matlab数学软件实验Word格式文档下载.docx
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matlab数学软件实验Word格式文档下载.docx
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(b)>
x=[743]
u=[xy]
1.3x=[743]
b=[x;
y]
【实验结果】
1.1a=
123
456
b=
9
7
5
3
0
c=
d=
e=
f=
397530
1.2(a)x=
743
y=
-1-2-3
u=-1-2-3743
(b)x=
743
u=
743-1-2-3
1.3x=
743
-1-2-3
实验二Matlab绘图
1、熟练掌握MATLAB二维曲线的绘制;
2、掌握图形的修饰;
3、掌握三维图形的绘制。
2.1>
x=(0:
0.4:
20);
y=sin(x).*exp(-0.4*x);
plot(x,y,'
*'
);
xlabel('
x'
ylabel('
y'
)
2.2x=(0:
r'
2.3>
plot(x,y,'
+'
x,y,'
xlabel('
2.1
2.2
2.3
实验三线性代数
1、熟练掌握MATLAB里的矩阵运算;
2、掌握利用MATLAB解线性方程组;
3.1>
A=[123;
014;
302]
B=[412;
321;
012]
C=A+B
D=A-B
E=A*B
3.3>
B=[3;
1]
3.5>
B=[321;
043;
006]
C=[102;
-110;
032]
D=[100;
-210;
527]
E=B+C*D
3.1
A=
014
302
B=
412
321
012
C=
535
335
314
D=
-311
-3-13
3-10
E=
10810
369
12510
3.3A=
1
16
11
3.5B=
043
006
102
-110
032
100
-210
527
14615
-353
4720
实验四多项式与插值
1、掌握Lagrange插值的基本原理;
2、掌握Matlab对多项式的各种计算;
3、编写Matlab实现Lagrange插值法的程序;
4、通过Matlab观察龙格现象。
4.3
(1)>
r=[34-1-3]'
poly(r)
(2)>
r=[021-3-5]'
4.6>
a=(5-1)*(5-2.5)*(5-4)*(5-6.1)*(5-7.2)*(5-10)
r=[12.546.17.210]'
4.7>
r=[-212]'
4.3r=
4
-1
-3
ans=
1-3-132736差5倍
(2)r=
2
-5
15-7-29300
4.6a=
-121.0000
r=
1.0000
2.5000
4.0000
6.1000
7.2000
10.0000
1.0e+003*
0.0010-0.03080.3682-2.16066.4462-9.01604.3920差-(1/121)倍
4.7r=
-2
1-1-44差4倍
实验五数值积分
1、掌握数值积分的基本原理;
2、编写Matlab对数值积分的实现程序;
3、掌握Matlab实现数值积分的命令。
5.1
(1)
n=2
x=0:
pi/8:
pi/4;
y=tan(x);
z=trapz(x,y)
n=4
pi/16:
n=8
pi/32:
n=16
pi/64:
(2)
0.5:
1;
y=exp(x);
x=0:
0.25:
0.125:
0.0625:
(3)
y=1./(2+x);
5.2
pi/4:
pi/2;
y=sin(x);
n=25
pi/50:
n=100
pi/200:
5.11
(a)
clear
a=0;
b=pi;
n=2;
fprintf('
nIError\n'
nIError
fork=1:
4
n=2*n;
h=(b-a)/n;
i=1:
n+1;
x=a+(i-1)*h;
f=1./(2+cos(x));
I=(h/3)*(f
(1)+4*sum(f(2:
2:
n))+f(n+1));
ifn>
2,I=I+(h/3)*2*sum(f(3:
n));
end
fprintf('
%3.0f%10.5ff\n'
n,I);
(c)
f=1./(1+sin(x).^2);
%3.0f%10.5f\n'
5.1
(1)n=2z=
0.3590
z=
0.3498
0.3474
0.3468
1.7539
1.7272
1.7205
1.7188
(3)n=2
0.4083
0.4062
0.4056
0.4055
0.9481
0.9871
0.9968
0.9997
5.11(a)
41.80766
81.81377
161.81380
321.81380
424.35227
824.35227
1624.35227
3224.35227
实验六数值微分
1、掌握差分近似的定义以及高阶导数的数值计算的基本原理;
2、编写相应的Matlab的实现程序。
6.1x=0
xd=[00.20000.40000.60000.80001.0000];
yd=[0.00008.696410.68008.74404.77270.0000];
a=0;
L=length(xd);
d=polyfit(xd-a,yd,L-1);
fact=[1];
fork=1:
L-1
fact=[factorial(k),fact];
deriv=d.*fact
x=0.5
a=0.5;
6.2
yd=[02.0004.00006.00008.0000];
ud=[0.00009.885315.491718.207519.0210];
L=length(yd);
d=polyfit(yd-a,ud,L-1);
6.1
x=0
deriv=
807.8125-891.1875576.1156-263.864466.3140-0.0000
X=0.5
807.8125-487.2813231.4984-70.3756-10.066510.0659
deriv=
-0.02500.2485-1.50856.2938-0.0000
实验七非线性方程求根
1、掌握非线性方程求根的几种算法:
二分法、牛顿法、割线法等;
2、编写Matlab对几种算法的实现及比较程序。
7.1
(a)x=0:
0.1:
20;
y=0.5*exp(x/3)-sin(x);
plot(x,y,x,zeros(size(x)));
(b)x=0:
y=log(1+x)-x.*x;
plot(x,y,x,zeros(size(x)))
7.4bisec_n('
fun_a'
1,2)
f_name=
fun_a
BisectionScheme
It.abcfa=f(a)fc=f(c)abs(fc-fa)
bisec_n('
4,5)
7,8)
7.5(a)bisec_n('
fun_c'
0,0.4)
fun_c
(b)x=0.299828/2
y=0.2969*sqrt(x)-0.126*x-0.3516*x^2+0.2843*x^3-0.1015*x^4
(b)
7.4
