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

I. Some basic Maple commands:

  maple                      to start Maple on acsu
  quit;                      stops Maple on acsu--note the semi-colon

  ^                          power,  e.g.  5^7
  *                          product, e.g. 5*7
  Pi                         3.14...  Note the capital letter

  ln(expr)
  exp(expr)                  Note that  e is entered as exp(1) in Maple
  sin(expr)
  arcsin(expr)
  diff(expr, x);             derivative of expression with respect to the variable  x 
  int(expr, x);              integral of expr with respect to variable x
  int(expr, x = a..b);       definite integral from a to b--two periods between a and  b
  simplify(expr);            simplifies the expression
  factor(expr);              factors the expression
  expand(expr);              multiplies out
  convert(expr,parfrac,x);   the partial fraction expansion of expr
  evalf(expr);               give numerical value of the expression
  %                          the previous computation (not necessarily the previous line)
  name := expr;              assigns the expr to name
  name := 'name';            unassigns name

  solve(expr = 0, x);        solves the expression for x
  fsolve(expr = 0, x);       solves numerically the expression for x

Examples of these commands:

> diff(sin(exp(5*x^2)),x);

                                  2            2
                    10 cos(exp(5 x )) x exp(5 x )

> int(x^3, x);

                                     4
                                1/4 x

> int(exp(x), x = 0..1);

                              exp(1) - 1

> simplify(ln(exp(3)));

                                  3

> evalf(Pi);

                             3.141592654

> convert(1/(1 - x^2),parfrac,x);

                               1           1
                       - 1/2 ----- + 1/2 -----
                             x - 1       x + 1

> factor(1-x^3);

                                   2
                        -(x - 1) (x  + x + 1)

> expand(%);

                                     3
                                1 - x

> ans := ";

                                        3
                            ans := 1 - x

> ans^2;

                                    3 2
                              (1 - x )

> ans := 'ans';

                              ans := ans

> solve(x^2 - 3*x + 2 = 0, x);
 
			      2, 1

> fsolve(x^3 + x - 3 = 0, x);
 
			    1.213411663

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

II. More sophisticated commands

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

To construct a table:

  for n from a to b by stepsize do expr(n) end do;

    Note: stepsize could be 0.1, for example

> for x from 0 to 1 by .1 do {x,x^2 - 3*x + 1} end do;
> 

                                {0, 1}


                              {.1, .71}


                              {.2, .44}


                              {.3, .19}


                              {.4, -.04}


                              {.5, -.25}


                              {.6, -.44}


                              {.7, -.61}


                              {.8, -.76}


                              {.9, -.89}


                             {1.0, -1.00}

To define a function:

  f := x -> expr;  (defines a function of one variable x)

  f := (x,y) -> expr; (defines a function of two variables x & y

Examples:

> f := x -> sqrt(x + 1);

> f(3);
       2

> f := (x,y) -> sqrt(x^2 + y^2);
				
> f(3,4);
         5

To apply a function to a list of values:

> seq(f(x),x=[a_1,a_2,a_3,a_4]);

Note: put evalf around whole expression above to get numerical values:

> evalf(seq(f(x),x=[a_1,a_2,a_3,a_4]));