Mathematica 2 Nd Edition

8/20/2019 Mathematica 2 Nd Edition

1/101

1

"# $%& '

!"#$%&:'() *$+, '"-(. '/012

3456 7$8+$5686+91390


2/101

2

()%*+ ,-./0

!"#!............................................................................................................................................4

$%&'()*+*HELP...............................................................................................................................8

&,-.()%/ 0&!"#!1 ..........................................................................................................................11

:;


3/101

3

K8+. B L 56!MNO...........................................................................................................................57

K8+. B L *E!MNO..........................................................................................................................62

&8 B ' .................................................................................................................72

K&IW L X-*%34/..................................................................................................................................76

V;&X B ? 2 B Y8! ;COZ86+NO...................................................................................................................76

[EZ 2 B Y8! ;COZ86+NO....................................................................................................................79

7&8)&9!-&!W /..............................................................................................................................84

!&I34.I = M 1 ..................................................................................................................................89

A02 B ;C+ ......................................................................................................................................89

;C+@( $Z8\@ O5 C6Z8!H2' *N A02 B ;C+ ........................................................................................................91

8ZX $* ;C......................................................................................................................................91

65Z55]5+9686;C......................................................................................................................91

;CZ;09;EO V+0"R ' .........................................................................................................................92

%:-::Y:32$%*%&,.......................................................................................................................98


4/101

4

!"$!

MathematicaD;/E;F2

;N ^/I+2

O;C

Q%J

+@$6

5 '_;$Z

O;C

*"B2Q

3'E!"`2

34%()

Z6

*R

aE8

'I;/E;F2

Z8?K8

4+&6Z86 6+NZ;R 'bB"bI.:;E Z6 Z8?K8 4+& P$8 *c#& PBV581988^E%IStephen Wolfram!2X 6%>5 *N 7


5/101


6/101

6

*+BBAI O8+NStyle'2 7$;8 PBJ Z6 8+>8 *2868 Q8*"$?. Q8 Y8%IAbortEvaluation;$Quit KernelO%"2 Z6

Evaluation6+R 6;T0E8.

(ZI:Z6Mathematica 5O%"2 4;&EvaluationO%"2KernelaE8.

*'2 y$+MI *2;&+N Z6 *R '$;C+BA02!&%d!"0#C !d *09;"d Z8%5Z8?K8 4+& Q8a


7/101

7

*6;T0E8 ;C+@(


8/101

8

%& '#()*,&Help

*R ;1&X Q8MathematicaaE8 O6;$Q D8Z%0E6 O8Z86aE8 Pb5 'I5;T02 O;C:

*6;E Q8 'b$P$+IP$+0`N 5%5ZO%"2 Q8 6;T0E8 ;CHelp'2'2 *R !d;ND;BW?> YX *BV58 r5+J ;$ Z%0E6 t$;I ;N Y8%I

YX *N "%N+28+


9/101

9

'2 686 7$;


10/101

10

1%2+34 56%7Mathematica 5.1:


11/101

11

-+(!"$! /(123*,#

-57& 8(9:&

*Q8 '(=8 :; Q8 6;T0E8)Space Bar (*N ;C+BA02 ;$ 68!)8 PBN

'2 'H(I ;`&X {+_ *V?"26%d.DZ%= *N [B#HI 6;5 ;C+BA02 *N Y686 Z8!H2 5 '"$?@$;> %5Z 56:

+BA02 4;& = DZ;/) ;$ Z8!H2

+BA02 4;& := DZ;/) ;$ Z8!H2


12/101

12

Z6 pqE 5 !d 'N;$QZ8 *(=;KhN DZ;/) ;$ Z8!H2 :58 %5Z Z6+BA02'2 Z8+,'&;2Q DZ;/) ;$ Z8!H2 456 %5Z Z6 'V5 6+B.

'2 'N;$QZ86%d 6Z85 */E;F2 L$ Z6 +BA02 *R 6%d.

*Z6Mathematica!"bB2 + c-2 8Z YX m%& +BA02 y$+MI ;N LBI;2%I8 Z%~ *N Z8?K8 4+& 5 a#B& +BA02 m%& y$+MI *N OQ;B&.

Q8 '9+NZ6 +BA02 m8%&8MathematicaQ8 !"IZ;/):

-Integer :iBF= 68!)8.

-Rational:;$%. 68!)8.

-Real:'HBHJ 68!)8.

-Complex:^(0c2 68!)8.

-String:;C *0dZ

-List:;C a#BV

-Graphics:LBK8+.

;N *R Q8 6;T0E8Z%0E6'2 +$Q6+R PBBMI 8Z ;`&X m%& Y8%I:

Head[+BA02 4;&]

*'2 +BA02 L$ Y6+R o;n O8+N6+R 6;T0E8 +$Q D8Z%0E6 Q8 Y8%I:

Clear[+BA02 4;&]

Remove[+BA02 4;&]

*'2 +$Q Z%0E6 Q86+R 6;T0E8 ;C+BA02 *B(R Y6+R o;n O8+N Y8%I:

Clear[“Global`*”]

*6;T0E8 +$Q Z%0E6 Q8 +BA02 L$ O8%0F2 7$;


13/101

13

-D=;$+ 4 FDH# I(D,(J! *O8+N'2 DZ;/) L$ O6!) */E;F26+R 6;T0E8 +$Q D8Z%0E6 Q8 Y8%I:

N[ DZ;/) ] ;$ DZ;/) //N

Z%0E6 P$8;I 8Z DZ;/) O6!) Z8!H27d[,ZY;-& '>5+9 Z6'2!C6.

*+$Q Z%0E6;I 8Z DZ;/) O6!) Z8!H2n[,ZY;-&'2!C6:

N[ DZ;/) , n ]

*(ZI:*N 'N;B0E6 O8+NO;C '>5+9+0R8Z;R Q8 '(/,%'2 6;T0E86%d:

%:P$+9X '>5+9

%% … %:68!MI +.8%;Cn!d;NnPB28!C6 '2 8Z +9X Q8 '>5+9.


