About
Enhanced solving of easier exercises from mathematical analysis (aimed at the difficulty level of freshmen students at the Faculty of Mathematics and Physics of the Charles University in Prague, Czech Republic). Written in Python as a Sagemath's module. Features investigations descriptive investigation of a realvalued function
 general properties (odd, even, periodic, constant)
 properties of 1st derivative (stationary points, increasing/decreasing intervals)
 properties of 2nd derivative (inflection points, convex/concave intervals)
 asymptotes (horizontal, vertical & oblique, with explained calculation)
 rendering the plot (with tangents at inflection points & autozoom option)
 two output formats  textbased (console/notebook) & LaTeXbased (pdf document  example)
Versions Todo  undefined further causes of undefinition: negative arguments of square roots (and their fourth, sixth root analogies...), arcsin & arccos arguments...
 stationary_points stationary points for xvalues where 1st derivative is not defined
 inflection_points dtto
 asymptotes verify proper functionality of periodical (vertical) asymptotes  e. g. in tan(x)
 monotonicity
 either improve splitting points by adding
stationary_points where 1st derivative is undefined  or find better way to locate these intervals (preferably using
solve that will find intervals of positive/negative 1st derivative)
 curvature dtto
 investigations
 simplify complex formulae of points for rendering in the plot (see TODO example in the docstring via
investigations? )
 betatests of periodical (vertical) asymptotes' rendering
 more comprehensible comments/documentation for autozoom feature
 tex_list linewrapping of long formulae (or when there are simply too many of them, as well)
 tex_investigations
 more detailed stepbystep explanations (see TODO part in the docstring via
tex_investigations? )  use of temporary files for LaTeX's source code (instead of fixed "/tmp/SageAlphaOut.tex")
 option for deleting such a temporary file
 texie other altenative versions (e. g. with Acrobat Reader, Evince...)
 further functionalities  e. g.:
 stepbystep solving of simpler integrals
 convergence/divergence of easier power series (with tutorials on which criteria to use)
 multidimensional stuff (implicit functions, Hessians, Lagrangians, ...)
 ...

Updating...
Karel Ha, Sep 24, 2012, 1:40 PM
Ċ Karel Ha, Sep 23, 2012, 5:46 AM
