数学实验报告

1、数学实验报告信息15 杨曲2110502105l 第一回1. Feigenbaum在做实验的时候，对超越函数y=r*sin(pi*x)(r为非负实数)进行了分叉与混沌的研究，试用迭代格式x(i)=r*sin(pi*x(i-1),做出相应的Feigenbaum图。思路：用axis，grid绘制网状坐标轴，以0.005对r进行微小改变，用fprintf指令绘图，并hold on观察图形即可。程序： hold onaxis(0.5,1,0,1);gridfor r=0.5:0.005:1 x=0.1; for i=2:150 x(i)=r*sin(pi*x(i-1); end pause(0.001

2、) fprintf(r=%.3fn,r) for i=101:150 plot(r,x(i),k.); endend结果：2. 求非线性方程组2x(1)2-x(1)*x(2)-5*x(1)+1;x(1)+3lgx(1)-x(2)2的解，初值如下：(1)x0=1.4,-1.5;(2)x0=3.7,2.7思路：先在文件编辑器中写下函数文件，再再命令框中使用求解命令。程序：函数文件function f=group1(x)f=2*x(1)2-x(1)*x(2)-5*x(1)+1;x(1)+3*log(x(1)-x(2)2命令框中：x,fval=fsolve(group1,1.4,-1.5)结果：x =

3、 1.3735 -1.5250fval = 1.0e-006 * 0.0313 -0.2032命令框中：x,fval=fsolve(group1,3.7,2.7)结果：x = 3.7568 2.7798fval = 1.0e-012 * 0.1066 -0.4512l 第二回、1. 第一题：某工厂利用甲乙两种原料生产A1，A2，A3三种商品，每月可供应的原料数量（单位：t），每万件产品所需各种原料的数量及每万件产品的价格如表1-1所示：原料每万件产品所需原料（t）每月原料供应量 （t）A1A2A3甲431 180 乙263 200价格（万元/万件）1254试制定每月的最优生产计划，使得总收益最

4、大。问题分析：该问题为最优化问题，设每月生产A1产品件，A2产品件，A3产品,则目标函数为min Z=-(12*x1+5*x2+4*x3),约束条件为： 产品原料A1A2A3供应甲431180乙263200价格1254s.t. 利 用MATLAB软件求解该线性规划问题，将利润最大问题化为求其负值的最小值问题程序如下：c=-12,-5,-4;a=4,3,1;2,6,3;b=180;200;vlb=0;0;0;vub=;x=linprog(c,a,b,vlb,vub)运行结果 Optimization terminated successfully.x = 34.0000 0.0000 44.00

5、00则由求解结果可知:每月生产A1产品34件，生产A2产品0件，生产A3产品44件时，可使总收益最大。2. 第二题：设有三种证券S1,S2,S3,期望收益率分别为10%，15%和40%，风险分别是10%，5%和20%，假定投资总风险用最大一种投资股票的风险来度量，且同期银行存款利率为=5%，无风险，为投资者建议一种投资策略(投资比例)，使其尽可能获得最大收益。问题分析：该问题为一线性加权问题，分析如下（1） 条件假设：假设投资三种证券和银行存款的资金分别为,总投资金M，并设三种证券之间是相互独立的, 设总风险度为a，且在投资的同一时期内各证券的收益率及风险均为定值，不受意外因素影响。（2） 建

6、立模型：净收益尽可能大：（为证券Si的期望收益率）总体风险尽可能小：(为证券Si的风险), i=0,1,2,3(3)模型求解：模型简化为：, i=0,1,2,3其中, i=0,1,2,3将题中数据带入模型得0.10.050.2, i=0,1,2,3如何给定风险度并没有一定的准则，不同的投资者承受风险的能力不同，本实验从a=0开始，以步长编写下面的程序进行循环搜索。程序如下：a=0;while(1.3-a)1 c=-0.05,0.10,0.15,0.40; aeq=1,1,1,1; beq=1; A=0,0,0,0;0,0.1,0,0;0,0,0.05,0;0,0,0,0.2; b=a;a;a;