14/101

14



15/101

15

2# #3C3! LE&3+ -M;EMathematica

*2;&+NMathematicaO6;$Q 'b$?BK 5 '_;$Z lN8%I O8Z865 ;C *0dZ 368!)8 ;N Z;R O8+N...'2Z6 *R !d;Na#BV+$Q*N'9+N

Z;d8 ;`&X Q8aE8 !d.Q8 lN8%I 6Z%2 Z6 +0-BN D;)h~8 Y6Z5X aE!N O8+NHelp!$+B@N L


16/101

16

*S;N iBF= ?> lN;I)Q8 +0.Z?N iBF= 6!) P$+0bk%R x: (

Celling[x]

*G(j2 Z!, lN;I:

Abs[x]

*a2h) lN;I:

Sign[x]

*lN;I< x >)*N iBF= 6!) P$+0b$6?&x: (

Round[x]

*L$ 5 +T= Q;N Z6 'K6;xI 6!) !BV%I lN;I:

Random[]

*Q;N Z6 ,;9 m%& Q8 'K6;xI 6!) !BV%I lN;Ia5 b:

Random[ +BA02 m%& , {a,b}]

*n:58

6!)

PB28

:

Prime[n]

*6!)n'2 :58 U28%) {+_ DZ%= *N 8Z!#$%&:

FactorInteger[n]

*+.8n!d;N :58True*&+.5False'2+N!&86+. :

PrimeQ[n]

*o+0-2 {+ - 2 P$+0bk%R m5n:

LCM[m,n]

*4%#H2 P$+0.Z?No+0-2 *B()m5n:


17/101

17

GCD[m,n]

*+.8n!d;N 6+KTrue*&+.5False'2+N!&86+. :

OddQ[n]

*!&;


18/101

18

*U#N lN;IJn(x):

BesselJ[n,x]

*U#N lN;IYn(x):

BesselY[n,x]

**0K;$ U$!MI U#N lN;IIn(x):

BesselI[n,x]

**0K;$ U$!MI U#N lN;IK n(x):

BesselK[n,x]

*;j9 lN;I:

Erf[x]

**(!"k*/I+2 Z!&8/ V O8n)Pn(x): (

LegendreP[n,x]

**(!"k *0#N85 Z!&8/ V O8)Pnm(x): (

LegendreP[n,m,x]

*;2;. lN;I)Γ (x): (

Gamma[x]

**( !"k*/I+2 aB2+C O8n)Hn(x): (

HermiteH[n,x]

**( !"k*/I+2 +.S O8n)Ln(x): (

LaguerreL[n,x]

**( !"k*0#N85 +.S O8)Lnm(x): (


19/101

19

LaguerreL[n,m,x]

*O5+R 0 "C;


20/101

20

*^(0c2 1 %B


21/101

21



22/101

22

-+(N5N! 4 /;DC I(D,(J!

'. / $5 Q8 'b$[`2 O;CMathematica'$;&8%IOS;ND;/E;F2 Z6 YX LB(/ D8Z;/) OQ;E'2 Z;d8[B"R :

**(!"k Z6 Y8%I ;$ {+_ L$ ̂ #NO8;C:

Expand[ *(!"kO8 ]

**(!"k *$?1I:58 U28%) *N O8)O+B.Z%0R;K: (

Factor[ *(!"kO8 ]

*6;EO+#R DZ;/) Y6+R :

Cancel[ O+#R DZ;/) ]

*6;E 5 DZ;/) !"k sBR+I;`&X Y6+R :

Together[ DZ;/);C ]

*'W?> O;C+#R *N +#R L$ *$?1I:

Apart[ O+#R DZ;/) ]

*6;E'I;g(g2 +#R L$ Y6+R :

Cancel[ 'I;g(g2 O+#R DZ;/) , Trig à True ]

*'I;g(g2

D8Z;/)

O+B.Z%0R;K

:

TrigFactor[ 'I;g(g2 DZ;/)]

*'I;g(g2 DZ;/) !"k sBR+I:

Together[ DZ;/)'I;g(g2 O;C , Trig à True ]


23/101

23

*'I;g(g2 DZ;/) ̂ #N:

TrigExpand[ 'I;g(g2 DZ;/) ]

*'2 'I;g(g2 'j9 D8Z;/) s#J+N 8Z 'I;g(g2 DZ;/)!#$%&:

TrigReduce[ 'I;g(g2 DZ;/) ]

*'$;


24/101

24



25/101

25

/;,P;Q57(K 4 (1(1

*/E;F2 O8+N;C

O+E5;${+ - (=;J'2

;CZ6

6%>%2

"%N+2

O;C6;


26/101

26

1%2+:


27/101

27

LE&3+ S=;U+

3!d !C;-2 *R Z%j&;5.L$ +@$6 r+~ Q8 5 +BA02 !"k ;$ L$ aE8 Pb


28/101

28

**jN;_ y$+MIf(x,y)O8+Nx5y,;9 O;C:

f [x_ /; x O5Z '~+d , y_ /; y O5Z '~+d ] = y 5 x s#J +N 'IZ;/)

*Mathematica6+R *>%I +$Q *0b& 56 *N !$;N lN8%I P$8 y$+MI Z6 'V5 6Z86 8Z '0-.Q;N lN8%I y$+MI aB(N;,:

1-'0-.Q;N *jN8Z y$+MI Z6'"$?@$;> Q8:=6%d 6;T0E8.

