Mathematica100例題教學(xué)文案

1、Good is good, but better carries it.精益求精，善益求善。Mathematica100例題TOCo1-3hzuHYPERLINKl_Toc142494583利用mathematica計(jì)算二重積分PAGEREF_Toc142494583h1HYPERLINKl_Toc142494584冪函數(shù)作圖PAGEREF_Toc142494584h2HYPERLINKl_Toc142494585函數(shù)多次迭代PAGEREF_Toc142494585h3HYPERLINKl_Toc142494586冒泡排序PAGEREF_Toc142494586h3HYPERLINKl_Toc

2、142494587鋼管切割PAGEREF_Toc142494587h3HYPERLINKl_Toc142494588工資序列PAGEREF_Toc142494588h4HYPERLINKl_Toc142494589表格輸出PAGEREF_Toc142494589h5HYPERLINKl_Toc142494590讀入數(shù)據(jù)、站點(diǎn)實(shí)測(cè)數(shù)據(jù)PAGEREF_Toc142494590h5HYPERLINKl_Toc142494591追蹤PAGEREF_Toc142494591h5HYPERLINKl_Toc142494592截?cái)嗲懈睿〝?shù)組應(yīng)用）PAGEREF_Toc142494592h6HYPERLINK

3、l_Toc142494593煤矸石PAGEREF_Toc142494593h7HYPERLINKl_Toc142494594旋轉(zhuǎn)體PAGEREF_Toc142494594h7HYPERLINKl_Toc142494595柱面PAGEREF_Toc142494595h7HYPERLINKl_Toc142494596定積分動(dòng)畫PAGEREF_Toc142494596h8HYPERLINKl_Toc142494597冪級(jí)數(shù)PAGEREF_Toc142494597h8HYPERLINKl_Toc142494598牛頓PAGEREF_Toc142494598h8HYPERLINKl_Toc1424945

4、99切線PAGEREF_Toc142494599h9HYPERLINKl_Toc142494600級(jí)數(shù)PAGEREF_Toc142494600h9HYPERLINKl_Toc142494601級(jí)數(shù)和PAGEREF_Toc142494601h9HYPERLINKl_Toc142494602二重積分的實(shí)驗(yàn)PAGEREF_Toc142494602h10HYPERLINKl_Toc142494603導(dǎo)數(shù)PAGEREF_Toc142494603h10HYPERLINKl_Toc142494604歐拉常數(shù)PAGEREF_Toc142494604h11HYPERLINKl_Toc142494605解不等式P

5、AGEREF_Toc142494605h11HYPERLINKl_Toc142494606動(dòng)態(tài)規(guī)劃PAGEREF_Toc142494606h11HYPERLINKl_Toc142494607四人追逐三人多人PAGEREF_Toc142494607h12HYPERLINKl_Toc142494608二分法PAGEREF_Toc142494608h13HYPERLINKl_Toc142494609模擬PAGEREF_Toc142494609h14HYPERLINKl_Toc142494610追蹤TracePAGEREF_Toc142494610h14HYPERLINKl_Toc142494611文

6、件的存放PAGEREF_Toc142494611h15HYPERLINKl_Toc142494612混沌PAGEREF_Toc142494612h15HYPERLINKl_Toc142494613隨機(jī)點(diǎn)的投擲PAGEREF_Toc142494613h16HYPERLINKl_Toc142494614蒙特卡羅法計(jì)算定積分PAGEREF_Toc142494614h16利用mathematica計(jì)算二重積分問題：曲面z122x2-2y2，zx2+y23所圍成的幾何體的體積先作圖：=0 x2+y2+3-zTrue;a-p,b,a,qbubble9,7,1,6,11,21鋼管切割Fori=0,i3,i+

7、,Forj=0,j4,j+,Fork=0,k=4,k+,If7.4-2.9i-2.1j-1.5k1.5&7.4-2.9i-2.1j-1.5k0,Printi,j,k,7.4-2.9i-2.1j-1.5k工資序列1.Clearx,b,cc=10,5,2,1,0.5,0.2,0.1,0.05,0.02,0.01;(*Inputx;*)Print工資序列x=58.58,47.35,95.62,88.88b=Table0,i,1,Lengthx,j,1,10;Fork=1,kLengthx,k+,bk,1=Floorxk/10;Fori=2,i10,i+,bk,i=Floor(xk-Takebk,i-