1,1.000000,1.5000002.000000,1.833730,-0.5656262.399e+000
2,1.500000,1.7500002.000000,1.166403,-0.5656261.732e+000
3,1.750000,1.8750002.000000,0.471645,-0.5656261.037e+000
4,1.875000,1.9375002.000000,0.000431,-0.5656265.661e-001
5,1.875000,1.9062501.937500,0.000431,-0.2702082.706e-001
6,1.875000,1.8906251.906250,0.000431,-0.1318551.323e-001
7,1.875000,1.8828131.890625,0.000431,-0.0649626.539e-002
8,1.875000,1.8789061.882813,0.000431,-0.0320793.251e-002
9,1.875000,1.8769531.878906,0.000431,-0.0157781.621e-002
10,1.875000,1.8759771.876953,0.000431,-0.0076628.093e-003
11,1.875000,1.8754881.875977,0.000431,-0.0036134.043e-003
12,1.875000,1.8752441.875488,0.000431,-0.0015902.021e-003
13,1.875000,1.8751221.875244,0.000431,-0.0005801.010e-003
14,1.875000,1.8750611.875122,0.000431,-0.0000745.051e-004
15,1.875061,1.8750921.875122,0.000178,-0.0000742.526e-004
16,1.875092,1.8751071.875122,0.000052,-0.0000741.263e-004
17,1.875092,1.8750991.875107,0.000052,-0.0000116.314e-005
18,1.875099,1.8751031.875107,0.000020,-0.0000113.157e-005
19,1.875103,1.8751051.875107,0.000004,-0.0000111.579e-005
20,1.875103,1.8751041.875105,0.000004,-0.0000037.893e-006
21,1.875104,1.8751041.875105,0.000000,-0.0000033.946e-006
Toleranceissatisfied.
Finalresult:
Root=1.875104
1,4.000000,4.5000005.000000,-16.849852,22.0505563.890e+001
2,4.500000,4.7500005.000000,-8.488787,22.0505563.054e+001
3,4.500000,4.6250004.750000,-8.488787,3.1732721.166e+001
4,4.625000,4.6875004.750000,-3.451716,3.1732726.625e+000
5,4.687500,4.7187504.750000,-0.351215,3.1732723.524e+000
6,4.687500,4.7031254.718750,-0.351215,1.3563331.708e+000
7,4.687500,4.6953134.703125,-0.351215,0.4890978.403e-001
8,4.687500,4.6914064.695313,-0.351215,0.0656024.168e-001
9,4.691406,4.6933594.695313,-0.143638,0.0656022.092e-001
10,4.693359,4.6943364.695313,-0.039226,0.0656021.048e-001
11,4.693359,4.6938484.694336,-0.039226,0.0131365.236e-002
12,4.693848,4.6940924.694336,-0.013058,0.0131362.619e-002
13,4.693848,4.6939704.694092,-0.013058,0.0000361.309e-002
14,4.693970,4.6940314.694092,-0.006512,0.0000366.548e-003
15,4.694031,4.6940614.694092,-0.003238,0.0000363.274e-003
16,4.694061,4.6940774.694092,-0.001601,0.0000361.637e-003
17,4.694077,4.6940844.694092,-0.000783,0.0000368.186e-004
18,4.694084,4.6940884.694092,-0.000374,0.0000364.093e-004
19,4.694088,4.6940904.694092,-0.000169,0.0000362.046e-004
20,4.694090,4.6940914.694092,-0.000067,0.0000361.023e-004
21,4.694091,4.6940914.694092,-0.000016,0.0000365.116e-005
Root=4.694091
1,7.000000,7.5000008.000000,414.377449,-215.8647686.302e+002
2,7.500000,7.7500008.000000,314.365774,-215.8647685.302e+002
3,7.750000,7.8750008.000000,121.483081,-215.8647683.373e+002
4,7.750000,7.8125007.875000,121.483081,-26.6443311.481e+002
5,7.812500,7.8437507.875000,52.242111,-26.6443317.889e+001
6,7.843750,7.8593757.875000,14.043821,-26.6443314.069e+001
7,7.843750,7.8515637.859375,14.043821,-5.9841102.003e+001
8,7.851563,7.8554697.859375,4.108278,-5.9841101.009e+001
9,7.851563,7.8535167.855469,4.10
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