7、a; vlb=0,0,0,0; vub=; x,val=linprog(c,A,b,aeq,beq,vlb,vub); a; x=x; Q=-val; fprintf(a=%5.5f,x1=%5.5f,x2=%5.5f,x3=%5.5f,x4=%5.5f,Q=%5.5f,a,x,Q) plot(a,Q,.) axis(0,0.3,0,0.5) hold on a=a+0.003;endxlabel(a),ylabel(Q)风险收益曲线：运行结果：a=0.0000 x1=1.0000 x2=0.0000 x3=0.0000 x4=0.0000 Q=0.0500 a=0.0030 x1=0.895

8、0 x2=0.0300 x3=0.0600 x4=0.0150 Q=0.0627 a=0.0060 x1=0.7900 x2=0.0600 x3=0.1200 x4=0.0300 Q=0.0755 a=0.0090 x1=0.6850 x2=0.0900 x3=0.1800 x4=0.0450 Q=0.0882 a=0.0120 x1=0.5800 x2=0.1200 x3=0.2400 x4=0.0600 Q=0.1010 a=0.0150 x1=0.4750 x2=0.1500 x3=0.3000 x4=0.0750 Q=0.1137 a=0.0180 x1=0.3700 x2=0.180

9、0 x3=0.3600 x4=0.0900 Q=0.1265 a=0.0210 x1=0.2650 x2=0.2100 x3=0.4200 x4=0.1050 Q=0.1392 a=0.0240 x1=0.1600 x2=0.2400 x3=0.4800 x4=0.1200 Q=0.1520 a=0.0270 x1=0.0550 x2=0.2700 x3=0.5400 x4=0.1350 Q=0.1647 a=0.0300 x1=0.0000 x2=0.2500 x3=0.6000 x4=0.1500 Q=0.1750 a=0.0330 x1=0.0000 x2=0.1750 x3=0.660

10、0 x4=0.1650 Q=0.1825 a=0.0360 x1=0.0000 x2=0.1000 x3=0.7200 x4=0.1800 Q=0.1900 a=0.0390 x1=0.0000 x2=0.0250 x3=0.7800 x4=0.1950 Q=0.1975 a=0.0420 x1=0.0000 x2=0.0000 x3=0.7900 x4=0.2100 Q=0.2025 a=0.0450 x1=0.0000 x2=0.0000 x3=0.7750 x4=0.2250 Q=0.2062 a=0.0480 x1=0.0000 x2=0.0000 x3=0.7600 x4=0.240

11、0 Q=0.2100 a=0.0510 x1=0.0000 x2=0.0000 x3=0.7450 x4=0.2550 Q=0.2137 a=0.0540 x1=0.0000 x2=0.0000 x3=0.7300 x4=0.2700 Q=0.2175 a=0.0570 x1=0.0000 x2=0.0000 x3=0.7150 x4=0.2850 Q=0.2212 a=0.0600 x1=0.0000 x2=0.0000 x3=0.7000 x4=0.3000 Q=0.2250 a=0.0630 x1=0.0000 x2=0.0000 x3=0.6850 x4=0.3150 Q=0.2287

12、 a=0.0660 x1=0.0000 x2=0.0000 x3=0.6700 x4=0.3300 Q=0.2325 a=0.0690 x1=0.0000 x2=0.0000 x3=0.6550 x4=0.3450 Q=0.2362 a=0.0720 x1=0.0000 x2=0.0000 x3=0.6400 x4=0.3600 Q=0.2400 a=0.0750 x1=0.0000 x2=0.0000 x3=0.6250 x4=0.3750 Q=0.2437 a=0.0780 x1=0.0000 x2=0.0000 x3=0.6100 x4=0.3900 Q=0.2475 a=0.0810

