WindowsXP, MATLAB软件三,实验属性:验证试验四,实验内容:步骤与结果1,绘制下列函数在给定条件下的图形:(1) 使用mesh命令绘制的网格图。(2)使用mesh命令绘制
18、的网格图。(3)使用surf命令绘制的曲面图。(4)使用surf命令绘制的曲面图。 syms x y z s u t x,y=meshgrid(-2:0.125:2,-3:0.125:3); z=2*x.2+3*y.2; meshc(x,y,z) x,y=meshgrid(-3:0.125:3); z=sqrt(x.2+y.2); meshc(x,y,z) x,y=meshgrid(-3:0.125:3,0:0.125:4); y=2*x.2; surf(x,y) x,y=meshgrid(-3:0.125:3); z=x.2+y.2; surf(x,y,z)2.绘制方程为的空间曲线图。 t=
19、0:pi/200:8*pi; x=2*cos(t); y=2*sin(t); z=2*t; plot3(x,y,z)3,绘制下列表格中所列数据的二维,三维条形图。X -3 -2 -1 0 1 2 3 Y 3 2 4 6 3 2 1 x=-3:1:3; y=3,2,4,6,3,2,1; bar(x,y) z=-3:1:3;3,2,4,6,3,2,1; bar3(x,y,detached)4.绘制矩阵的三维条形图。 z=9 6 4;2 4 1;1 2 3; bar3(z,detached)5. 求下列函数的偏导数:(1) 已知(2) 已知(3) 设;(4) 设; z=tan(x/y); dfx=d
20、iff(z,x) dfx = (1+tan(x/y)2)/y dfy=diff(z,y) dfy = -(1+tan(x/y)2)*x/y2 d2fxy=diff(dfx,y) d2fxy = -2*tan(x/y)*(1+tan(x/y)2)*x/y3-(1+tan(x/y)2)/y2 z=atan(y/x); dfx=diff(z,x) dfx = -y/x2/(1+y2/x2) dfy=diff(z,y) dfy = 1/x/(1+y2/x2) d2fxy=diff(dfx,y) d2fxy = -1/x2/(1+y2/x2)+2*y2/x4/(1+y2/x2)2 z=x2*log(y)
21、; x=u/v;y=3*u-2*v; dfx=diff(z,u) dfx = 2*u/v2*log(3*u-2*v)+3*u2/v2/(3*u-2*v) dfx=diff(z,v) dfx = -2*u2/v3*log(3*u-2*v)-2*u2/v2/(3*u-2*v)6. 求下列重积分:(1) 计算二重积分(2) 计算 s=1-x/2-2*y; sl=int(s,y,-2,2) sl = 4-2*x int(sl,-1,1) ans = 8 s=x*y2; sl=int(s,y,-sqrt(2*x),sqrt(2*x) sl = 4/3*x(5/2)*2(1/2) int(sl,0,0.5
22、) ans = 1/21实验结果:通过本次实验,学会了求多元函数的偏导数,高阶偏导数以及重积分,线性积分,但开始在求符合函数的偏导数过程中,出了小的差错,忘记将带有中间变量的函数转化为带有最终变量的函数,在以后的实验中,尽量不犯相同或类似的错误。 实验四 无穷级数及曲线拟合一,实验目的:掌握级数求和于级数展开,学会调用taylor级数运算器,使用各种命令函数求多项式的简单运算以及曲线拟合。二,实验环境或设备:WindowsXP, MATLAB软件三,实验属性:验证试验四,实验内容:步骤与结果1,求下列无穷级数的和函数: syms x y z u t n k r r1=symsum(2/3)(n
23、-1),n,1,inf) r1 = 3 r2=symsum(-1)n*(1/n2),n,1,inf) r2 = -1/12*pi22,将下列函数展开成5阶Maclaurin级数: syms x y z u v s t z=x2/(x-3); taylor(z,5,x) ans = -1/3*x2-1/9*x3-1/27*x4 s=x2*exp(-x); taylor(s,5,x) ans =x2-x3+1/2*x43,将下列函数在指定点处展开成6阶taylor级数: s=x/(3-2*x); taylor(s,6,x,1)ans = -2+3*x+6*(x-1)2+12*(x-1)3+24*(
24、x-1)4+48*(x-1)5 s=x2*log(x); taylor(s,6,x,1) ans =x-1+3/2*(x-1)2+1/3*(x-1)3-1/12*(x-1)4+1/30*(x-1)5 4,计算多项式 t=1 -2 0 0 0 3 -2; poly2sym(t) ans = x6-2*x5+3*x-2 polyval(t,2)ans =45,多项式试计算两多项式的乘积pq及乘积pq的伴随矩阵,特征值,并求商p/q. s=1 0 0 -2 0 -1 1; t=2 1 0 0 -3 1; st=conv(s,t)st =Columns 1 through 11 2 1 0 -4 -5
25、 -1 1 7 -2 3 -4 Column 12 1 poly2sym(st) ans = 2*x11+x10-4*x8-5*x7-x6+x5+7*x4-2*x3+3*x2-4*x+1 compan(st)ans =Columns 1 through 6 -0.5000 0 2.0000 2.5000 0.5000 -0.5000 1.0000 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26、0 0 0 0 0 0 0 0 0Columns 7 through 11 -3.5000 1.0000 -1.5000 2.0000 -0.5000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 1.0000 0 0 0 0 0 1.0000 0 0 0 0 0 1.0000 0 z=eig(ans)z = -1.3190 -0.8013 + 0.9042i -0.8013 - 0.9042i -0.1996 + 1.1080i -0.1996 - 1.1080i -0.1452 +
