Документ взят из кэша поисковой машины. Адрес оригинального документа : http://qilab.phys.msu.ru/people/zhdanov/teaching/seminar-1-2-Introduction-to-Mathematica.pdf Дата изменения: Mon Feb 4 18:40:06 2008 Дата индексирования: Mon Oct 1 20:16:50 2012 Кодировка:

Mathematica I .
, (File, Edit, Sell, Format,Input,Kernel .). , , (notebook). , . . . , , File->new, File->open, File->save ( *.nb) * File->Palettes->
* Basic input.

1) 3 : 1) , 2) , 3) , .. (Cells) , **: (Format->Style) input . In[45]:= t = 3 + 2 . output Out[45]= 5 title, subtitle, text ... , .. Э
** , , .., , text : Cell->Cell Properties->Cell Evaluatable. , Save . Edit->Preferences, LookUp : WindowToolbars LookUp. WindowToolbars "EditBar" Apply.

2) . . input. . Kernel->Evaluation->Evaluate Notebook. , ";". 3) a=b ( Set[a,b]) a b a:=b ( SetDelayed[a,b]) a b ClearAll[a] a 4)
In[494]:= Out[494]=

3) 4): 3 1) In[477]:= ClearAll@F, xD; 2) In[467]:= ClearAll@F, xD;
x F@x_D = 3 - 1; 2 F@8D x
5 4

F@x_D = 2x2;
18

F@3D

3)

In[472]:=

x = 4;

x = 4;

Out[480]= Out[481]=

Out[470]= Out[471]=

F@8D x
11 4

F@x_D :=

x 3 - 1; 2

Out[475]= Out[476]=

x 3 - 1; 2 ClearAll@F, xD; F@8D x
F@8D x

x = 4;

F@x_D :=



<>

[Ctrl + /]

6) : ESC <> ESC
=2.7

5) ,,'' Х a a F@xD x
a [ctrl +^] [ctrl +@] [ctrl +-]

ESC int ESC F[x] ESC dd ESC x

ESC prod ESC



=3.14

=(-1)

1/2




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ee

pi

ii

inf

th

ps

II.
) 1- 2- : m={1,3,5,r,t}; M={{a11,a12} ,{a21,a22}}; : m=List[1,3,5,r,t]; : n={{1,3,5,r,t}}; 2- 1 5. ) : Table[F[x,x2...,xn],{x, xmin,xmax, step}, {x2,...},{xn,...}] ­ n- , F. Range[xmin,xmax,step]- xmin xmax step. ) : m[[2]]; M[[1,2]]; n[[1,2]]. M[[1]], M 1- {a11,a12}. ) : Append[m, elem]; Prepend[m, elem]; Insert[m, elem,pos]; m elem , pos. Delete[m,pos] pos. Take[m,{nmin,nmax}] ­ m nmin nmax. . i 1 0 0y ) : Dimensions[m]; j z j z j z ) : DiagonalMatrix[{1,2,3}] ­ j 0 2 0 z; j z IdentityMatrix[n] nxn . Transpose[M]- k 0 0 3 { M . Inverse[M] ­ . Det[M]- . Tr[M]- . ) : Dot[M1,M2], M1. M2 ) Eigenvectors[d], Eigenvalues[d], Eigensystem[d]- d.x=mx (m-, m--). LinearSolve[d, y]- d.x=y. ) : : MatrixForm[M] ( M// MatrixForm); TableForm[M] ( M// TableForm).

III.
1) Simplify[expr] FullSimplify[expr] ­ expr Expand[expr] ­ expr. Collect[expr, {x1,x2..}] ­ , x1,x2.... TrigExpand[expr] TrigReduce[expr] , Expand Collect . TrigToExp[expr] ­ expr - ExpToTrig[expr] ­ , TrigToExp[expr]. 2) ReplaceAll[F,{x->expr1,y->expr2...}]- F x expr1 y expr2 .... : F/.{x->expr1,y->expr2}.


ReplaceRepeated[F,{x->expr1,y->expr2...}] ­ ReplaceAll , F . : F//.{x->expr1,y->expr2}. D[f[x], {x,n}]- n- f(x): n f HxL Derivative[n1,n2,n3][f][a,b,c]- n1+ n2+ n3 f xn f(x1,x2,x3) {a,b,c}. n1 x2n2 xn3 x1 Integrate[f[x],x] ­ - f(x). x2 Integrate[f[x],{x,x1,x2}] ­ x1 f H x L ,, x x2 NIntegrate[f[x],{x,x1,p1,p2,...x2}] ­ x1 f H x L ,, x , imax ; p1,p2...- f(x). Sum[f[i], {i, imin, imax}] NSum[f[i], {i, imin, imax}] ­ , f HiL i=imin . imax Product[F[i], {i, imin, imax}] NProduct[F[i], {i, imin, imax}] ­ . - F HiL i=imin .

IV., ,

V.