2-!&%d y$+MI ;


29/101

29



30/101

30

8&;B*@& 4 F*V! X "K

"K D,(J! '2 6;T0E8 +$Q D8Z%0E6 Q8 !J */E;F2 O8+N6%d:

*!Jf(x)Z6x = a:

Limit[ f[x] , x à a ]

* aE8Z !Jf(x)Z6x = a:

Limit[ f[x] , x à a , Direction à -1 ]

* tk !Jf(x)Z6x = a:

Limit[ f[x] , x à a , Direction à +1 ]

*!Jf(x , y)Z6(a,b):

Limit[ f[x , y] , { x à a , y à b } ]

F*V! D,(J! '2 6;T0E8 +$Q D8Z%0E6 Q8 G0-2 */E;F2 O8+N[B"R :

**/E;F2f `(x)3f ``(x)5f ``` (x)5: ...

f’[x] , f’’[x] , f’’’[x] , …

*G0-2 */E;F2n48:

D[ f[x] , {x , n}]

Derivative[n][f][x]

:{;,]

**/E;F2?@AB

:


31/101

31

D[ f[x] , x]

**/E;F2CDE

FGH

:

D[ f[x] , {x , n}]

**/E;F2IJK

LMNOPQRST…UVW :

D[ f[x1 , x2 , x3 , … , xk ], x1 , x2 , x3 , … , xk ]

X{YZ,[\,…,]^ } _[`a,bc,…,de]

**/E;F2

fgh

ijklmnopqrstuvw…xyz{|:

D[ f[x1 , x2 , x3 , … , xk ] , {x1 , n1} , {x2 , n2} , {x3 , n3} , … , {xk ,nk }]

Derivative[n1 , n2 , n3 , … , nk ][f][x1 , x2 , x3 , … , xk ]

*G0-2 */E;F2n48f(x)Z6x = a:

Derivative[n][f][a]

*

*/E;F2

}~•

!"#

$%&'(

)*+,-

.…/012

3

Z6(45,67,89,…,:;):

Derivative[n1 , n2 , n3 , … , nk ][f][a1 , a2 , a3 , … , ak ]

D,(J!8&;B*@& :8+@0&8 */E;F2 O8+N'2 PBM2;& 5 PBM2 O;CZ6 6%>%2 "%N+2 O;C6;


32/101

32

*:8+@0&8 */E;F2< f (x)dx=

>:

Integrate[ f[x] , { x , a , b }]

* :8+@0&8

*/E;F2

< < f (x,y)dxdy?

@

A

B:

Integrate[ f[x , y] , { x , a , b } , { y , c , d }]

(ZI:*/E;F2 O8+N:8+@0&8;CPBM2 O:8+@0&8 O6!) */E;F2 ;$ 5 O6!) DZ%= *NUJ UN;,+B ' PBM2 O;C*N &%K D8Z%0E6 Z6

O;>IntegrateQ8 NIntegrate'2 6;T0E86%d.

(ZI:

Q8 'b$

OptionO;C*"$?.

!J

;$ :8+@0&8

*/E;F2

Z6

O6+NZ;R

Assunptions'2

YX

L


33/101

33



34/101

34


35/101

35

2# LE&3+ Y,2Mathematica

Mathematica[BC8%9 Z;d8 YX O;C */"> Q8 '9+N *N LBK8+. a


36/101

36



37/101

37


38/101

38

[+=;") O8Z86 sBI+I *N *R !"R xY8%I *N2+=;") Z\> 3x+=;") U$Z%0R;K 5x'2!d;N.a#BV 56 PB"f


39/101

39

**0dZ L$ O;C+0R8Z;R U2;d '0#BV 6;1$8:

Characters[ “ *0dZ 4;& “]

*'2 iBF= 6!) 4;,Z8 U2;d '0#BV!C6:

IntegerDigits[ iBF= 6!) ]

Q8 '9+N;N Z;R D8Z%0E6a#BV;CQ8 !"IZ;/):

*a#BV L$ :%~)a#BV +=;") 68!MI: (

Length[ a#BV 4;& ]

*6;MN8a#BV L$)a#BV p$!&8 +C D8+BBAI 65!J: (

Dimensions[ a#BV 4;& ]

**TV%2k 8!0N8 Q8 a#BV L$ 48:

Part[ a#BV 4;& , k ]

a#BV 4;& [[ k ]]

**TV%2k a#BV L$ 48 0&8 Q8;` :

Part[ a#BV 4;& , -k ]

a#BV 4;& [[ -k ]]

*a#BV Z6a#BV L$ +x") +C *R O!MN56 O;C'2 aE8+x") Y6Z5X aE!N O8+N Y8%I j+x") Z6 6%>%2 48)a#BV(i48

Z%0E6 Q8 '(=8 a#BVD86+R 6;T0E8 +$Q:

a#BV 4;& [[ i ]][[ j ]] , a#BV 4;& [[ i , j ]]


40/101

40

a#BV +BBAI O8+N +$Q D8Z%0E6'2 Z8+, 6;T0E8 6Z%2 ;C!&+B. :

*a#BV >U2;d O!$! n'2 +N 8Z '(=8 a#BV :58 *$8Z6!&86+. :

Take[ a#BV 4;& , n ]

*a#BV >U2;d O!$! n'2 +N 8Z '(=8 a#BV +9X *$8Z6!&86+. :

Take[ a#BV 4;& , -n ]

*a#BV >*$8Z6 U2;d O!$! O;Cm;I 48n'2 +N 8Z '(=8 a#BV 48!&86+. :

Take[ a#BV 4;& , { m , n } ]

**$XZ6n'2 r\J 8Z '(=8 a#BV 48!"R :

Delete[ a#BV 4;& , n ]

**$XZ6n'2 r\J +9X Q8 8Z '(=8 a#BV 48!"R :

Delete[ a#BV 4;& ,- n ]

*a#BV >*$XZ6

YX

Z6

*R

O!$!

m;I 48

n!d

r\J

48'2

+N 8Z !&8!&86+.