8、1.Takec,i-1)/ci;bk,10=(xk-Takebk,9.Takec,9)/c10Print結(jié)果Print10元,5元,2元,1元,5角,2角1角,5分,2分,1分b/MatrixFormPrint合計(jì):Print10元,5元,2元,1元,5角,2角1角,5分,2分,1分Plusb2.提示輸入Clearx,b,cc=10,5,2,1,0.5,0.2,0.1,0.05,0.02,0.01;Print工資序列Inputxm=Lengthx;b=Table0,i,1,m,j,1,10;Fork=1,km,k+,bk,1=Floor(xk/10);Fori=2,i10,i+,bk,i=Fl

9、oor(xk-Takebk,i-1.Takec,i-1)/ci;bk,10=(xk-Takebk,9.Takec,9)/c10Print結(jié)果Print10元,5元,2元,1元,5角,2角1角,5分,2分,1分b/MatrixFormPrint合計(jì):Print10元,5元,2元,1元,5角,2角1角,5分,2分,1分Plusb3.輸入輸出表格輸出templist1=1,2,3;templist2=4,5,6;templist3=7,8,9;FrameBoxTableFormtemplist1,templist2,templist3,TableDirectionsRow,Column,TableA

10、lignmentsCenter,TableHeadingsa,b,c,None/DisplayForm讀入數(shù)據(jù)、站點(diǎn)實(shí)測(cè)數(shù)據(jù)ReadListM:cumcmallC2005DataFORECASTf7292_dis2.txt,Numberdata1=ReadListM:cumcmallC2005DataMEASURING020618.SIX,Number,Number,Number,Number,Number,Number,Number;a=Table0,i,91,j,3;Fori=0,i91,i+;ai,1=data1i,2;ai,2=data1i,3;Ifdata1i,40.1,0;ai,3

11、=data1i,4;a;ListPlot3DaListContourPlota追蹤GraphicsArrowyt_:=0.5*t;xt_:=100-02*t;Fori=1,i50,i+,ShowGraphicsLine0,0,0,100,100,100,100,0,0,0,GraphicsArrowxi,0,0,yi,GraphicsText敵,0,yi+1,Text変,xi+3,0,PointSize.025,RGBColor1,0,0,Pointxi,0,PointSize.025,RGBColor0,1,0,Point0,yi,PlotRangeAll,AxesTrue截?cái)嗲懈睿〝?shù)組應(yīng)用

12、）1.FL_:=WhichMaxL4,L5,L6,L7,L8/r,L9/rL8/r,L+0,0,-L8,0,0,0,0,-L8,0,r*L1*L2,MaxL4,L5,L6,L7,L8/r,L9/rL9/r,L+0,0,-L9,0,0,0,0,0,-L9,r*L1*L2,MaxL4,L5,L6,L7,L8/r,L9/rL6,L+0,-L6,0,0,0,-L6,0,0,0,L1*L3,MaxL4,L5,L6,L7,L8/r,L9/rL7,L+0,-L7,0,0,0,0,-L7,0,0,L1*L3,MaxL4,L5,L6,L7,L8/r,L9/rL4,L+-L4,0,0,-L4,0,0,0,0,0,

13、L2*L3,MaxL4,L5,L6,L7,L8/r,L9/rL5,L+-L5,0,0,0,-L5,0,0,0,0,L2*L3,True,0;L=10,14.5,10,6,1,7,5.5,0,6,145.;r=1;FL2.NestListF,L,6煤矸石旋轉(zhuǎn)體1.Clearf,x,t,y,z,i,s;fx_=Sint+1.5;Fori=1,i-2.5,2.5,-2.5,2.5,0,6,AxesLabel-x,y,z2.柱面Clearx,y,i,z,t1,t2;y=Sinx;Dot1=ParametricPlot3Dx,y,z,z,-0.01,0,x,-Pi,Pi,DisplayFunction-

