第一次试验20114930陈颖

1、重庆大学学生实验报告实验课程名称_数学实验_开课实验室_DS1404_学院2011年级 自动化 专业班01班学生姓名陈颖 学 号20114930开课时间_至_学年第_学期总成绩教师签名数学与统计学院制开课学院、实验室：自动化、DS1404实验时间：2013年3月12日课程名称数学实验实验项目名称基础实验实验项目类型验证演示综合设计其他指导教师温罗生成 绩基础实验一、实验内容1回忆你所学过的数学函数，并给出x=3.56时以下函数的值.sign(x), xa(a =3),sin( x),cos( x), tan(x2),2tan(x), ax(a 二 3),ex,ln( x),log3x,x,ar

2、csin(x),6&,2x2x ：sinxMlnx=3.56;a=3;y1=sig n(x)y2=xAay3=s in(x)y4=cos(x)y5=ta n(:乂人2)y6=2*ta n(x)y7=aAxy8=exp(x)y9=log(x)y10=log(x)/log(3)y11= floor(x)y12=as in(x)y13=xA(1/6)y14=sqrt(2*xA2+4*x/(log(x+exp(x)*si n(x)/(2*xA2)结果：y1 =1；y2 =45.1180；y3 =-0.4063；y4 =-0.9137；y5 =0.1076；y6 =0.8893；y7 =49.9

3、519y8 =35.1632；y9 =1.2698；y10 =1.1558；y11 =3；y12 =1.5708 - 1.9426i；y13 =1.2357；y14 =6.19062.利用帮助了解向量函数max, min, sum, mean, sort, length，矩阵函数rand, size的功能和用法。操作步骤：先用函数rand生成一个10X15的矩阵，再使用上面提到的函数，看看产生什么样的输出。程序:2x2A=ra nd(10,15)Amax=max(A)Ami n=min(A)Asum=sum(A)Amea n=mea n(A)Asort=sort(A)Ale ngth=le n

4、gth(A)结果：Colu mns 1 through 130.68200.51860.39090.43170.87970.09420.65440.42350.04240.97300.83140.01550.8178 0.5985 0.4076 0.09080.07140.64900.80340.98410.26070.47090.82000.26650.5216 0.8003 0.06050.16720.59440.69590.71840.15370.09670.45380.39930.10620.0225 0.6999 0.9686 0.28100.81810.43240.52690.37

5、240.42530.63850.53130.44010.8175 0.8253 0.41680.19810.31270.03360.32510.52710.72240.08350.65690.48970.16150.06880.10560.45740.1499 0.13320.62800.33950.17880.31960.61100.87540.65960.17340.29200.9516Colu mns 14 through 150.95770.9160Amin =Colu mns 1 through 130.04240.08350.06050.01550.05270.03260.1564

6、0.12060.1078 0.0225 0.0336 0.1056 0.09080.4229 0.5309 0.77880.5181Colu mns 14 through 150.94360.22400.63770.66780.95770.84440.24070.34450.67610.78050.28910.67530.67180.00670.69510.60220.06800.38680.25480.91600.92030.70110.56120.37630.29040.05270.66630.88190.19090.61710.73790.53910.66920.42830.26530.

7、26910.69810.19040.48200.82440.42280.66650.36890.12060.98270.54790.17810.46070.58950.73020.94270.12800.98160.22620.34390.41770.99910.15640.38460.58410.98310.17110.85550.58300.10780.30150.03260.64480.25180.9063Amax =Colu mns 1 through 130.81810.97300.83140.98410.98310.99910.98160.58950.98270.87970.699

8、90.96860.8754Colu mns 14 through 150.06800.0067Asum =Colu mns 1 through 134.58185.04245.00594.05595.59574.78015.77063.63325.65214.07614.1509 5.92094.0335Colu mns 14 through 155.43475.4482Amea n =Colu mns 1 through 150.45820.50420.50060.40560.55960.47800.57710.36330.56520.40760.41510.59210.40330.5435

9、0.5448Asort =Colu mns 1 through 130.04240.08350.06050.01550.05270.03260.15640.12060.1078 0.0225 0.03360.10560.09080.07140.13320.29200.10620.26910.12800.19040.19090.2653 0.1615 0.06880.32510.15370.09670.17340.39090.16720.30150.17110.36890.22620.29040.17880.09420.40760.26650.14990.43240.39930.19810.41

10、770.17810.46070.25180.34390.2607 0.3196 0.53130.28100.5216 0.4538 0.41680.33950.42280.53910.56120.37630.58410.31270.47090.61100.42350.6596 0.5186 0.52690.37240.54790.66630.64480.38460.61710.42290.53090.65440.44010.6820 0.6490 0.62800.43170.73790.66650.66920.42830.73020.42530.59850.71840.45740.72240.