27、0.9261i -0.1452 - 0.9261i 1.2876 0.8773 0.6054 0.3409 ss=real(z)ss = -1.3190 -0.8013 -0.8013 -0.1996 -0.1996 -0.1452 -0.1452 1.2876 0.8773 0.6054 0.3409 u,v=deconv(s,t)u = 0.5000 -0.2500v =Columns 1 through 6 0 0 0.2500 -2.0000 1.5000 -2.2500 Column 7 1.2500实验结果:通过本次试验,学会了进行级数求和与级数展开以及多项式的简单运算,需注意:进
28、行级数展开的时候,一元函数和二元函数所对应的函数调用格式。实验5 符号函数的求解1 实验目的: 通过使用matlab,学会了求符号线性方程(组),非线性符号方程以及常微分方程的解。2 实验环境:windows xp 下的matlab 7.03 实验属性:验证实验4 实验内容1,求下列高次方程的解。(1)(2) syms x y z a b solve(x4-3*a*x3+4*a2*x-2)ans =3/4*a+1/12*3(1/2)*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)
29、+4*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)+1/12*6(1/2)*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)*(27*a2*(216*a4-243*a2+3*(-5184*a9-129
30、6*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+4*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)-2*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+4*(
31、216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)-72*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+51
32、84*a8+6561*a4)(1/2)(1/3)+4*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)*a3+48*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+4*(216*a4-243*a2+3*
33、(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)-96*a2*3(1/2)*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+81*a3*3(1/2)*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+51
34、84*a8+6561*a4)(1/2)(1/3)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)/(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+4*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-129
35、6*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)(1/2) 3/4*a+1/12*3(1/2)*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+4*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6
36、561*a4)(1/2)(1/3)(1/2)-1/12*6(1/2)*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+4*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a
37、2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)-2*(27*a2*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)+4*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)+144*a3-96)/(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(1/3)(1/2)*(216*a4-243*a2+3*(-5184*a9-1296*a6-6912*a3+1536+5184*a8+6561*a4)(1/2)(2/3)-72*(27*a2*(216*a4-243*a2+3*
链接地址:https://www.31doc.com/p-1983817.html