14、Identity;t2=ParametricPlot3Dx,y,z,z,0,5,x,-Pi,-Pi+2Pi*i/20,PlotRange-Pi,Pi,-1,1,0,5,DisplayFunction-Identity;Showt1,t2,DisplayFunction-$DisplayFunction,Boxed-False,AxesLabel-x,y,z,LightSources-Pi,0,23,RGBColor0,1,0,i,1,21,2定積分動(dòng)畫Clearf,x,y,a,b,m,tt1,g1,g2,g3,i,x1,x2;fx_=1/x2;a=1.;b=15.;m=100;tt1=;g1=

15、Plotfx,x,a,b,PlotStyle-RGBColor1,0,0,DisplayFunction-Identity;g2=ParametricPlota,t,t,0,fa,PlotStyle-RGBColor1,0,0,DisplayFunction-Identity;g3=ParametricPlotb,t,t,0,fb,PlotStyle-RGBColor1,0,0,DisplayFunction-Identity;Fori=0,i$DisplayFunction,PlotLabel-:1,x2,:1-1/x1,PlotRange-0,15,0,1,AxesLabel-x,y,Ax

16、es-True冪級(jí)數(shù)Clearf,g,x,y,k,n;fx_=Sinx;gx_=Sum(-1)(k-1)x(2k-1)/(2k-1)!,k,1,n;DoPlotfx,gx,x,-4Pi,4Pi,PlotStyle-RGBColor1,0,0,RGBColor0,1,0,PlotRange-4Pi,4Pi,-2,2,AxesLabel-x,y,PlotLabel-n,n,1,10牛頓Cleara,b,f,x,i,j,n,m,t1,t2;a=0;b=1.;fx_=3x2;AbsolutePointSize2,DisplayFunction-Identity,ListPlotTaket2,n,Pro

17、log-AbsolutePointSize2,PlotStyle-RGBColor0,0,1,DisplayFunction-Identity,Plot1,m,0,60,PlotStyle-RGBColor0,1,0,DisplayFunction-Identity,DisplayFunction-$DisplayFunction,PlotRange-0,60,0,2,AxesLabel-,n,1,60,2切線Clearf,j,x,h,y,a;fx_=x4+x2;a=1.6Forj=1,j1,PlotRange-1,3,0,40,PlotStyle-RGBColor0,0,1,RGBColor

18、0,1,0,RGBColor1,0,0,AxesLabel-x,y級(jí)數(shù)Clearf,x,y,n,b,k;fx_=Which-2Pi=x-Pi,1,-Pi=x0,-1,0=xPi,1,Pi=xRGBColor1,0,0,RGBColor0,1,0,PlotRange-2Pi,2Pi,-1.5,1.5,AxesLabel-x,y,PlotLabel-k,k,1,61,10級(jí)數(shù)和Clearm,j,i,t1,t2,t3,nm=100;t1=TableSum1/j(1/2),j,1,i/N,i,1,m;t2=TableSum1/j,j,1,i/N,i,1,m;t3=TableSum1/j2,j,1,i/

19、N,i,1,m;DoShowListPlotTaket1,n,DisplayFunction-Identity,PlotStyle-RGBColor1,0,0,ListPlotTaket2,n,PlotStyle-RGBColor0,1,0,DisplayFunction-Identity,ListPlotTaket3,n,PlotStyle-RGBColor0,0,1,DisplayFunction-Identity,DisplayFunction-$DisplayFunction,PlotRange-0,m,0,20,Prolog-PointSize.014,AxesLabel-,n,1,

20、m,5二重積分的實(shí)驗(yàn)Clearf,x,y,a,b,c,d,s,fz,xyz,gg,i,m,n,j,k,h,pp1,pp2,step,fg,bc;fg=16;bc=2;t=Tablepi,i,1,fg;Dopi=0,i,1,fg;fx_,y_=1-(x2+y2)/4;a=-1;b=1;c=-1;d=1;s=0;Dostep=2/h;m=(b-a)/step;n=(d-c)/step;gg=;xyz=FlattenTablex,y,fx,y/N,x,a,b,step,y,c,d,step,1;Dok=(j-1)m;Dofz=(xyzi+j-1+k,3+xyzi+j+k,3+xyzi+j+m+k,3