13、x1=0.0000 x2=0.0000 x3=0.5950 x4=0.4050 Q=0.2512 a=0.0840 x1=0.0000 x2=0.0000 x3=0.5800 x4=0.4200 Q=0.2550 a=0.0870 x1=0.0000 x2=0.0000 x3=0.5650 x4=0.4350 Q=0.2587 a=0.0900 x1=0.0000 x2=0.0000 x3=0.5500 x4=0.4500 Q=0.2625 a=0.0930 x1=0.0000 x2=0.0000 x3=0.5350 x4=0.4650 Q=0.2662 a=0.0960 x1=0.0000

14、x2=0.0000 x3=0.5200 x4=0.4800 Q=0.2700 a=0.0990 x1=0.0000 x2=0.0000 x3=0.5050 x4=0.4950 Q=0.2737 a=0.1020 x1=0.0000 x2=0.0000 x3=0.4900 x4=0.5100 Q=0.2775 a=0.1050 x1=0.0000 x2=0.0000 x3=0.4750 x4=0.5250 Q=0.2812 a=0.1080 x1=0.0000 x2=0.0000 x3=0.4600 x4=0.5400 Q=0.2850 a=0.1110 x1=0.0000 x2=0.0000

15、x3=0.4450 x4=0.5550 Q=0.2887 a=0.1140 x1=0.0000 x2=0.0000 x3=0.4300 x4=0.5700 Q=0.2925 a=0.1170 x1=0.0000 x2=0.0000 x3=0.4150 x4=0.5850 Q=0.2962 a=0.1200 x1=0.0000 x2=0.0000 x3=0.4000 x4=0.6000 Q=0.3000 a=0.1230 x1=0.0000 x2=0.0000 x3=0.3850 x4=0.6150 Q=0.3037 a=0.1260 x1=0.0000 x2=0.0000 x3=0.3700

16、x4=0.6300 Q=0.3075 a=0.1290 x1=0.0000 x2=0.0000 x3=0.3550 x4=0.6450 Q=0.3112 a=0.1320 x1=0.0000 x2=0.0000 x3=0.3400 x4=0.6600 Q=0.3150 a=0.1350 x1=0.0000 x2=0.0000 x3=0.3250 x4=0.6750 Q=0.3187 a=0.1380 x1=0.0000 x2=0.0000 x3=0.3100 x4=0.6900 Q=0.3225 a=0.1410 x1=0.0000 x2=0.0000 x3=0.2950 x4=0.7050

17、Q=0.3262 a=0.1440 x1=0.0000 x2=0.0000 x3=0.2800 x4=0.7200 Q=0.3300 a=0.1470 x1=0.0000 x2=0.0000 x3=0.2650 x4=0.7350 Q=0.3337 a=0.1500 x1=0.0000 x2=0.0000 x3=0.2500 x4=0.7500 Q=0.3375 a=0.1530 x1=0.0000 x2=0.0000 x3=0.2350 x4=0.7650 Q=0.3412 a=0.1560 x1=0.0000 x2=0.0000 x3=0.2200 x4=0.7800 Q=0.3450 a

18、=0.1590 x1=0.0000 x2=0.0000 x3=0.2050 x4=0.7950 Q=0.3487 a=0.1620 x1=0.0000 x2=0.0000 x3=0.1900 x4=0.8100 Q=0.3525 a=0.1650 x1=0.0000 x2=0.0000 x3=0.1750 x4=0.8250 Q=0.3562 a=0.1680 x1=0.0000 x2=0.0000 x3=0.1600 x4=0.8400 Q=0.3600 a=0.1710 x1=0.0000 x2=0.0000 x3=0.1450 x4=0.8550 Q=0.3637 a=0.1740 x1

19、=0.0000 x2=0.0000 x3=0.1300 x4=0.8700 Q=0.3675 a=0.1770 x1=0.0000 x2=0.0000 x3=0.1150 x4=0.8850 Q=0.3712 a=0.1800 x1=0.0000 x2=0.0000 x3=0.1000 x4=0.9000 Q=0.3750 a=0.1830 x1=0.0000 x2=0.0000 x3=0.0850 x4=0.9150 Q=0.3787 a=0.1860 x1=0.0000 x2=0.0000 x3=0.0700 x4=0.9300 Q=0.3825 a=0.1890 x1=0.0000 x2