:

Delete[ a#BV 4;& , { m , n } ]

*+x")xY;b2 Z6 8Zn'2 Z8+, a#BV 48!C6:

Insert[ a#BV 4;& , x , n ]

*+x")xY;b2 Z6 8Zn'2 Z8+, +9X Q8 a#BV 48!C6:

Insert[ a#BV 4;& , x , -n ]

*+x")n;N 8Z a#BV 48x'2 w%)!"R :

ReplacePart[ a#BV 4;& , x , n ]


41/101

41

*+x")n;N +9X Q8 8Z a#BV 48x'2 w%)!"R :

ReplacePart[ a#BV 4;& , x , - n ]

*'2 sI+2 '.Z?N */I+2 e;E8 +N 8Z a#BV!"R :

Sort[ a#BV 4;& ]

*'2 pb)+N 8Z a#BV +=;") sBI+I!"R :

Reverse[ a#BV 4;& ]

*a#BV L$ *N ;`&X U$!/I 5 a#BV 56 :;xI8:

Join[ a#BV1 , a#BV2 ]

*a#BV 56 m;8:

Union[ a#BV1 , a#BV2 ]

*a#BV 56 o8+0d8:

Intersection[ a#BV1

, a#BV2

]

*a#BV [


42/101

42

*0b&:Q8 ;I56Option[`2 O;CZ%0E6TableFormaE8 DZ;/)Q8:

1-TableAlignments:'2 *R aV;J *E Z6 !&8%IRight3Left5Center Y%0E Y6+R sI+2 O8+N 5 !d;NQ8 ;C

65+B2 Z;R *N ̂ E5 ;$ tk 3 aE8Z)7Bn Z8!H2w+KLeftaE8. (

2-TableHeadings:'2 *R aV;J Z6 !&8%I None3AutomaticDZ%= *N ;$ 5{ rowlist , columnlist }

!d;N.


43/101

43



44/101

44

/;DC I^#(U!(@ 4 I^#(U!

O8+N JZ%0E6 Q8 '2% DS6;M2 U Solve;$ NSolve'2 6;T0E86%d.{8%> 6%>5 DZ%= Z63{8%>;C

a#BV L$ Y5Z6+$Q Ubd *NZ8+,aK+. !"C8%9:

{ { x à x1 } , { xà x2 } , … }

'Hj"2 O5;#I a2h) Q8 *R ad86 *>%I !$;N *V6;M2 L$ P0d%& O8+N)=( =36%d 6;T0E8*V6;M2 :;g2 Y8%") *Nx2+3x=0Z6

MathematicaDZ%= *Nx^2+3 x==0'2 *0d%&6%d.

*Ubd'(R Z%0E6SolveaE8 +$Q DZ%= *N:

Solve[ O+/> DS6;M2 a#BV , DS%`12 a#BV ]

a#BV Z66S%RX Q8 6;T0E8 *N OQ;B& [Bd;N *0d86 :%`12 L$ 5 *V6;M2 L$ +.8 &%K O;C){}(' DS6;M2 a#BV , DS%`12 a#BV ]

DZ;/) /.Solution

4;& &%K Z%0E6 Z6Solution5 aE8 OZ;B098YX O;> *N'2%I6+R 6;T0E8 O+@$6 4;& +C Q8 Y8.


45/101

45

*O+/> DS6;M2 D;,58 'C;. Z%0E6 ;NSolve 0#B& UJ UN;,!" .aV;J P$8 Z6DS6;M2 *R 'IZ%=Z6 3O6!)+B ' +028Z;n O8Z86

d;/& " '2 ! Y8%I6;T0E8 ;NZ%0E6 Q8 NSolveYX ;C6+R UJ O6!) DZ%= *N 8Z.;I 8Z {8%> +$Q Z%0E6n'2 [,Z!C6:

NSolve[ O+/> DS6;M2 a#BV , DS%`12 a#BV , n ]

'j9 +B ' DS6;M2 UJ O8+NZ6MathematicaY8%I '26;T0E8 +$Q D8Z%0E6 Q86+R :

*m5+d *jH& 5 PI%B& %5Z ;N *V6;M2 UJx0:

FindRoot[ O+/> *V6;M2 , { x , x0 } ]

*m5+d ";H& 5 a&;bE %5Z ;N *V6;M2 UJx05x1:

FindRoot[ O+/> *V6;M2 , { x , x0 , x1 } ]

*Q;N Z6 *V6;M2 UJ[a,b]m5+d *jH& ;N 5x0:

FindRoot[ O+/> *V6;M2 , { x , x0 , a , b } ]

*m5+d *jH& ;N DS6;M2 ;@0E6 UJ(x0 , y0 , … ):

FindRoot[ O+/> DS6;M2 a#BV , {{ x , x0 } , { y , y0 } , …} ]

(ZI:m5+d *jH& Y6+R8!Bn O8+N3&%K D8Z%0E6 Z6'2Y8%IlN8%I;M2 r+~ 566D;x0c2 ;@0E6 L$ Z6 8Z *V)Z%0E6 ;NPlot(

Q8 6;T0E8 ;N 5 6+R [EZl~;HI *jH& Z86%


46/101

46

*D8Z%0E6 Q8 +@$6 'b$O+/> DS6;M2 UJ'2 Z;R *N S;N a,6 *N Q;B& 4;@"C Z6 *R Z%0E6 65ZInterpolateRoot*R aE8

L$*BV58 +$6;H2 ;N 8Z *V6;M2a5 b'2 UJ!"R :

InterpolateRoot[ O+/> *V6;M2 , { x , a , b } ]

!B"R *>%I*R :58 !$;N Z%0E6 P$8 Q8 6;T0E8 O8+NPackage*N "%N+2InterpolateRoot6+R 6%V +$Q Z%0E6 ̂ E%I 8Z:

Needs["FunctionApproximations`"]

(ZI:Z6Mathematica 5Y6+R 6%V O8+NPackage6%d '2 6;T0E8 +$Q Z%0E6 Q8:


47/101

47



48/101

48


49/101

49


50/101

50

_=;+(! 4 (12E(1

p$+I;2 5 ;CZ86+NY;!B(R Q8 ;CTab'2 6;T0E8 e5;2 ;$ 56%d.

