Matlab数学实验报告05

数学实验报告实验名称 Matlab高等数学相关运算 学 院 机械工程学院 专业班级工业101 姓 名于洋 学 号41040318 2011年10月26日一、 【实验目的】掌握Matlab高等数学相关的运算；初步运用概率统计相关的功能。二、 【实验任务】1、在钢线碳含量对于电阻效应的研究中，得到以下数据。分别用一次，三次，五次多项式拟合曲线来拟合这组数据并画出图形。碳含量x0.100.300.400.550.700.800.95电阻 y1518192122.623.8262、已知在某实验中测得某质点的位移s和速度v随时间t变化如下：t00.51.01.52.02.53.0v00.47940.84150.99750.90930.59850.1411s11.522.533.543、由方程所确定的隐函数的导数。4、求下列定积分：I II III 5、用三种方法求下列积分的数值。I IIIII6、绘制下列数组的频数直方图：6.8,29.6,33.6,35.7,36.9,45.2,54.8,65.8,43.4,53.8,63.7,69.9,70.7,79.5,97.9,139.4,157.07、若样本为85,86,78,90,96,82,80,74，求样本均值、标准差、中位数、极差和方差。三、 【实验程序】1、 x=0.10,0.30,0.40,0.55,0.70,0.80,0.95; y=15,18,19,21,22.6,23.8,26 p1=polyfit(x,y,1); p3=polyfit(x,y,3); p5=polyfit(x,y,5); disp(1),f1=poly2str(p1,x)； x1=0.10,0.30,0.40,0.55,0.70,0.80,0.95; y1=polyval(p1,x1); y3=polyval(p3,x1); y5=polyval(p5,x1); plot(x1,y1,-,x1,y3,k-,x1,y5); legend(一次拟合,三次拟合,五次拟合)2、t=0,0.5,1.0,1.5,2.0,2.5,3.0;v=0,0.4794,0.8415,0.9975,0.9093,0.5985,0.1411;s=1,1.5,2,2.5,3,3.5,4;pvt=polyfit(t,v,1);pst=polyfit(t,s,1);psv=polyfit(v,s,1); t1=0,0.5,1.0,1.5,2.0,2.5,3.0;v1=0,0.4794,0.8415,0.9975,0.9093,0.5985,0.1411; y1=polyval(pvt,t1); y2=polyval(pst,t1); y3=polyval(psv,v1); polt(t1,y1,-,t1,y2,k-,v1,y3)； plot(t1,y1,-,t1,y2,k-,v1,y3); legend(v-t,s-t,s=v)3、 syms x y F=exp(y)+x*y-exp(1); dF_dx=diff(F,x); dF_dy=diff(F,y); pretty(-dF_dx/dF_dy)4、I syms x int(x/(1+sqrt(1+x),1/2,2)II syms x int(sin(x)7,0,pi/2)III syms x int(1-x2)6,1,0)5、I x=0:0.01:3; y=exp(-0.5*x)*sin(x+pi/6)； y=exp(-0.5*x).*sin(x+pi/6); t=length(x); s1=sum(y(1:(t-1)*0.01; s2=sum(y(2:t)*0.01; s3=trapz(x,y); s4=quad(jifen,0,3)II clear all x=0:0.01:2.5; y=exp(-x); t=length(x); s1=sum(y(1:(t-1)*0.01; s2=sum(y(2:t)*0.01; s3=trapz(x,y); s4=quad(jifen,1,2.5)；III x=0:0.01:2; y=exp(3*x).*sin(2*x); t=length(x); s1=sum(y(1:(t-1)*0.01; s2=sum(y(2:t)*0.01; s3=trapz(x,y); s4=quad(jifen,0,2)6、 load A.txt hist(A,10) hist(A,20) hist(A,6)7、 mean(A) median(A) range(A) var(A) std(A)四、 【实验结果】1、1f1 = 12.5503 x + 13.9584 disp(3),f3=poly2str(p3,x)3f3 = 8.9254 x3 - 14.6277 x2 + 19.2834 x + 13.2132 disp(5),f5=poly2str(p5,x)5f5 = 146.1598 x5 - 386.879 x4 + 385.5329 x3 - 178.8558 x2 + 49.9448 x + 11.44812、 disp(v-t),f1=poly2str(pvt,t)v-tf1 = 0.052093 t + 0.48862 disp(s-t),f2=poly2str(pst,t)s-tf2 = 1 t + 1 disp(s-v),f3=poly2str(psv,v)s-vf3 = 0.41 v + 2.26763、 y - - x + exp(y)4、Ians = - (3(1/2)*(2(1/2) - 4)/2 - 3/2IIans = 16/35IIIans = -1024/30035、Is1 = 1.0946 s2=sum(y(2:t)*0.01s2 = 1.0888 s3=trapz(x,y)s3 =1.0917s4 =1.0917IIs4 = 0.2858 s3=trapz(x,y)s3 = 0.9179 s2=sum(y(2:t)*0.01s2 = 0.9133 s1=sum(y(1:(t-1)*0.01s1 =0.9225IIIs1 = -28.2201 s2=sum(y(2:t)*0.01s2 = -31.2733 s3=trapz(x,