Solve[{eqn1,eqn2,...}, {var1,var2,...}] ­ - - eqn1,eqn2,... var1,var2,... eqn leftside = = rightside. : Solve[X^2+2X==0,X] : {{Xь-2},{Xь0}}. NSolve[{eqn1,eqn2,...}, {var1,var2,...}] ­ , Solve, . : NSolve[X^2+2X==0,X] : {{Xь-2.},{Xь0.}}. DSolve[{eqn1,eqn2,...}, {F1[var1],F2[var2],...}{var1,var2,...}] ­ - - eqn1,eqn2,... F1[var1],F2[var2],... var1,var2,... eqn leftside==rightside. , 1 ( C1,C2... C[1],C[2]...). NDSolve[{eqn1,eqn2,...}, {F1[var1],F2[var2],...}{var1,var2,...}] ­ , DSolve, . , , eqn () .
In[1]:=

Plot@8Sin@xD,Cos@xD<, 8x, 0, <, In[26]:= PlotStyle 88Hue@0D, Thickness@0.1D<, 8RGBColor@0, 1, 0D, Thickness@0.01D, Dashing@80.05, 0.025 1 0.5 0.5 -0.5 1 1.5 2 2.5 3

VI. ()

p = Plot3D@Sin@xD Cos@yD, 8x, 0, <, 8y, 0, 0 1

In[2]:=

ParametricPlotA8Sin@tD, Cos@tD<, 9t, 0, 3
-1
1 0.5 -1 -0.5 -0.5 0.5 1



1 0.5 0 -0.5 -1 0

2

2

VI:

-1

3 2.5 2 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3

=E

2 1 2 1 30

3

3 1 0.5 0 -0.5 -1 3

2

1

0

3 2.5 2 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3


1) Evaluate Mathematica, , , . . Evaluate . Plot[Evaluate[Table[BesselJ[n, x], {n, 1, 4}]], {x, 0, 10}] 2) , F , . F, Re[F], Im[F] Abs[F]. 3) ListPlot[{{x1,y1},{x2,y2},...}], ListPlot3D[{{z11,z12,..},{z21,z22,..},..}], ListDensityPlot[ {{z11,z12,..}, {z21,z22,..},..}], ListContourPlot[{{z11,z12,..},{z21,z22,..},..}], yi ­ xi .

VII.
Eliminate[{eqn1,eqn2,...}, {var1,var2,...}] - var1,var2,... eqn1,eqn2,.... FindRoot[{eqn1,eqn2,...},, {{var1,value1},{var2,value2}...}] ­ , var1=value1, var2=value2,..., value1, value2,... .

VIII.
Min[list] , Max[list] ­ list. FindMinimum[F[x,y,...],{x,x0},{y,y0},...] ­ F[x,y,...] x=x0,y=y0,..., x0, y0,... - .
: ConstrainedMin , , . Mathematica 5 Minimize,Maximize,NMinimize,NMaximize.

IX.
1) : : ) Put[expr1,expr2,expr3,... "file.ext"] ( expr>>"filename"); ­ , file.ext expr1,expr2.... ) PutAppend[expr1,expr2,expr3,... "file.ext"] ( expr1>>>"filename"); Save["filename",exr2,expr3,...] ­ expr1,expr2... file.ext ( ). :
In[1]:=



a@b_, c_D = 2 bc; M = 81, 2<;M >> "G:\1.dat"; a >>> "G:\1.dat"; Save@"G:\2.dat", M, aD;

G:\1.dat
{1, 2} a

G:\2.dat

M = {1, 2} a[b_, c_] = 2*b*c

: ) expr=Get["file.ext"] ( expr=<<"filename")- ) ReadList["file.ext",{type1,type2,...},n] ­ . ,{type1,type2,...} n, n , . 2) Export Import Export["file.ext", expr] - expr file.ext , ext. Export["file.ext ", expr, "format"] - expr file.ext "format".


expr =Import["file.ext"] - expr file.ext, ext. expr =Import["file.ext "format"] - expr file.ext, "format". "format"- , Mathematica - , , . : In[28]:= P = Plot@Sin@xD, 8x, 0, 6>"G:\MyFile[Dcm="<>ToString[Dcm]<>"].dat"; data "MyFile[Dcm=3].dat" , ToExpression["data1=<ToString[Dcm]<>"].dat" ]; data1 , .

X.
1) Module. Module[{var1, var2,...},expr1; expr2;.... ;exprn] ­ expr1; expr2;..., var1, var2,... , .. expr1; expr2;.... ;exprn; . exprn ";", Module exprn, , . In[29]:= a = 1; b = 2; Module@8a<,a = b + 1; b = a;D ; 8a, b< : ( b , Out[29]= 81, 3< a ­)

2) Do. In[2]:= z = 1; Do@z = F@zD, 85 ( ..3) )

In[1]:= In[2]:=

4) . If[condition, t] If[condition, t, f, u] ­ condition ( a>b,a
MyFactorial@n_D := Module@8i<,For@i = 1; k = 1, i < n + 1, i ++,k = k iD;kD MyFactorial@4D Out[2]= 24 start test incr body


Switch[expr, expr1, todo1, expr2, todo2,... ] ­ expr expr1,expr2,... true , todoi.