(ZI:Z6Mathematica 5+1"n Q8Create Table/Matrix/PaletteO%"2 Z6 l,85Input)+/&;B2 !B(R ;NShift +

Ctrl + C(6;T0E86%d '2.


51/101

51

**$XZ6 +.8'2 !"d;N !"


52/101

52

(ZI:68!)8 {+_ a2h) Q8 *jH& O;1N +.8)3 'V;9 O;>*;$ 5((Z86+N 6%d 6;T0E8'2 {+_ [C Z6 *TV%2 *TV%2 ;C5 !&%d

aE8 Z86+N 6!) O;1N {8%>.

*Z86+N 56 '>Z;9 {+_O!MN *EV15V2:

Cross[ V1 , V2 ]

(ZI:'2 8Z '>Z;9 {+_Z%0E6 ^E%I Y8%IV1×V26;*;$ 5((p$+I;2 6%d 6;T0E8'2 {+_ [C Z6 *TV%2 *TV%2 ;C!&%d.

*p$+I;2 6;`&8+I */E;F2:

( Transpose[ p$+I;2 ] ) // MatrixForm

**/I+2 PBBMI)Y%0E 5 ;C+jE 68!MIO;C(p$+I;2:

Dimensions[ p$+I;2 ]

*^(0c2 1 %B


53/101

53

Det[ p$+I;2 ]

*'MN+2 p$+I;2 6Z PBBMI)'(=8 +j, +=;") l: (

Tr[ p$+I;2 ]

*6%>5 DZ%= Z6 'MN+2 p$+I;2 e%bM2 p$+I;2:

( Inverse[ p$+I;2 ] ) // MatrixForm

*Y8%In 2 p$+I;2 48'MN+ :

( MatrixPower[ p$+I;2 , n ] ) // MatrixForm

*p$+I;2eA :

( MatrixExp[ p$+I;2 ] ) // MatrixForm

**/I+2 '&;


54/101

54

CharacteristicPolynomial[ p$+I;2 , x ]

*p$+I;2 +$6;H2 / $5:

Eigenvalues[ p$+I;2 ]

*;I O6!) DZ%= *N p$+I;2 +$6;H2 / $5nZ;-)8 [,Z:

Eigenvalues[ N[ p$+I;2 , n ] ]

* / $5p$+I;2 O;CZ86+N:

Eigenvectors[ p$+I;2 ]


55/101

55



56/101

56


57/101

57

a


58/101

58

*Z%0E6PlotO8Z86Option;N *R aE8 O6;$Q O;CP0d%&Z%0E6Options[Plot]Z%0E6 3 aE8 !C;-2 UN;,Plot8+


59/101

59

PlotStyle à Hue[ h , s , b ]

(ZI: N &%K Z%0E6 P0d%&DZ%= * Hue[h]:6;M2Hue[h,1,1]aE8.

*8Z 'HK8

*N O6%


60/101

60

Show[ Graphics[ Disk[ {x,y} ,r ] , DefaultColor à Hue[n] , BackColor à Hue[m] ]]

-Z6Mathematica 6:

Graphics[{ Hue[n] , Disk[ {x,y} ,r ] }]

**jH& [EZ(x,y)'@&Z:

-Z6Mathematica 5:

Show[ Graphics[ Point[ {x,y} ] , DefaultColor à Hue[n] , BackColor à Hue[m] ]]

-Z6Mathematica 6:

Graphics[{ Hue[n] , Point[ {x,y} ] }]

(ZI:686 Z8+, ?B& 8Z ";H& Q8 '0#BV 3*jH& L$ O;> *N Y8%I '2 &%K Z%0E6 Z6.

(ZI:Z%0E6 Q8 !MN *E Z6 ";H& [EZ O8+NGraphics3D6+R 6;T0E8 Y8%I '2.

*[EZ^9'@&Z*0#bd'2 U=5 [C *N 8Z ";H& *R O8!"R *"B2Q 0 &Z ;N:

-Z6Mathematica 5:

Show[ Graphics[ Line[ {{ x1, y1},{ x2 , y2 }, … } ] , DefaultColor à Hue[n] , BackColor à

Hue[m]]]

-Z6Mathematica 6:

Graphics[{ Hue[n] , Line[ {{ x1, y1},{ x2 , y2 }, … } ] }]

*UBj0#2 [EZ8%cV6 0 &Z ;N:

-Z6Mathematica 5:

Show[ Graphics[ { Hue[n] ,Rectangle[ {{ x1, y1},{ x2 , y2 } } ] }]]

-Z6Mathematica 6:


61/101

61

Graphics[{ Hue[n] , Rectangle[ {{ x1, y1},{ x2 , y2 } } ] }]

(ZI:Z%0E6GraphicsO8Z86Option'2 *( Q8 *R aE8 O+@$6 6;$Q O;C*N Y8%I'. / $5Axes à True;$'. / $5

Frame à True;CZ%F2 7$;


62/101

62

*O;`B"F"2 [EZr=f 1(θ)3r=f 2(θ)5 ...Q;N Z6a< θ < b:

PolarPlot[{ f 1[θ] , f 2[θ] , … } , { θ , a , b } ]

(ZI:

Z6Mathematica 5

Z%0E6 Q8 6;T0E8

O8+N

PolarPlot6+R

6%V

8Z +$Q

*0#N

8!$;N

8!0N8

:


63/101

63

Z%0E6 !"&;2 ?B& Z%0E6 P$8PlotO8Z86Option'2 Z;d8 ;`&X Q8 '9+N *N ;1"$8 Z6 ;2 *R aE8 O6;$Q O;C[B"R :

