[seanhunter]

One thing I would add for people who are new to this is you can do

??something; to get the internal help. So say I want to know how to solve ODEs in maxima, do

??ode; …and you’ll get help. It generally does a search and presents a numbered list of options and you’ll want to type a number and a semicolon.

[seanhunter]

Some other useful things:

1)solve to solve a system and “variable: expression” will assign that expression to that variable. You can then substitute the results into a later expression using a “,”. So you might do

   solns:solve([x+3*y=5,5*x-2*y=4],[x,y]);
   z:%e^(x,y),solns;

That will solve the system and then substitute those solutions into the expression for z.

2)pi, e, and the imaginary unit are called %pi, %e and %i respectively.

3)The symbolic solver is a lot less powerful than mathematica but you can do

   load(“to_poly_solve”);

To get a polynomial solver that will at least get you all the roots of polynomials and does better on most trigonometric equations.

   load(“drawdf”);

Is useful for drawing vector fields, phase portraits and that type of thing.

4) you can use a single quote to delay evaluation of something. Like say you want to write a differential equation and you don’t want it to actually try to evaluate the derivative inline, you can write something like

   osc:‘diff(x,t,2) + r*’diff(x,t) + k*x = p*cos(omega\*t);

…for a forced harmonic oscilator. Or whatever. This is useful if you want to mess with the expression a bit before you try to solve the expression (eg doing substitutions or whatnot).*