21、+xyzi+j+m+k+1,3)/4;pp1=xyzi+j-1+k,1,xyzi+j-1+k,2,0;pp2=xyzi+j+m+k+1,1,xyzi+j+m+k+1,2,fz;ph+=step2fz;gg=Appendgg,Graphics3DCuboidpp1,pp2,i,1,m,j,1,n;Showgg,PlotRange-a,b,c,d,0,1,PlotLabel-:ph,h,1,fg,bc導(dǎo)數(shù)Clearf,x,g,n,y,i;fx_=x2;gx_=x5+x;n=30;DoShowPlotfx,f0-(f0-(1-i/n)-f0)/(1-i/n)(x-0),x,-1,0,DisplayF

22、unction-Identity,PlotStyle-RGBColor0,0,1,RGBColor0,1,0,Plotgx,g0+(g0+(1-i/n)-g0)/(1-i/n)(x-0),x,0,1,DisplayFunction-Identity,PlotStyle-RGBColor0,0,1,RGBColor1,0,0,DisplayFunction-$DisplayFunction,AxesLabel-x,y,i,0,29,2及時(shí)接車的模擬PrintRND1,*,RND2,*,x,*,t2,*,RND3,*,t1,*,RND4,*,t3,*,Ti;DoRND3=NRandom,3;t1=

23、Which0RND30.7,0,0.7RND30.9,5,0.9RND31.0,10;RND1=NRandom,3;RND2=NRandom,3;x=NSqrt-2*LogRND1*Cos2*Pi*RND2,3;t2=N2*x+30,3;RND4=NRandom,3;t3=Which0RND40.3,28,0.3RND40.7,30,0.7RND40.9,32,0.9RND4t3,1,0;PrintRND1,*,RND2,*,x,*,t2,*,RND3,*,t1,*,RND4,*,t3,*,T,i,=,Ti,i,1,50;P=NSumTi,i,50/50,4*100;PrintTheProba

24、bilityofmeetingis:,P,%歐拉常數(shù)TableFormTablen,NSum1/i,i,1,n-Logn+1,N1/n,n,1,1000解不等式0,x動(dòng)態(tài)規(guī)劃ClearX,U,V,x,y,z;X=Tablexi,i,5;U=Tableui,i,5;V=Tablevi,i,5;v6=0;fx_,y_,z_:=5y+4(x-y)+z;gx_,y_:=0.9x-0.1y;k=5;Whilek=1,xh=fxk,uk,vk+1/.xk+1-gxk,uk;IfDxh,uk0,uk=xk;vk=xh/.uk-xk,uk=0;vk=xh/.uk-0;k-;x1=1000;i=2;Whilei

25、5,xi=N0.9xi-1-0.1ui-1;i+;PrintX=,XPrintU=,UPrintX-U=,X-UPrintMAXPRICE=,V1四人追逐三人多人1t=10;dt=0.02;v=1;n=t/dt;robit=0,10,10,10,10,0,0,0;Fori=1,in,i+,Forj=1,j4,j+,xx1=robitj,i,1;yy1=robitj,i,2;Ifj4,xx2=robitj+1,i,1;yy2=robitj+1,i,2,xx2=robit1,i,1;yy2=robit1,i,2;dd=Sqrt(xx2-xx1)2+(yy2-yy1)2/N;xx1=xx1+v*dt

26、*(xx2-xx1)/dd;yy1=yy1+v*dt*(yy2-yy1)/dd;robitj=Appendrobitj,xx1,yy1;g1=ListPlotrobit1,PlotJoinedTrue,DisplayFunctionIdentity;g2=ListPlotrobit2,PlotJoinedTrue,DisplayFunctionIdentity;g3=ListPlotrobit3,PlotJoinedTrue,DisplayFunctionIdentity;g4=ListPlotrobit4,PlotJoinedTrue,DisplayFunctionIdentity;g5=L

