Software
Maxima
http://maxima.sourceforge.io/
- designed primarily for *symbolic* computations
- similar functionality as Maple or Wolfram Mathematica
- typical problems:
[DEMO] :
derivatives and antiderivatives (primitive functions),
limits, Taylor / Laurent expansions, partial fractions,
residues, simplifications / expansions of expressions
(polynomials, rational functions, trigonometric functions),
matrix and vector calculations
- ODE problems:
[DEMO] :
linear equation with constant coefficients and given initial conditions;
matrix exponential; Laplace transform and its inverse
- the plotdf command will plot the 2d phase picture with specific orbits.
- Maxima can also plot various 2d or 3d objects
(see e.g. a tutorial [pdf]) or export the formulas in LaTex or console form
(see the commands tex or grind).
Octave
http://octave.org
- designed primarily for *numeric* computations
- similar (and largely compatible) to Matlab
- typical problems: numerical integration, matrix calculations
- pictures and orbits can be computed / plotted
-
simple graphs [DEMO];
numerical solutions to ODEs [DEMO];
numerical methods [DEMO];
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