11、80030.65690.48970.92030.69810.85550.48200.82440.59440.63850.77880.51810.81750.82530.80340.95160.94270.70110.88190.58300.90630.8178 0.6959 0.82000.52710.81810.97300.83140.98410.98310.99910.98160.58950.98270.87970.69990.96860.8754Colu mns 14 through 150.06800.00670.24070.22400.25480.34450.28910.38680.

12、63770.60220.6718 0.6678 0.6761 0.67530.69510.78050.94360.84440.95770.9160Ale ngth =153设有分块矩阵A二E332其中E,R,O,S分别为单位阵、随机阵、零阵和对角阵，试编写一个命令。2 3S2 2M文件，计算验证A2=ER+RSL提示：先产生一个矩阵A，计算出A2;另一方面，计算矩阵!0s2一E R RS，比较结果是否一致。一0S程序：R=ra nd(1,2);B=ra nd(3,2);C=diag(R);A=eye(3) B;zeros(2,3) C;A1=AA2A2=eye (3) B+B*C;zeros(

13、2,3)。人2if (A仁=A2) the an swer is rightelse the an swer is wrongen d;结果：A1 =1.0000000.74760.401101.000000.49040.7142001.00000.15820.2255000 10.001300000 0.0309A2 =1.0000000.74760.401101.000000.49040.7142001.00000.15820.2255000 10.001300000 0.0309ans = the an swer is right4.4.回忆线性代数的一些基本概念以及基本的运算，查找可以

14、使用哪些命令实现(1)方阵的行列式矩阵的秩(3)方阵的幕方阵的逆阵向量组的秩(5)向量组的正交化(7)方阵的特征向量和特征值分别举出至少一个例子说明其用法A=ra nd(4,3);B=A(1:3,:);C=A(1:1,:);a1=1 2 3;a2=2 3 4;a3=3 4 5;han glieshi=det(B)juzhe nzhi=ra nk(A)fan gzhe nm i=24Bfan gzhe nni=pin v(B)xia nglia ngzuzhi=ra nk(a1;a2;a3)Q,R=qr(a1;a2;a3);Qtezhe ngzhi=eig(B)P,D=eig(B)；P结果：ha

15、n glieshi = :0.3734juzhe nzhi =3fan gzhe nmi =1.68331.85431.10901.19341.94441.19541.42011.46131.7909fan gzhe nni =1.7824 -1.78700.2308-0.22541.4891-0.4161-0.92600.10621.3214xia nglia ngzuzhi =2Q =-0.26730.87290.4082-0.53450.2182-0.8165-0.8018-0.43640.4082tezhe ngzhi =1.64810.4516 + 0.1505i0.4516 - 0

16、.1505iP =0.57380.5016 - 0.4656i 0.5016 + 0.4656i0.46460.0251 + 0.2414i 0.0251 - 0.2414i0.6745-0.6875-0.68755.在同一个坐标下作出y1=1+x, y2=1+x+x2/2, y3=1+x+x2/2!+x3/3!, y4=ex，这四，说明Taylor公条曲线的图形式说明了什么问题。程序：x=li nspace(-5,5,100);y1=1+x;y2=1+x+x92/2;y3=1+x+x.A2/2+x.A3/factorial(3);y4=exp(x);plot(x,y1, r ,x,y2, b

17、 ,x,y3, g ,x,y4, k) text(4.5,0,1+x);text(4,16,1+x+x2/2,);text(3.5,28,1+x+x2/2!+x3/3!);text(4,80, exp(x);结果：6.用subplot分别在不同的坐标系下作出四条曲线: 丄21）概率曲线y二e2） 四叶玫瑰线：=sin2 V； （polar函数）3t31 +t33） 叶形线2| 3ty二-y1 t3（4）曳物线程序:x=-5:0.1:5; thetas=0:0.01:2*pi; t=1:0.1:5;x =l n1 - 1 - y23d-y2y仁exp(-x.A2);yy2=s in (theta

18、s); x3=3*t心+L3); y3=3*t.A2./(1+t.A3); y=linspace(-1,1,100);x4=log(1+sqrt(1-y.A2)./y-sqrt(1-y.A2);x5=log(1-sqrt(1-y.A2)./y+sqrt(1-y.A2);subplot(2,2,1),plot(x,y1),title( subplot(2,2,2),polar(thetas,y2),title( subplot(2,2,3),plot(x3,y3),title( subplot(2,2,4),plot(x4,y,x5,y),title( axis(-50 50 -1 1)7.作出

