Mathematica100例题共14页文档.docx

Mathematica100例题共14页文档.docx

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Mathematica100例题共14页文档

利用mathematica计算二重积分

问题：

曲面z＝12－2x^2-2y^2，z＝x^2+y^2＋3所围成的几何体的体积

先作图：

<

debll=InequalityPlot3D[12-2x^2-2y^2-z>=0x^2+y^2+3-z<=0,{x},{y},{z},Axes->True];

<

Shadow[debll,XShadowFalse,YShadowFalse]

得到

得到

.0992********

幂函数作图

1.

f[x_,n_]:

=x^n;

a[n_]:

=Plot[x^n,{x,0,2},PlotStyleRGBColor[0.2n,0.8,1-0.1n]];

A=Array[a,5];

Show[A,AxesTrue,AxesLabel{"x","y"},AspectRatioAutomatica]

2

f[n_]:

=x^n;f/@{1,2,3,4};

Plot[Evaluate[f/@{1,2,3,4}],{x,0,1}]

3.

f[n_]:

=x^n;f[{1,2,3,4}];

Plot[Evaluate[f[{1,2,3,4}]],{x,0,1}]

4.

Plot[Evaluate[Table[x^i,{i,6}]],{x,0,2}]

5.

Clear[f];

f[n_]:

=x^n;

Plot[Evaluate[Map[f,{1,2,3,4,5,6}]],{x,0,2}]

6.

Plot[Evaluate[x^Range[6]],{x,0,2}]

Ｓｉｎ函数多次迭代

1.

Plot[{Nest[Sin,x,10],Nest[Sin,x,50],Nest[Sin,x,100]},{x,0,4Pi},PlotStyle{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]}]

2.

Plot[{Nest[Sin,x,100],Nest[Sin,x,500],Nest[Sin,x,1000]},{x,0,4Pi},PlotStyle{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]}]

冒泡排序

bubble[x_List]:

=x//.{p___,a_,b_,q___}/;b>a->{p,b,a,q}

bubble[{9,7,1,6,11,21}]

钢管切割

For[i=0,i<3,i++,

For[j=0,j<4,j++,

For[k=0,k<=4,k++,

If[7.4-2.9i-2.1j-1.5k<1.5&&7.4-2.9i-2.1j-1.5k0,Print[{i,"",j,"",k,"",7.4-2.9i-2.1j-1.5k}]

工资序列

1.

Clear[x,b,c]

c={10,5,2,1,0.5,0.2,0.1,0.05,0.02,0.01};

（*Input[x];*）

Print["工资序列"]

x={58.58,47.35,95.62,88.88}

b=Table[0,{i,1,Length[x]},{j,1,10}];

For[k=1,kLength[x],k++,

b[[k,1]]=Floor[x[[k]]/10];

For[i=2,i<10,i++,

b[[k,i]]=Floor[（x[[k]]-Take[b[[k]],i-1].Take[c,i-1]）/c[[i]]]

b[[k,10]]=（x[[k]]-Take[b[[k]],9].Take[c,9]）/c[[10]]

Print["结果"]

Print["10元","5元","2元","1元","5角","2角""1角","5分","2分","1分"]

b//MatrixForm

Print["合计:

"]

Print["10元","5元","2元","1元","5角","2角""1角","5分","2分","1分"]

Plus@@b

2.提示输入

Clear[x,b,c]

c={10,5,2,1,0.5,0.2,0.1,0.05,0.02,0.01};

Print["工资序列"]

Input[x]

m=Length[x];

b=Table[0,{i,1,m},{j,1,10}];

For[k=1,km,k++,

b[[k,1]]=Floor@（x[[k]]/10）;

For[i=2,i<10,i++,

b[[k,i]]=Floor[（x[[k]]-Take[b[[k]],i-1].Take[c,i-1]）/c[[i]]]

b[[k,10]]=（x[[k]]-Take[b[[k]],9].Take[c,9]）/c[[10]]

Print["结果"]

Print["10元","5元","2元","1元","5角","2角""1角","5分","2分","1分"]

b//MatrixForm

Print["合计:

"]

Print["10元","5元","2元","1元","5角","2角""1角","5分","2分","1分"]

Plus@@b

3.输入输出

表格输出

templist1={1,2,3};

templist2={4,5,6};

templist3={7,8,9};

FrameBox[

TableForm[{templist1,templist2,templist3},TableDirections{Row,Column},TableAlignmentsCenter,TableHeadings{{"a","b","c"},None}]