20、=0.0000 x3=0.0550 x4=0.9450 Q=0.3862 a=0.1920 x1=0.0000 x2=0.0000 x3=0.0400 x4=0.9600 Q=0.3900 a=0.1950 x1=0.0000 x2=0.0000 x3=0.0250 x4=0.9750 Q=0.3937 a=0.1980 x1=0.0000 x2=0.0000 x3=0.0100 x4=0.9900 Q=0.3975 a=0.2010 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2040 x1=0.0000 x2=0.0000 x3

21、=0.0000 x4=1.0000 Q=0.4000 a=0.2070 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2100 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2130 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2160 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2190 x1=0.0000 x2=0.0000 x3=0.0000 x4

22、=1.0000 Q=0.4000 a=0.2220 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2250 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2280 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2310 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2340 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=

23、0.4000 a=0.2370 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2400 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2430 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2460 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2490 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0

24、.2520 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2550 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2580 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2610 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2640 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2670 x1=0

25、.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2700 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2730 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2760 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2790 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2820 x1=0.0000 x2=0

26、.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2850 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2880 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2910 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2940 x1=0.0000 x2=0.0000 x3=0.0000 x4=1.0000 Q=0.4000 a=0.2970 x1=0.0000 x2=0.0000 x3=0

27、.0000 x4=1.0000 Q=0.4000 （4）结果分析：从执行结果以及上图我们可得以下结论：1） 风险大，收益也大；2） 当投资越分散时，投资者承担的风险越小，这与题意一致，即冒险的投资者会出现集中投资的情况，保守的投资者则会尽量分散投资；3） 上图曲线表示当风险水平给定时能获得的最大收益率；4） 分别在a=0.2010和a=0.0390附近有两个转折点，在a=0.0390点左边，显示风险增加时，利润增长较快；在a=0.0390点右边，且在a=0.2010点左边风险增加时，利润增长较缓慢；在a=0.2010点右边风险增加时，利润无变化。对风险厌恶型投资者来说，应该选择曲线左边的转折点

28、a=0.0390点为最优投资组合，约是Q=19.75%，投资方案如下表所示：风险度收益0.03900.19750.02000.28000.56000.1400对风险喜好型投资者来说，应该选择曲线左边的转折点a=0.0390点为最优投资组合，约是Q=40.00%，投资方案如下表所示：风险度收益0.20100.40000.00000.02500.78000.19503.第三题：某单位有300万元可用于投资，共有6个项目可供选择，其投资额分别为40，60，80，50，90，70（万元），预计三年可获利润分别为10，12，15，11，16，13（万元），试确定一种投资可使得三年获得的利润最大。问题分析

29、：投资方式的挑选要满足在总投资额小于300万元的前提下，取得最大收益值，即可视为一个0-1规划问题。 1 ，第j种方式被选择 令 0 ，第j种方式未被选该问题的数学模型是： maxZ=实验程序：k=1;zl=10,12,15,11,16,13;sy=40,60,80,50,90,70;for g1=0:1 for g2=0:1 for g3=0:1 for g4=0:1 for g5=0:1 for g6=0:1 fa=g1,g2,g3,g4,g5,g6; if sy*fa=300 fazl(k,1:6)=fa; k=k+1; end end end end end endendfalr=fa

30、jz*zl;f,i=max(falr)xuanfa=fazl(i,1:6)fatz=sy*xuanfa运行结果：f = 61i = 58xuanfa = 1 1 1 1 0 1结果分析：利用01规划得，此公司可选择除第五种外的投资类型从而获得最大利润，最大利润为61万元。l 第三回1. 用以下公式计算值n=input(请输入n的值：);s=0;sa=0;sb=0;sc=0;sd=0;digits(22);for k=1:n s=s+4*(-1)(k+1)/(2*k-1); sa=sa+1/(2*k-1)2; sb=sb+(-1)(k-1)/k2; sc=sc+(-1)(k-1)/(2*k-1)

