实验3 Chapter Two 符号演算和数值计算 (2

1、 徐州工程学院数理学院数学应用软件实验报告课 程（实验序号）数学应用软件实验 3 实验地点、日期数学建模机房 2011 年 3 月 23 日主要仪器设备计算机使用的软件名称Mathematica实验类型演示性实验验证性实验综合性实验设计性实验研究性实验班级： 09信计（2）姓名： 孙源学号： 20090402250一、实验名称：符号演算和数值计算二、实验目的：掌握用Mathematica来解决基本的数学问题的方法三、实验内容： 极限LimitTanx,x®Pi/2,Direction®-1LimitTanx,x®Pi/2,Direction®1False

2、LimitSqrtx2+3 x-x,x®Infinity3/2PlotSqrtx2+3 x-x,x,0,50LimitLimit(x x y)/(x x+y y),y®Infinity,x®Infinity=LimitLimit(x x y)/(x x+y y),x®Infinity,y®InfinityFalseLimit(1+x/n)n,n®InfinityãxLimitSinx/x,x®01微分Dx4+3 xx-5,x4 x3+3 xx (1+Logx)fx_:=x xf'x2 xDSina x Co

3、sx y,xa Cosa x Cosx y-y Sina x Sinx yDSina x Cosx y,x,y-x y Cosx y Sina x-a x Cosa x Sinx y-Sina x Sinx yDSinx/(x+Cos2 x),x,4Sinx/(x+Cos2 x)-6 Sinx (4 Cos2 x)/(x+Cos2 x)2+(2 (1-2 Sin2 x)2)/(x+Cos2 x)3)+(4 Cosx (1-2 Sin2 x)/(x+Cos2 x)2+4 Cosx (-(24 Cos2 x (1-2 Sin2 x)/(x+Cos2 x)3)-(6 (1-2 Sin2 x)3)/(

4、x+Cos2 x)4-(8 Sin2 x)/(x+Cos2 x)2)+Sinx (96 Cos2 x2)/(x+Cos2 x)3-(16 Cos2 x)/(x+Cos2 x)2+(144 Cos2 x (1-2 Sin2 x)2)/(x+Cos2 x)4+(24 (1-2 Sin2 x)4)/(x+Cos2 x)5+(64 (1-2 Sin2 x) Sin2 x)/(x+Cos2 x)3)%/.x®0.3331.47123Dtgx,y/TraditionalFormây g(0,1)(x,y)+âx g(1,0)(x,y)Dtgx,y,x/TraditionalF

5、ormg(1,0)(x,y)+ây/âx g(0,1)(x,y)Dtgx,y,x,Constants®yg(1,0)x,yDgx,y,xg(1,0)x,yDgx,y,x,NonConstants®yDy,x,NonConstants®y g(0,1)x,y+g(1,0)x,y积分Integratex x+3 x+5,x5 x+(3 x2)/2+x3/3F1 = (x+1)/(x x+3 x+5)F2 = IntegrateF1,xF3 = DF1,x(1+x)/(5+3 x+x2)-(ArcTan(3+2 x)/)+1/2 Log5+3 x+x

6、2-(1+x) (3+2 x)/(5+3 x+x2)2)+1/(5+3 x+x2)PlotF1,F2,F3,x,-2,2SimplifyF3-(-2+2 x+x2)/(5+3 x+x2)2)NIntegrate(1+x)/(x6+2 x+4),x,0,10.289831RegionPloty£x x&&y³-x2,x,-1,1,y,-1,1Integratex x-y,x,-1,1,y,-x2,x24/5级数jizhu = SeriesSinx,x,0,10x-x3/6+x5/120-x7/5040+x9/362880+Ox11Normaljizhux-x3

7、/6+x5/120-x7/5040+x9/362880Seriesgx,y,x,0,3,y,1,2(g0,1+g(0,1)0,1 (y-1)+1/2 g(0,2)0,1 (y-1)2+Oy-13)+(g(1,0)0,1+g(1,1)0,1 (y-1)+1/2 g(1,2)0,1 (y-1)2+Oy-13) x+(1/2 g(2,0)0,1+1/2 g(2,1)0,1 (y-1)+1/4 g(2,2)0,1 (y-1)2+Oy-13) x2+(1/6 g(3,0)0,1+1/6 g(3,1)0,1 (y-1)+1/12 g(3,2)0,1 (y-1)2+Oy-13) x3+Ox4Normal%g

8、0,1+x g(1,0)0,1+1/2 x2 g(2,0)0,1+1/6 x3 g(3,0)0,1+(-1+y) (g(0,1)0,1+x g(1,1)0,1+1/2 x2 g(2,1)0,1+1/6 x3 g(3,1)0,1)+(-1+y)2 (1/2 g(0,2)0,1+1/2 x g(1,2)0,1+1/4 x2 g(2,2)0,1+1/12 x3 g(3,2)0,1)FindMinimumSinx,x,0.5-1.,x®-1.5708FindMinimumSinx y Expx x,x,0.2,y,0.3FindMinimum:sdprec: Line search unable to find a sufficient decrease in the function value with NoBreakMachinePrecisionNoBreak digit precision. -9.87492102