*4;&;N ;CZ%F2 OZ8\. “x”3“y”5“z”:

AxesLable à { “x” , “y” , “z” }

*D;x0c2 O;CZ%F2 7$;


64/101

64


65/101

65

D8Z%0E6 +N %()'bBK8+. D8Z%0E6 &%K6;$Q Z;B#NO+@$6*( Q8ListPlot3D)m;TIZ8 *$8ZX [EZ O8+N!MN *E Z6 Z86(3

ContourPlot3D)+BA02 *E lN;I Q8+I Z86%


66/101

66

SetDirectory[ “ +v& 6Z%2 +B#2 “]

7Bn +B#2 Z6 U$;K [$+/& Z;R *N 8Z Z%0E6 P$8 +.8'2 +B9 aE8 +$Q DZ%= *N *R w+K6%d:

sx& +B#2 \ Wolfram Research \ Mathematica \ 5.1

3-U$;K 6;1$8 O8+N 8Z +$Q Z%0E6gif 4;& ;N'2 Z;R *N 8%cV6 Q8!&8 5[$+N: Export[ “ U$;K 4;& . gif “ , *$8ZX 4;& , ImageSize à { +$%xI :%~ , +$%xI w+) } ]

*0b&:'&%"R +B#2 [B&8!N *b&8 O8+NMathematicaZ%0E6 Q8 a#BkDirectory[]'2 6;T0E8[B"R .

V;g2 Y8%") *NZ6 OQ;E o+F02 Q8 ' Mathematica 5*N+$Q D8Z%0E6!B"R *>%I:

i = 0 ;

Do [ i = i +1 ; g[ i ]=Plot[ Sin[ x – 2 t ] , { x , 0 , 10 Pi }] , { t , 0 , 3 , 0.1 } ] ;

n = i ;

gg = Table[ g[ i ] , { i , 1 , n } ] ;

SetDirectory [ “ C : \ Documents and Settings \ All Users \ Application Data \ Mathematica “ ]

Export[ “wave.gif “ , gg , ImageSize à { 100 , 350 } ]

f;J*! 4 gV


67/101

67

Animate [ graphic[t , u] , {t , t1 , t2 } , {u , u1 , u2 } ]

DZ;/) P$8 Z6graphic[t , u]+028Z;n 56 *N *0#N85 *R 'C8%cV6 'bBK8+. +x") +C !&8%I '2t5u!d;N 3aE8.

Z%0E6AnimateO8Z86OptionQ8 !"IZ;/) ;C YX Q8 '9+N *R aE8 O6;$Q O;C:

*P-B PBBMI)xD8Z;/) Q8 'b$ !&8%I '2Forward3Backward;$ForwardBackward!d;N: (

AnimationDirection à x

*P-B


68/101

68

1%2+6%734

Mathematica 5.1:


69/101

69


70/101

70


71/101

71

i lNZ%0E6 ;N Y8%I[[ ]]YX *N;C8!Bn 'E+0E6

6+R .

Q8 OZ;B#N Z6{8%> UB#&8+T$6 DS6;M2'(B(FIi$+=aE8 Z8%d6 Z;B#N YX */E;F2 *b"$8 ;$ 5 6Z8!& 6%>536Z8%2 P$8 Z6

!d !C8%9 4QS O6!) O;C %5Z Q8 6;T0E8.


72/101

72

**V6;M2 L$ O6!) {8%> Y6Z5X aE!N O8+NOQ+2 ;$ *BV58 ^$8+d ;N +028Z;n Y5!N UB#&8+T$6Z%0E6 Q8 + c-2 NDSolve

'2 6;T0E86%d3aE8 +$Q DZ%= *N Z%0E6 P$8 '(R Ubd:

NDSolve[ { *V6;M21 , *V6;M22 , … , "+d1 , "+d2 , … } , {y1[x] ,y2[x] , … } , {x , a, b } ]

3Z%0E6 P$8Q;N Z6 O6!) DZ%= *N 8Z 'V%.'2 ;2+. *V6;M2 5 +@"$!$5+d *V6;M2 3 ehnS *V6;M2 3 ]%2 *V6;M2 L$?BK Z6 'W?> UB#&8+T$6 DS6;M2 P$+0 UB#&8+T$6 DS6;M2 UJ O8+NDSolve5NDSolve'2 6;T0E8 +$Q DZ%= *N6%d:

DSolve[ { UB#&8+T$6 *V6;M2 , OQ+2 ;$ *BV58 ̂ $8+d } , y , { x1 , x2 , … }]

NDSolve[ { UB#&8+T$6 *V6;M2 , ;$ *BV58 ̂ $8+dOQ+2 } , y , { x1 , a1 , b1 } , { x2 , a2 , b2 } , …]


73/101

73

UBj0#2 sMb2 +N8 Z6 8Z *V6;M2 456 Z%0E6a1 < x1 < b13a2 < x2 < b25....!"R '2 UJ O6!) DZ%= *N.

*56 UH0#2 O;C+BA02 68!MI +.86!)!d;N3{8%>*V6;M2'2 8Z6+R [EZ +$Q Z%0E6 ^E%I Y8%I )'>5+9Z%0E6 NDSolve

+BA02 Z6Solution+B9!daE8(:

Plot3D[ Evaluate [ y[x1,x2] / . Solution ] , { x1 , a1 ,b1 } , { x2 , a2 , b2 }]

*'2 UB#&8+T$6 DS6;M2 UJ O8+N5 *$Z%K U$!/I 3 ehnS U$!/I 3 '&8%I O+E %5Z Q8 Y8%I...O8+N 3 6+R 6;T0E8 ?B&s#R

+0-BN D;)h~8UB#&8+T$6 DS6;M2 UJ O;C %5Z 6Z%2Z6*NHelpZ8?K8 4+&!B"R *M>8+2.