31、3; sd=sd+sin(2*k-1)/(2*k-1)3;ends=vpa(s,20)sa=vpa(sqrt(8*sa),20)sb=vpa(sqrt(12*sb),20)sc=vpa(32*sc)(1/3),20)sd=vpa(1+sqrt(1+32*sd)/2,20)一：请输入n的值：100 s = 3.1315929035585536866 sa = 3.1384079670670912421 sb = 3.1414981140356497136 sc = 3.1415925860524653856 sd = 3.1415925997563931560二：请输入n的值：1000000 s

32、 = 3.1415916535897743245 sa = 3.1415923352799697277 sb = 3.1415926535887819249 sc = 3.1415926535897932385 sd = 3.1415926535898179850经上两个实验结果发现，在同一叠加次数下，它们的精度依次递增。再运行上述程序，发现如下情况：其中第一种要精确到第六位换算了1000000次第二种换算了150000次，第三种要精确到第六位换算了近1000次，第4种和第五种约经历100次就能精确到第七位；所以它们逼近速度也依次上升。2.利用蒙特卡洛方法近似计算实验任务2：基于关系式 cs=

33、0;n=input(请输入叠加次数：);for i=1:n a=rand(1,2); if a(2)=sqrt(a(1)2+a(2)2)&(a(3)d) plot(ax,ay,b,bx,by,gh,cx,cy,rp,dx,dy,y*); pause(0.1) hold on t=t+dt; ax=ax+v(1)*dt*(bx-ax)/sqrt(ax-bx)2+(by-ay)2); ay=ay+v(1)*dt*(by-ay)/sqrt(ax-bx)2+(by-ay)2); bx=bx+v(2)*dt*(cx-bx)/sqrt(cx-bx)2+(by-cy)2); by=by+v(2)*dt*(c

34、y-by)/sqrt(cx-bx)2+(by-cy)2); cx=cx+v(3)*dt*(dx-cx)/sqrt(dx-cx)2+(cy-dy)2); cy=cy+v(3)*dt*(dy-cy)/sqrt(dx-cx)2+(cy-dy)2); dx=dx+v(4)*dt*(ax-dx)/sqrt(ax-dx)2+(dy-ay)2); dy=dy+v(4)*dt*(ay-dy)/sqrt(ax-dx)2+(dy-ay)2); plot(ax,ay,bp,bx,by,y*,cx,cy,gO,dx,dy,y); end please input v:100 100 100 100v = 100 10

35、0 100 100 please input v:100 200 344 67v = 100 200 344 67 l 第四回1.练习一 有一形状较为复杂，但表面很光滑的曲面工件，通过科学手段，将其放置于某一空间坐标系下，测得曲面上若干个点的坐标如下：X y-5-4-3-2-1012345-513.6-8.2-14.8-6.61.40-3.81.413.616.80-4-8.2-15.8-7.92.23.800.67.310.10-16.8-3-14.8-7.92.5 5.82.302.75.10-10.1-13.7-2-6.62.25.93.0-0.301.90-5.1-7.3-1.4-11

36、.43.82.3-0.3-0.900-1.7-2.7-0.63.80000000000001-3.80.62.71.7000.90.3-2.3-3.8-1.421.47.35.10-1.700.3-3.1-5.8-2.26.6313.610.10-5.1-2.70-2.3-5.8-2.57.914.8416.80-10.1-7.3-0.60-3.8-2.27.915.88.25016.3-13.6-1.43.80-1.46.614.88.2-13.6程序如下：x=-5:1:5;y=-5:1:5;xb,yb=meshgrid(x,y);zb(1,:)=13.6,-8.2,-14.8,-6.6,1

