Mathematica Quick Reference

Extracted by Lyle Long (PSU Aerospace Eng.) from a Mathimatica notebook tutorial, written by Chris Duffy (PSU Civil Eng.)

To Start

math or mathematica (notebooks) (typed at the Unix command prompt)

To Stop

Quit (typed at the Mathematica command prompt)

Parentheses and Brackets & Misc

( ) groups objects, ie (a+b)/(c+d)

[ ] function arguments, ie Sin[x]

{ } list elements { 1.2, 2.0, 3.0 }

% refers to previous output line

%% refers to second previous output line

Clear [ x ]

Equal Signs

x = y set x = y right now

x == y test whether x and y are equal

x := y set delayed

Help

?Plot gives help on Plot

??Plot gives detailed help on Plot

Simple Arithmetic

(2.389 + 8.21)*(12^2 + 4 - 7)

2 Pi / 3

E^(I Pi)

N[E^(I Pi)]

Plotting

Plot[ Cos[x], { x , -3 Pi, 3 Pi }]

Plot3D[ x^2 + y^2, {x,-10,10}, {y,-10,10}]

ContourPlot[ x^2+y^2, {x,-10,10}, {y,-10,10}]

Plot [ { f[x], g[x]}, { x, -3, 3} ]

ParametricPlot[{Cos[2 x], Sin[2 x]}, {t, 0, 2 Pi}]

Display [ "file.dat", Out[3] ]

Symbolic Algebra

Expand [ (x+y) ( x^2 - x y + y^2 )]

Factor [ x^3 + y^3 ]

Simplify [ (x+y) ( x^2 - x y + y^2)]

Apart [ (a x + b) / ( (x-r) (x-s) ) ]

Together [ a/b + c/d ]

Numerator [ ( a + b ) / ( c + d ) ]

Denominator [ ( a + b ) / ( c + d ) ]

Cancel [ x ]

Functions

f[x_,y_] := x^2 + y^2 + Sin[x]

f[1,2]

Equations

Solve [ a x^2 + b x + c == 0, x]

Solve [ a x + b y == f, c x - d y == g},{x,y}]

FindRoot [ x^3 + x^2 + x + 1 == 0, {x,1}]

Sums and Series

Sum [ x^i / i! , {i,0,5}]

Series [ Sin[x], {x,0,7} ]

Complex Numbers

z = ( 4 + I ) / ( 1 - I )

Re[ z ]

Im [ z ]

Abs [ z ]

Conjugate [ z ]

Solve [ x^4 + x == 0, x ]

Differentiation

D [ x^3, x ], first derivative

D [ x^3, {x, 2} ], second derivative

D [ Exp [ x^2 + y^2 ] , x ], partial derivative

f [ x_ ] := x / ( x^2 + 1 )

f ' [x]

D [ f[x], x ]

Integration

Integrate [ Sin[ x + pi ], x ]

Integrate [ Sin[ x + pi ], {x, -Pi, Pi} ]

Integrate [ x^2 + y^2, x, y ]

Matrices

A = { {1, 0, 2}, {7, 1, 6}, {9, 1, 3} }

Inverse [ A ]

Transpose [ A ]

Det [ A ]

B = { 1, 2, -1 }

LinearSolve [ A, B ]

x = Inverse[ A ].B

A.x

Differential Equations

DSolve [ { y'[t] + y[t] == 1, y[0]==0}, y[t],t]

NDSolve [ { y'[t] + y[t] == 1, y[0]==0},y[t],{t,0,5}]

Saving and Reading

Save [ "file.dat", A, B, x, Out[3] ]

Display [ "file.dat", % ], where % is graphics

Read [ "file.dat" ]

Dump [ "file.dat" ]

Write [ "file.dat", Out[1], Out[2] ]

Packages

On Suns:

$Path=Join[$Path, {"/tmp_mnt/usr/apps/mathematica2.2/Packages/"}]

On IBM RS/6000:

$Path=Join[$Path, {"/usr/local/math/Packages/"}]

On SGI's:

$Path=Join[$Path, {"/tmp_mnt/usr/local/math/Packages/"}]

<<Trigonometry.m

<<VectorAnalysis.m

etc.

Common Functions

Abs

Erf

Exp

Sqrt

Sign

Log

Prime

Mod

N[Pi, 100]

Trigonometry

ArcCos

ArcCosh

ArcCot

ArcSec

ArcSin

ArcSinh

ArcTanh

ArcTan

Cos

Cosh

Coth

Csc

Csch

Sec

Sech

Sin

Sinh

Tan

Tanh