]//DisplayForm

读入数据、站点实测数据

ReadList["M:

\\cumcmall\\C2019Data\\FORECAST\\f7292_dis2.txt",Number]

data1=ReadList["M:

\\cumcmall\\C2019Data\\MEASURING\\020618.SIX",{Number,Number,Number,Number,Number,Number,Number}];

a=Table[0,{i,91},{j,3}];

For[i=0,i<91,i++;a[[i,1]]=data1[[i,2]];a[[i,2]]=data1[[i,3]];

If[data1[[i,4]]<0.1,0;

a[[i,3]]=data1[[i,4]]]

a;

ListPlot3D[a]

ListContourPlot[a]

追踪

<

y[t_]:

=0.5*t;

x[t_]:

=100-02*t;

For[i=1,i<50,i++,

Show[

Graphics[Line[{{0,0},{0,100},{100,100},{100,0},{0,0}}]],

Graphics[{Arrow[{x[i],0},{0,y[i]}]}],Graphics[

Text["敌",{0,y[i+1]}],

Text["変",{x[i+3],0}],

{PointSize[.025],RGBColor[1,0,0],Point[{x[i],0}]},

{PointSize[.025],RGBColor[0,1,0],Point[{0,y[i]}]}

PlotRangeAll

AxesTrue

截断切割（数组应用）

1.

F[L_]:

=Which[Max[L[[4]],L[[5]],L[[6]],L[[7]],L[[8]]/r,L[[9]]/r]L[[8]]/r,

L+{0,0,-L[[8]],0,0,0,0,-L[[8]],0,r*L[[1]]*L[[2]]},

Max[L[[4]],L[[5]],L[[6]],L[[7]],L[[8]]/r,L[[9]]/r]L[[9]]/r,

L+{0,0,-L[[9]],0,0,0,0,0,-L[[9]],r*L[[1]]*L[[2]]},

Max[L[[4]],L[[5]],L[[6]],L[[7]],L[[8]]/r,L[[9]]/r]L[[6]],

L+{0,-L[[6]],0,0,0,-L[[6]],0,0,0,L[[1]]*L[[3]]},

Max[L[[4]],L[[5]],L[[6]],L[[7]],L[[8]]/r,L[[9]]/r]L[[7]],

L+{0,-L[[7]],0,0,0,0,-L[[7]],0,0,L[[1]]*L[[3]]},

Max[L[[4]],L[[5]],L[[6]],L[[7]],L[[8]]/r,L[[9]]/r]L[[4]],

L+{-L[[4]],0,0,-L[[4]],0,0,0,0,0,L[[2]]*L[[3]]},

Max[L[[4]],L[[5]],L[[6]],L[[7]],L[[8]]/r,L[[9]]/r]L[[5]],

L+{-L[[5]],0,0,0,-L[[5]],0,0,0,0,L[[2]]*L[[3]]},

True,0];

L={10,14.5,10,6,1,7,5.5,0,6,145.};r=1;

F[L]

2.

NestList[F,L,6]

煤矸石

旋转体

1.

Clear[f,x,t,y,z,i,s];

f[x_]=Sin[t]+1.5;

For[i=1,i<=20,i++,

ParametricPlot3D[{f[t]Cos[s],f[t]Sin[s],t},{t,0,2Pi},

{s,0,2Pii/20},

PlotRange->{{-2.5,2.5},{-2.5,2.5},{0,6}},

AxesLabel->{x,y,z}]]

2.

柱面

Clear[x,y,i,z,t1,t2];

y=Sin[x];

Do[t1=ParametricPlot3D[{x,y,z},{z,-0.01,0},

{x,-Pi,Pi},DisplayFunction->Identity];

t2=ParametricPlot3D[{x,y,z},{z,0,5},

{x,-Pi,-Pi+2Pi*i/20},PlotRange->{{-Pi,Pi},{-1,1},{0,5}},

DisplayFunction->Identity];

Show[t1,t2,DisplayFunction->$DisplayFunction,

Boxed->False,AxesLabel->{x,y,z},

LightSources->{{{-Pi,0,23},RGBColor[0,1,0]}}],

{i,1,21,2}]

定积分动画

Clear[f,x,y,a,b,m,tt1,g1,g2,g3,i,x1,x2];

f[x_]=1/x^2;a=1.;b=15.;m=100;tt1={};

g1=Plot[f[x],{x,a,b},PlotStyle->{RGBColor[1,0,0]},

DisplayFunction->Identity];

g2=ParametricPlot[{a,t},{t,0,f[a]},

PlotStyle->{RGBColor[1,0,0]},DisplayFunction->Identity];

g3=ParametricPlot[{b,t},{t,0,f[b]},

PlotStyle->{RGBColor[1,0,0]},DisplayFunction->Identity];