37、.4,0,-3.8,1.4,13.6,16.8,0;zb(2,:)=-8.2,-15.8,-7.9,2.2,3.8,0,0.6,7.3,10.1,0,-16.8;zb(3,:)=-14.8,-7.,2.5,5.8,2.3,0,2.7,5.1,0,-10.1,-13.7;zb(4,:)=-6.6,2.2,5.9,3.0,-0.3,0,1.9,0,-5.1,-7.3,-1.4;zb(5,:)=1.4,3.8,2.3,-0.3,-0.9,0,0,-1.7,-2.7,-0.6,3.8;zb(6,:)=0,0,0,0,0,0,0,0,0,0,0;zb(7,:)=-3.8,0.6,2.7,1.7,0,0,

38、0.9,0.3,-2.3,-3.8,-1.4;zb(8,:)=1.4,7.3,5.1,0,-1.7,0,0.3,-3.1,-5.8,-2.2,6.6;zb(9,:)=13.6,10.1,0,-5.1,-2.7,0,-2.3,-5.8,-2.5,7.9,14.8;zb(10,:)=16.8,0,-10.1,-7.3,-0.6,0,-3.8,-2.2,7.9,15.8,8.2;zb(11,:)=0,16.3,-13.6,-1.4,3.8,0,-1.4,6.6,14.8,8.2,-13.6;mesh(xb,yb,zb)xc=-5:0.25:5;yc=-5:0.25:5;xcb,ycb=meshgri

39、d(xc,yc);zcb=interp2(xb,yb,zb,xcb,ycb);mesh(xcb,ycb,zcb)（1）（2）所有点的竖坐标：zcb =Columns 1 through 613.6000 8.1500 2.7000 -2.7500 -8.2000 -9.85008.1500 3.5875 -0.9750 -5.5375 -10.1000 -10.84382.7000 -0.9750 -4.6500 -8.3250 -12.0000 -11.8375-2.7500 -5.5375 -8.3250 -11.1125 -13.9000 -12.8313-8.2000 -10.1000

40、 -12.0000 -13.9000 -15.8000 -13.8250-9.8500 -10.7875 -11.7250 -12.6625 -13.6000 -11.5250-11.5000 -11.4750 -11.4500 -11.4250 -11.4000 -9.2250-13.1500 -12.1625 -11.1750 -10.1875 -9.2000 -6.9250-14.8000 -12.8500 -10.9000 -8.9500 -7.0000 -4.6250-12.7500 -10.7375 -8.7250 -6.7125 -4.7000 -2.6875-10.7000 -

41、8.6250 -6.5500 -4.4750 -2.4000 -0.7500-8.6500 -6.5125 -4.3750 -2.2375 -0.1000 1.1875-6.6000 -4.4000 -2.2000 0.0000 2.2000 3.1250-4.6000 -2.8000 -1.0000 0.8000 2.6000 3.2000-2.6000 -1.2000 0.2000 1.6000 3.0000 3.2750-0.6000 0.4000 1.4000 2.4000 3.4000 3.35001.4000 2.0000 2.6000 3.2000 3.8000 3.42501.

42、0500 1.5000 1.9500 2.4000 2.8500 2.56870.7000 1.0000 1.3000 1.6000 1.9000 1.71250.3500 0.5000 0.6500 0.8000 0.9500 0.85620 0 0 0 0 0-0.9500 -0.6750 -0.4000 -0.1250 0.1500 0.2813-1.9000 -1.3500 -0.8000 -0.2500 0.3000 0.5625-2.8500 -2.0250 -1.2000 -0.3750 0.4500 0.8438-3.8000 -2.7000 -1.6000 -0.5000 0.6000 1.1250-2.5000 -1.3062 -0.1125 1.0812 2.2750 2.5313-1.2000 0.0875 1.3750 2.6625 3.9500 3.93750.1000 1.4813 2.8625 4.2438 5.6250 5.34381.4000 2.8750 4.3500 5.8250 7.3000 6.75004.4500 5.3375 6.2250 7.1125 8.0000 6.95627.5000 7.8000 8.1000 8.4000 8.7000 7.162510