19、曲面1)Z =sin(r x2y2)x = (1 cos u )cos v,2)y = (1 cosu)sin v,z 二 sin u,程序：1、x=li nspace(-10,10,100); y=x;x y=meshgrid(x,y);z=si n(pi*sqrt(x.A2+y.A2); mesh(x,y,z)o-50.5052y1=exp(-x.)21.510.50.51x3=3*t./(1+t.3),y3=3*t.2./(1+t.3)1.5y1=exp(-x.A2)y2=si n(thetas) )x3=3*t./(1+t.A3),y3=3*t.A2./(1+t.A3)曳物线)u (0

20、,2 二)v (0,2-)2、u=li nspace(0,2*pi,100); v=li nspace(0,2*pi,100);u v=meshgrid(u,v);X=(1+C0S(U).*C0S(V)； y=(1+cos(u).*si n(v); z=s in( u);mesh(x,y,z)8.建立一个命令M-文件：求所有的 水仙花数”，所谓水仙花数”是指一个三位数, 和等于该数本身。例如，153是一个水仙花数，因为153=13+53+33。for bai=1:9for shi=0:9for ge=0:9shu 1=bai*100+shi*10+ge;shu2=baiA3+shL3+geA3

21、;r.1-I5:50-5-5-10-1010.50-0.5-11010其各位数字的立方H1100110.50-0.5-1345if (shu 1=shu2)vpa(shul)en d;en d;en d;en d;结果：ans =153.0ans =370.0ans =371.0补充题目：通过查找资料完成下面的图形：(1)要求为：有坐标刻度，有坐标说明(包括希腊字母的)，有in set图形，有lege nd。figure;t=lin space(0,5,100);t1=li nspace(0,5,100);y仁si n(t);y2=cos(t);y3=t;plot(t,y1, r*,t,y2,

22、 go );axis( equal);set(xlabel( e ), FontSize,12, Color ,r);set(ylabel(Lyapunov exponent), FontSize,12, Color , g);legend(入1=sin( e ),入2=cos( e );axes( Position,0.18,0.8,0.3,0.1);plot(t1,y3);set(gcf, Color , w);02461.5七入1=s in( e)入2=cos( s.)1 5 0 5 1 5 L - - - o o 1- -tnenopxe vonugy545ans =407.01O61

23、041O-31O2345(2)计算一个弹性小球，在高度h自由下落，每次和地面接触时能量损失20%，小于1毫米时认为不再弹起。计算物体运动的轨迹，并作出模拟的动画。程序：function y=dow n(h)g=9.8; time=sqrt(2*h/g);for t=0:0.1:timey=h-0.5*g*t*t;plot(0,y, o , markersize ,10, markerfacecolor ，r);axis(-1,1,0,10);pause(0.1);en d;function y=up(h)g=9.8; time=sqrt(2*h/g);for t=time:0.1:0y=h-0

24、.5*g*t*t;plot(0,y, o , markersize ,10, markerfacecolor , r);axis(-1,1,0,10);pause(0.1);en d;clear;flag=0;h=9;while (h0.001) if (flag=0)dow n( h);flag=rem(flag+1,2);h=h*0.8;elseup(h*0.8);flag=rem(flag+1,2);h=h*0.8;en d;en d;应用实验（或综合实验）一、实验内容某医院住院部病床非常紧张，导致许多需要手术的病人因为没有住院床位而排队等候，也导致等待手术的病人越积越多。以该院眼科为例

25、，门诊每天开放，住院部共有病床79张。该医院眼科手术主要分四大类：白内障、视网膜疾病、青光眼和外伤。表1.2中给出了2008年7月13日至2008年9月11日这段时间里各类病人的情况。医院希望通过合理安排病床、增设病床等措施提高自身服务水平。为此，首先要对当前病人门诊、 手术和住院的情况进行统计分析。1） 给出各类病人从第1次手术到出院的住院天数的平均值、标准差和分布规律，并作出第1次手术到出院的住院天数频数的直方图。2） 求出各类病人从门诊到入院的平均等待时间，从入院到第1次手术的平均等待时间，平均住院 时间；二、实验结果及分析由所给数据整理得：白内障第一次手术刀出院天数的平均值5标准差1.215369978门诊到入院的平均等待时间12.68306011