For[i=0,i

tt1=Append[tt1,Graphics[{RGBColor[0,1,0],

Rectangle[{x1,0},{x2,f[x2]}]}]];

Show[tt1,g1,g2,g3,DisplayFunction->$DisplayFunction,

PlotLabel->{____:

"[1",x2"]",____:

1-1/x1},

PlotRange->{{0,15},{0,1}},

AxesLabel->{x,y},Axes->True]]

幂级数

Clear[f,g,x,y,k,n];

f[x_]=Sin[x];

g[x_]=Sum[（（-1）^（k-1））x^（2k-1）/（2k-1）!

{k,1,n}];

Do[Plot[{f[x],g[x]},{x,-4Pi,4Pi},

PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0]},

PlotRange->{{-4Pi,4Pi},{-2,2}},

AxesLabel->{x,y},PlotLabel->{n"____________"}],

{n,1,10}]

牛顿

Clear[a,b,f,x,i,j,n,m,t1,t2];

a=0;b=1.;f[x_]=3x^2;

<

t1=Table[Sum[f[a+（b-a）i/j]/j,{i,1,j}],{j,1,61}];

t2=Table[Sum[f[a+（b-a）i/j]/j,{i,0,j-1}],{j,2,62}];

Do[Show[ListPlot[Take[t1,n],

Prolog->AbsolutePointSize[2],

DisplayFunction->Identity],

ListPlot[Take[t2,n],

Prolog->AbsolutePointSize[2],

PlotStyle->RGBColor[0,0,1],

DisplayFunction->Identity],

Plot[1,{m,0,60},PlotStyle->RGBColor[0,1,0],

DisplayFunction->Identity],

DisplayFunction->$DisplayFunction,

PlotRange->{{0,60},{0,2}},

AxesLabel->{_____,______}],

{n,1,60,2}]

切线

Clear[f,j,x,h,y,a];

f[x_]=x^4+x^2;a=1.6

For[j=1,j<=20,j*=1.1;h=1/j;

Plot[{f[x],f[a]+f'[a]（x-a）,

f[a]+（f[a+h]-f[a]）/h（x-a）},{x,1,3},

AspectRatio->1,PlotRange->{{1,3},{0,40}},

PlotStyle->{RGBColor[0,0,1],RGBColor[0,1,0],

RGBColor[1,0,0]},AxesLabel->{x,y}]]

ｆｏｕｒｅｒ级数

Clear[f,x,y,n,b,k];

f[x_]=Which[-2Pi<=x<-Pi,1,-Pi<=x<0,-1,0<=x

Pi<=x<=2Pi,-1];

b[n_]=（1-（-1）^n）2/n/Pi;

Do[Plot[{f[x],Sum[b[n]Sin[nx],{n,1,k}]},{x,-2Pi,2Pi},

PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0]},

PlotRange->{{-2Pi,2Pi},{-1.5,1.5}},

AxesLabel->{x,y},PlotLabel->{k"____________"}],

{k,1,61,10}]

级数和

Clear[m,j,i,t1,t2,t3,n]

m=100;

t1=Table[Sum[1/j^（1/2）,{j,1,i}]//N,{i,1,m}];

t2=Table[Sum[1/j,{j,1,i}]//N,{i,1,m}];

t3=Table[Sum[1/j^2,{j,1,i}]//N,{i,1,m}];

Do[Show[ListPlot[Take[t1,n],

DisplayFunction->Identity,

PlotStyle->RGBColor[1,0,0]],

ListPlot[Take[t2,n],

PlotStyle->RGBColor[0,1,0],

DisplayFunction->Identity],

ListPlot[Take[t3,n],

PlotStyle->RGBColor[0,0,1],

DisplayFunction->Identity],

DisplayFunction->$DisplayFunction,

PlotRange->{{0,m},{0,20}},

Prolog->PointSize[.014],

AxesLabel->{__________,__________}],

{n,1,m,5}]

二重积分的实验

Clear[f,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=Table[p[i],{i,1,fg}];

Do[p[i]=0,{i,1,fg}];

f[x_,y_]=1-（x^2+y^2）/4;a=-1;b=1;c=-1;d=1;s=0;