27、istPlot0,10,10,10,10,0,0,0,PlotJoinedTrue,DisplayFunctionIdentity;Showg1,g2,g3,g4,g5,DisplayFunction$DisplayFunction2t=10;dt=0.02;v=1;n=t/dt;robit=10,0,5,8.660254037844386,0,0;Fori=1,in,i+,Forj=1,j3,j+,xx1=robitj,i,1;yy1=robitj,i,2;Ifj3,xx2=robitj+1,i,1;yy2=robitj+1,i,2,xx2=robit1,i,1;yy2=robit1,i,2

28、;dd=Sqrt(xx2-xx1)2+(yy2-yy1)2/N;xx1=xx1+v*dt*(xx2-xx1)/dd;yy1=yy1+v*dt*(yy2-yy1)/dd;robitj=Appendrobitj,xx1,yy1;g1=ListPlotrobit1,PlotJoinedTrue,DisplayFunctionIdentity;g2=ListPlotrobit2,PlotJoinedTrue,DisplayFunctionIdentity;g3=ListPlotrobit3,PlotJoinedTrue,DisplayFunctionIdentity;g5=ListPlot0,0,10

29、,0,5,8.660254037844386,0,0,PlotJoinedTrue,DisplayFunctionIdentity;Showg1,g2,g3,g5,DisplayFunction$DisplayFunction二分法2.fx_=Sinx-x+1;aa=0.;bb=10.;eps=0.01;g1=Plotfx,x,aa,bb,DisplayFunctionIdentity;Fori=1,i10,i+,cc=(aa+bb)/2;g4=GraphicsRGBColor1,0,1,PointSize0.02,Pointaa,0;g5=GraphicsRGBColor1,0,1,Poin

30、tSize0.02,Pointbb,0;g2=GraphicsRGBColor1,0,0,PointSize0.02,Pointcc,0;g3=GraphicsRGBColor1,0,0,PointSize0.02,Pointcc,fcc;Showg1,g2,g3,g4,g5,DisplayFunction$DisplayFunction,PlotRange0,10,f0,f10;Iffcc*faa0,bb=cc,aa=cc模擬fx_,y_:=Ifxy,1,0;(*Black,1;White,0*)FA_:=fA1,A2,fA2,A3,fA3,A4,fA1,A4a=TableRandomInt

31、eger,i,1,4;bb=NestListF,a,4GA_:=ShowGraphicsCircle0,0,1,PointSize.055,RGBColorA1,A1,A1,PointCos0,Sin0,PointSize.055,RGBColorA2,A2,A2,PointCosPi/2,SinPi/2,PointSize.055,RGBColorA3,A3,A3,PointCosPi,SinPi,PointSize.055,RGBColorA4,A4,A4,PointCos3*Pi/2,Sin3*Pi/2,PlotRangeAll,AspectRatioAutomatic,AxesTrue

32、MapG,bb追蹤Tracejiechengn_:=n*jiechengn-1;jiecheng0=1;Tracejiecheng10jiecheng10,10jiecheng10-1,10-1,9,jiecheng9,9jiecheng9-1,9-1,8,jiecheng8,8jiecheng8-1,8-1,7,jiecheng7,7jiecheng7-1,7-1,6,jiecheng6,6jiecheng6-1,6-1,5,jiecheng5,5jiecheng5-1,5-1,4,jiecheng4,4jiecheng4-1,4-1,3,jiecheng3,3jiecheng3-1,3-1

33、,2,jiecheng2,2jiecheng2-1,2-1,1,jiecheng1,1jiecheng1-1,1-1,0,jiecheng0,1,11,1,21,2,32,6,46,24,524,120,6120,720,7720,5040,85040,40320,940320,362880,10362880,3628800Tracejiecheng4,jiecheng_,TraceForwardTrueTracejiecheng4,jiecheng_Tracejiecheng4,jiecheng_,TraceForwardAll循環(huán)Fori=1;t=1,i4,i+,t=t2+1;PrinttFort1=1;i=1,i4,i+,t1=t12+1;