大学高数项目作业.doc

大连东软信息学院课程（单元）项目研究报告系别班级成绩姓名项目名称 利用Mathmatic解决关于多元函数的实际问题提交日期2011年6月3日项目内容根据老师给出的题目和数据，利用mathmatic软件解决实际问题，利用Mathmatic软件，首先使用“多元函数你和指令Fit”拟合函数，然后，在使用“多元函数绘图指令Plot3DListplot”画出图像，在求出偏导，从人求出最终答案。并总结项目目的 为了能够更好地讲数学知识运用于解决实际问题上，将数学更好地与实际生活联系起来，同时也为了让我们对数学知识更深刻的了解，和对数学软件Mathmatic的运用。并且能够在团队共同的努力下完成目标，增加了小组成员的凝聚力，增加团队能力。研究过程包括问题的分析，用到的变量符号的说明，研究的详细步骤和过程，研究的结论，对结论优劣的简单分析，改进方向, 以及完成本项目对自己学习本课程有哪些促进等. 1）首先我们探讨了该怎样进行这个实验，数据调查，分析实验步骤。（2）研究课题有了定向，小组成员就要分工了，对数据分析，处理。（3）使用Mathmatic解决问题，第一步，像Mathmatic中导入数据f=0.,0.,-8.10324,0.,0.125,-8.86098,0.,0.25,-8.70833,0.,0.375,-8.67279,0.,0.5,-8.43833,0.,0.625,-8.27937,0.,0.75,-8.30903,0.,0.875,-8.46757,0.,1.,-8.38238,0.125,0.,-8.77868,0.125,0.125,-8.25574,0.125,0.25,-8.48891,0.125,0.375,-8.50661,0.125,0.5,-8.63111,0.125,0.625,-8.61387,0.125,0.75,-7.874,0.125,0.875,-8.789,0.125,1.,-8.016,0.25,0.,-8.26577,0.25,0.125,-8.5836,0.25,0.25,-8.16196,0.25,0.375,-8.13002,0.25,0.5,-8.51087,0.25,0.625,-8.79877,0.25,0.75,-8.03872,0.25,0.875,-8.24623,0.25,1.,-8.78629,0.375,0.,-8.13568,0.375,0.125,-8.55102,0.375,0.25,-7.86779,0.375,0.375,-8.33788,0.375,0.5,-8.48779,0.375,0.625,-8.05114,0.375,0.75,-8.01005,0.375,0.875,-8.00026,0.375,1.,-7.92357,0.5,0.,-8.51704,0.5,0.125,-8.29237,0.5,0.25,-8.25015,0.5,0.375,-7.87301,0.5,0.5,-8.48866,0.5,0.625,-8.09981,0.5,0.75,-7.86813,0.5,0.875,-8.17034,0.5,1.,-8.21419,0.625,0.,-8.92698,0.625,0.125,-8.25539,0.625,0.25,-8.22001,0.625,0.375,-7.98359,0.625,0.5,-8.40419,0.625,0.625,-8.25535,0.625,0.75,-7.95277,0.625,0.875,-8.2982,0.625,1.,-8.40858,0.75,0.,-8.88122,0.75,0.125,-8.36967,0.75,0.25,-8.10206,0.75,0.375,-8.21322,0.75,0.5,-8.58908,0.75,0.625,-8.21704,0.75,0.75,-8.46002,0.75,0.875,-8.79303,0.75,1.,-8.21768,0.875,0.,-8.33622,0.875,0.125,-8.90449,0.875,0.25,-8.57666,0.875,0.375,-8.19268,0.875,0.5,-8.88057,0.875,0.625,-8.4678,0.875,0.75,-8.55311,0.875,0.875,-8.83791,0.875,1.,-8.56775,1.,0.,-8.5267,1.,0.125,-8.13237,1.,0.25,-8.51631,1.,0.375,-8.50842,1.,0.5,-8.97163,1.,0.625,-8.52972,1.,0.75,-8.58884,1.,0.875,-8.08969,1.,1.,-8.82707输入数据：0.,0.,-8.10324,0.,0.125,-8.86098,0.,0.25,-8.70833,0.,0.375,-8.67279,0.,0.5,-8.43833,0.,0.625,-8.27937,0.,0.75,-8.30903,0.,0.875,-8.46757,0.,1.,-8.38238,0.125,0.,-8.77868,0.125,0.125,-8.25574,0.125,0.25,-8.48891,0.125,0.375,-8.50661,0.125,0.5,-8.63111,0.125,0.625,-8.61387,0.125,0.75,-7.874,0.125,0.875,-8.789,0.125,1.,-8.016,0.25,0.,-8.26577,0.25,0.125,-8.5836,0.25,0.25,-8.16196,0.25,0.375,-8.13002,0.25,0.5,-8.51087,0.25,0.625,-8.79877,0.25,0.75,-8.03872,0.25,0.875,-8.24623,0.25,1.,-8.78629,0.375,0.,-8.13568,0.375,0.125,-8.55102,0.375,0.25,-7.86779,0.375,0.375,-8.33788,0.375,0.5,-8.48779,0.375,0.625,-8.05114,0.375,0.75,-8.01005,0.375,0.875,-8.00026,0.375,1.,-7.92357,0.5,0.,-8.51704,0.5,0.125,-8.29237,0.5,0.25,-8.25015,0.5,0.375,-7.87301,0.5,0.5,-8.48866,0.5,0.625,-8.09981,0.5,0.75,-7.86813,0.5,0.875,-8.17034,0.5,1.,-8.21419,0.625,0.,-8.92698,0.625,0.125,-8.25539,0.625,0.25,-8.22001,0.625,0.375,-7.98359,0.625,0.5,-8.40419,0.625,0.625,-8.25535,0.625,0.75,-7.95277,0.625,0.875,-8.2982,0.625,1.,-8.40858,0.75,0.,-8.88122,0.75,0.125,-8.36967,0.75,0.25,-8.10206,0.75,0.375,-8.21322,0.75,0.5,-8.58908,0.75,0.625,-8.21704,0.75,0.75,-8.46002,0.75,0.875,-8.79303,0.75,1.,-8.21768,0.875,0.,-8.33622,0.875,0.125,-8.90449,0.875,0.25,-8.57666,0.875,0.375,-8.19268,0.875,0.5,-8.88057,0.875,0.625,-8.4678,0.875,0.75,-8.55311,0.875,0.875,-8.83791,0.875,1.,-8.56775,1.,0.,-8.5267,1.,0.125,-8.13237,1.,0.25,-8.51631,1.,0.375,-8.50842,1.,0.5,-8.97163,1.,0.625,-8.52972,1.,0.75,-8.58884,1.,0.875,-8.08969,1.,1.,-8.82707然后第二步：输入“多元函数你和指令Fit”，进行函数拟合输入指令是：得到拟合函数：第三步：输入“多元函数绘图指令Plot3D”进行绘制图像：输入指令是：得到图像如图：第四步：输入“求偏导数指令D”进行求偏导，输入指令：求得偏导结果：1.19043 -2.32212 x-0.294179 y,0.508425 -0.294179 x-0.496519 y,-2.32212,-0.496519,-0.294179第五步，为求最值，所以需要让一阶偏导数fx ，fy 等于零，输入指令：Solve1.1904281250601303 -2.3221202501201867 x-0.2941786666667507 y0,0.5084250620490685 -0.2941786666667507 x-0.49651886483877145 y0,x,y得到输出结果：x0.413998,y0.778693最后一步：求最值，输入指令zx=0.413998077221635,y=0.77869278907450