74/101

74



75/101

75


76/101

76

/2E A

CoordinateSystem

* A02 7$;


77/101

77

*D;x0c2 [0#BE L$ O;C+BA02 65!J 7$;


78/101

78

*OZ86+N Y8!B2 56 '>Z;9 {+_ */E;F2F5G'&%"R D;x0c2 [0#BE Z6:

CrossProduct[ F , G ]

*OZ86+N Y8!B2 56 '>Z;9 {+_ */E;F2F5GD;x0c2 [0#BE L$ Z6:

CrossProduct[ F , G , D;x0c2 ;@0E6 4;& ]

**E {+_ */E;F2OZ86+N Y8!B2 *E +V;bE8 *&;. F5G5H'&%"R D;x0c2 [0#BE Z6:

ScalarTripleProduct[ F , G , H ]

**E {+_ */E;F2OZ86+N Y8!B2 *E +V;bE8 *&;. F5G5HD;x0c2 [0#BE L$ Z6:

ScalarTripleProduct[ F , G , H , D;x0c2 ;@0E6 4;& ]

*+V;bE8 Y8!B2 Y;$68+. */E;F2f '&%"R D;x0c2 ;@0E6 Z6:

Grad[ f ]

*+V;bE8 Y8!B2 Y;$68+. */E;F2f D;x0c2 ;@0E6 L$ Z6:

Grad[ f , D;x0c2 ;@0E6 4;& ]

*+V;bE8 Y8!B2 PBEhnS */E;F2f '&%"R D;x0c2 ;@0E6 Z6:

Laplacian[ f ]

*+V;bE8 Y8!B2 PBEhnS */E;F2f D;x0c2 ;@0E6 L$ Z6:

Laplacian[ f , D;x0c2 ;@0E6 4;& ]

*OZ86+N Y8!B2 p&8•Z%$6 */E;F2F'&%"R D;x0c2 ;@0E6 Z6:

Div[ F ]

*OZ86+N Y8!B2 p&8•Z%$6 */E;F2FD;x0c2 ;@0E6 L$ Z6:

Div[ F , D;x0c2 ;@0E6 4;& ]


79/101

79

*:+R */E;F2)5;I(OZ86+N Y8!B2F'&%"R D;x0c2 ;@0E6 Z6:

Curl [ F ]

*:+R */E;F2)5;I(OZ86+N Y8!B2FD;x0c2 ;@0E6 L$ Z6:

Curl [ F , D;x0c2 ;@0E6 4;& ]

*OZ86+N Y8!B2 PBEhnS */E;F2F'&%"R D;x0c2 ;@0E6 Z6:

Laplacian [ F ]

*OZ86+N Y8!B2 PBEhnS */E;F2FD;x0c2 ;@0E6 L$ Z6:

Laplacian [ F , D;x0c2 ;@0E6 4;& ]

/2E /(1 h&"


80/101

80

*O!MN *E OZ86+N Y8!B2 [EZ:

-Z6Mathematica 5:


81/101

81



82/101

82


83/101

83


84/101

84

I(D,(J!2(!k/

686 ;N Z;R D8Z%0E6 Q8 O68!MI 7cN P$8 Z6Y;BN 8Z ;C'2[B"R .+0-BN D;)h~8 Y!$6 O8+NOZ;2X O;CZ;R *N "%N+2*NHelp

Z8?K8 4+&!B"R m%>Z.3;C 686 ;N Z;R O8+NY8%I '2;C YX L$ a#BV L$ Z6 8ZO!MN)Z86+N(O8+N OZ;2X D8Z%0E6 Q8 5 686 Z8+,

6%d 6;T0E8 ;C 686 a#BV:

686 a#BV 4;&;C = { 6861 , 6862 , … , n 686 }

OZ;2X D8Z%0E6 Q8 '9+NMathematicaQ8 !"IZ;/):

*686 [


85/101

85

Variance[ 4;&686 a#BV;C ]

*686 Z;BM2 r8+F&8 */E;F2;C:

StandardDeviation[ 686 a#BV 4;&;C ]

*oZ;`k */E;F2q48:

Quantile[ 686 a#BV 4;&;C , q ]

*686 Y6+R sI+2;C:

Sort[ 686 a#BV 4;&;C ]

*686 [EZ;C:

ListPlot[ 686 a#BV 4;&;C , Options ]

(ZI:Q8Option[`2 O;CZ%0E6ListPlot6Z8%2 *N Y8%I '26+R Z;d8 +$Q:

PlotStyle à PointSize[n]

PlotRange à { { xmin , xmax} , { ymin , ymax} }

*O8+NFit8%cV6 Z86%


86/101

86



87/101

87


88/101

88


89/101

89

-[=3@ !(@;E

(1;*! *Z6 *2;&+N P0d%& O8+NMathematica[BE;"-N 8Z ;`&X m%& 5 ;C+/A02 !$;N 8!0N8.'T(0c2 m8%&8 O8Z86 8%0F2 4;FV Q8 ;C+BA02

Ug2Integer 3Real3Complex3String3Graphic3List 5...'2!"d;N.'2 [C 6+NZ;R Q%J 4;FV Q8 8Z ;C+BA02*N Y8%I

6+R [B#HI *0E6 56:

1-/3)*3) /&,3L[(!:'2 y$+MI O6;) Z%~ *N ;C+BA02 P$8!d *09;"d *2;&+N UR Z6 5 !&%d!&8.

2-1


90/101

90

1-'&;EZ Y8%I)^(

2-[B#H& 5 {+_* )5( /

3-G$+TI5 l+)5-(

**jN8Z O;C+@((

-+0bk%R )=(

-O5;#2+0bk%R )


91/101

91

(1;*! E -1#2&"$! 4 /2&lB=(C %5Z;C+BA02 *N 'C6Z8!H2 5 OZ8\@$;> O;C)+@( +@$6 %5Z !"k

Q8 !"IZ;/):

-i ++:7$8?K8 pni!J85 Q8!&8 *N.

