This document contains some basic Mathematica commands to get you started
plus some more sophisticated commands.

I. Some basic Mathematica commands:

  math                       to start Mathematica on ubunix (a linux command)
  Quit                       stops Mathematica on ubunix
                               All Mathematica commands start with capital letter

 enter key                   tells Mathematica to execute a command
  or shift-enter
  ^                          power,  e.g.  5^7
  *                          product, e.g. 5*7
                               note: a space can also be used 5 7
  Pi                         3.14...  Note the capital letter
  E                          2.718... Note the capital letter


  Plot[expr,{x,a,b}]         Plot expr from a to b (x is the variable)
  Log[expr]                  ln of the expression 
  Exp[expr]                  E^expr
  Sin[expr]
  ArcSin[expr]               note the capital S
  D[expr, x]                 derivative of expression with respect to the variable  x 
  Integrate[expr, x]         integral of expr with respect to variable x
  Integrate[expr, {x,a,b}]   definite integral from a to b--two periods between a and  b
  Simplify[expr]             simplifies the expression
  Factor[poly]               factors a polynomial
  FactorInteger[n]
  Expand[expr]               multiplies out
  Apart[expr]                the partial fraction expansion of expr
  expr//N                    numerical value
  N[expr, n]                 numerical value of expr to n decimal places 
  NSolve[expr1==expr2]       numerical solution of expr1 = expr2
  %                          results of the previous computation (not necessarily the previous line)
  name := expr               assigns the expr to name
                               note the colon
                               note that no result is printed out
  name                       prints out whatever has been assigned to name
  name = .                   unassigns name

  Series[expr,{x,a,n}]       finds series up to n-1 power of x-a
  Normal[series]             converts a series to a polynomial 

Examples of these commands:

> D[Sin[Exp[5 x^2]],x]

               2           2
            5 x         5 x
Out[1]= 10 E     x Cos[E    ]

> Integrate[x^3, x]

          4
        x
Out[2]= --
        4

> Integrate[E^x, {x,0,1}]

                              -1 + E

> Simplify[Log[E^3]]

                                  3

> N[Pi]

                             3.14159

> N[Pi,30]

                3.14159265358979323846264338328

> Apart[1/(1 - x^2)]
            -1           1
Out[7]= ---------- + ---------
        2 (-1 + x)   2 (1 + x)

> Factor[1-x^3]

                             2
Out[8]= -((-1 + x) (1 + x + x ))

> Expand[%]

             3
Out[9]= 1 - x

> term := 3 - x

> term

                            3 - x

> term^2

                                    3 2
                              (1 - x )

> ans := 'ans';

                              ans := ans

==============================================================================

II. More sophisticated commands

------------------------------------------------------------------------------

To construct a table:

Table[expr in terms of n,{n,begin,end, stepsize}]
  note square brackets for Table, curly brackets for n values
  stepsize is optional; if omitted then it is 1

Table[n^2,{n,2,8}]
Out[12]= {4, 9, 16, 25, 36, 49, 64}