Do[step=2/h;

m=（b-a）/step;n=（d-c）/step;gg={};

xyz=Flatten[Table[{x,y,f[x,y]}//N,{x,a,b,step},

{y,c,d,step}],1];

Do[k=（j-1）m;

Do[fz=（xyz[[i+j-1+k,3]]+xyz[[i+j+k,3]]

+xyz[[i+j+m+k,3]]+xyz[[i+j+m+k+1,3]]）/4;

pp1={xyz[[i+j-1+k,1]],xyz[[i+j-1+k,2]],0};

pp2={xyz[[i+j+m+k+1,1]],xyz[[i+j+m+k+1,2]],fz};

p[h]+=step^2fz;

gg=Append[gg,Graphics3D[Cuboid[pp1,pp2]]],{i,1,m}

],{j,1,n}];

Show[gg,PlotRange->{{a,b},{c,d},{0,1}},

PlotLabel->{______:

p[h]}],{h,1,fg,bc}]

导数

Clear[f,x,g,n,y,i];

f[x_]=x^2;g[x_]=x^5+x;n=30;

Do[Show[Plot[{f[x],f[0]-（f[0-（1-i/n）]-f[0]）/（1-i/n）（x-0）},

{x,-1,0},DisplayFunction->Identity,

PlotStyle->{RGBColor[0,0,1],RGBColor[0,1,0]}],

Plot[{g[x],g[0]+（g[0+（1-i/n）]-g[0]）/（1-i/n）（x-0）},

{x,0,1},DisplayFunction->Identity,

PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0]}],

DisplayFunction->$DisplayFunction,

AxesLabel->{x,y}],{i,0,29,2}]

及时接车的模拟

Print["RND1","***","RND2","***","x","***","t2","***","RND3","***","t1","***","RND4","***","t3","***","T[i]"];

Do[RND3=N[Random[],3];

t1=Which[0

RND1=N[Random[],3];

RND2=N[Random[],3];

x=N[Sqrt[-2*Log[RND1]]*Cos[2*Pi*RND2],3];

t2=N[2*x+30,3];

RND4=N[Random[],3];

t3=Which[0

T[i]=If[t1+t2>t3,1,0];

Print[RND1,"***",RND2,"***",x,"***",t2,"***",RND3,"***",t1,"***",RND4,"***",t3,"***","T[",i,"]=",T[i]],{i,1,50}];

P=N[Sum[T[i],{i,50}]/50,4]*100;

Print["TheProbabilityofmeetingis:

",P,"%"]

欧拉常数

TableForm[Table[{n,N[Sum[1/i,{i,1,n}]-Log[n+1]],N[1/n]},{n,1,1000}]]

解不等式

<

InequalitySolve[x（x^2-2）（x^2-3）>0,x]

动态规划

Clear[X,U,V,x,y,z];

X=Table[x[i],{i,5}];

U=Table[u[i],{i,5}];

V=Table[v[i],{i,5}];

v[6]=0;

f[x_,y_,z_]:

=5y+4（x-y）+z;

g[x_,y_]:

=0.9x-0.1y;

k=5;

While[k>=1,

xh=f[x[k],u[k],v[k+1]]/.x[k+1]->g[x[k],u[k]];

If[D[xh,u[k]]>0,

u[k]=x[k];

v[k]=xh/.u[k]->x[k],

u[k]=0;

v[k]=xh/.u[k]->0;

k--;

x[1]=1000;

i=2;

While[i5,

x[i]=N[0.9x[i-1]-0.1u[i-1]];

i++;

Print["X=",X]

Print["U=",U]

Print["X-U=",X-U]

Print["MAXPRICE=",V[[1]]]

四人追逐三人多人

1

t=10;dt=0.02;v=1;n=t/dt;robit={{{0,10}},{{10,10}},{{10,0}},{{0,0}}};

For[i=1,in,i++,For[j=1,j4,j++,xx1=robit[[j,i,1]];yy1=robit[[j,i,2]];

If[j4,xx2=robit[[j+1,i,1]];yy2=robit[[j+1,i,2]],xx2=robit[[1,i,1]];yy2=robit[[1,i,2]]];

dd=Sqrt[（xx2-xx1）^2+（yy2-yy1）^2]//N;

xx1=xx1+v*dt*（xx2-xx1）/dd;yy1=yy1+v*dt*（yy2-yy1）/dd;

robit[[j]]=Append[robit[[j]],{xx1,yy1}]]];

g1=ListPlot[robit[[1]],PlotJoin