-i - -:7C;R pni!J85 Q8!&8 *N.

-++ i:7$8?K8 7Bni!J85 Q8!&8 *N.

-- - i:7C;R 7Bni!J85 Q8!&8 *N.

-i += a:7$8?K8iQ8!&8 *Na.

-i - = a:7C;R iQ8!&8 *Na.

-i *= a:U$!BIi*Ni*a.

-i /=a:U$!/Ii*Ni /a.

%5Z Z6 C; &%K O37Bn Z67$8?K8)7C;R (7$8?K8 +BA02 8!0N8)7C;R ('2 E 5 !N;$'2 */E;F2 6Z85 pq 6%d3pn Z6 'V5

7$8?K8)7C;R (*/E;F2 6Z85 +BA02 8!0N8pqE !d7$8?K8)7C;R ('2!N;$.

(1 =&2k

*$8ZX Q8 'b$ ;C[`2 +=;")6+NZ;R+n 5*2;&+N Z6'#$%&'$;1&X Q8 5 !"0#Ca#BV *N "%N+2 7cN Z6 *R p$+I;2 5 ;C6Z%2 ;C

0K+. Z8+, 'EZ+N[B"R '2 OZ866%9 ;C YX 6Z%2Z6 |FN Q8 ;1"$8 Z6 3!&8 * .

(1 '# n4;M 4 #424 *2;&+N Q8 '9+N Z6686 ]5+9 5 65Z5 *N Q;B& ;C;C3!d;N '2)]5+9 5 65Z5 6Z%2Z6;C 686;NQ8 6;T0E8U$;K;CO!MN 7cN Z6

a/F=!d !C8%9(.P$+05+9 68!)8 O!"N

'2 Q;B& DZ%= Z6 *R 6Z86 6%>56+R m%>Z ;`&X *N Y8%I.


92/101

92

-6;*?o /(12(*M(, '2 *R Z%j&;86%d:

Which[ "+d1 , Z%0E61 , "+d2 , Z%0E62 , … ]

*Z;09;ESwitch:Z8!H2 8!0N8'2 */E;F2 8Z DZ;/)'2 *#$;H2 ;C 4+K ;N !MN !"R + 3;"02 Z8!H2 ad86 '&8%c


93/101

93

O8+N Z8+bI Z;09;EZ+b2 4;1&8 (5 'V+0"R D8Z%0E6 '9+NQ8 6Z%2 56 *R P$+0


94/101

94

*2868 Z6!"kZ%0E6+@$6 [`238ZaE8 Pb8 Y;b28 Z%0E6 P$8n'2 *B&; * !C6'2 y,%02 8Z YX !-bN :%~ +0-BN Z%0E6 O8+>8 +.8 5!"R :

TimeConstrained[ D8Z%0E6 ;$ Z%0E6 , n]

*;I ;`&X Q;B& 6Z%2 *vK;J *R 'I8Z%0E6 O8+>8 Y;b28 Z%0E6 P$8n'2 8Z !d;N a$;N5 !C6+. *&'2 y,%02 8Z Z%0E6 O8+>8!"R :

MemoryConstrained[ D8Z%0E6 ;$ Z%0E6 , n]


95/101

95



96/101

96


97/101

97


98/101

98

(1 '# n4;M 4 #424

!&8 !d +B9 '"02 U$;K L$ Z6 *R [B"R Z;R '$;C 686 O5Z [$Z86 Q;B& 6Z8%2 '9+N Z6)*2;&+N L$ '>5+9 !&8%I '2 U$;K P$8

!d;N 'I;/E;F2.(

*N ;C 686 65Z5 O8+NMathematicaZ%0E6 Q8Import'2 6;T0E86%d) .686 Y6+R 6Z85 O8+N Z%0E6 P$8 '(R aV;J Z6;C

U$;K m8%&8 Q8*N ;CMathematica'2 Z8+, 6;T0E8 6Z%26+B. .(Z%0E6 Z6ImportU$;K 4;& !$;N8+ ;C!""R8!> ;N Z8Tab.

P$8 ;27cN;N 8ZQ8 6;T0E86;E :;g2 L$Z6Mathematica 5 I'2 iB_% [BC6.'"02 U$;K !B"R w+K4;& *N O8

FreeFall.txt686 O5;J *R [$Z86Q 6Z%2Z6 '$;C' L$ Y;b2 5 a)+E 3 Y;2'2'2 4;1&8 68QX "%HE *R !d;N!C6.


99/101

99

Z6 U$;K P$8 +.8Desktop3!d;N !d +B9 +I%Bq2;R 686 Y6+R 6Z85 O8+NO;CYX ^BF2 Z6Mathematica3D8Z%0E6 Q8

'2 6;T0E8 +$Q[B0R :

SetDirectory[ “C:\Documents and Settings\Administrator\Desktop” ]

x = Import[ “FreeFall.txt” , “Table” ]

686 65Z5 %F&8Z ;C“Table”686 Z8+,+BA02 ;I [$8x*$8ZX L$ DZ%= *N)*/I+2 ;N O!MN56 ;1"$8 Z621×3(!d;N.+=;")x

'2 8Z^E%I Y8%Ix[[i , j ]]*R 0 < i < 2250 < j < 4686 Y;-&.[$Z86 hg2:

x[[1,1]]=”Time” , x[[3,3]]=0.049000

Z%0E6 ;NDimensions[ x ]'26;MN8 *N Y8%I*$8ZX x)65!Ji5 j(6+R 8!Bn 'E+0E6.'2 :;JO5Z 'C8%cV6 D;B(


100/101

100



101/101

Date post:	07-Aug-2018
Category:	Documents
Upload:	mohammad
View:	217 times
Download:	0 times