You are here: Introduction > Description
Description
Mathgrapher is a FREE mathematical graphing tool for 2D and 3D functions and data. It includes
linear and nonlinear curve fitting, integration and analysis of coupled ordinary differential equations (ODE's)
and multidimensional iterative maps, matrix operations, Lindenmayer systems and some cellular automata.
MathGrapher ranks between graphical calculators and fullfledged mathematical tools like Mathematica.
It is powerfull, easy to use and will probably meet your demands, and its free!.
Mathgrapher contains a large number of demonstrations showing you step by step how the results shown in this website are produced.
You are invited to download a fully functional version of Mathgrapher.
Install Mathgrapher, start the Demonstrations and see what Mathgrapher can do for you.
Functions in 2D and 3D
MathGrapher is a graphical calculator for functions of the form F(x) and F(x,y)
containing up to 20 subfunctions. Many special functions are included. Cartesian as well as polar coordinates can be
chosen and functions can be represented in patametrized form (2D). F(x,y) can be represented in 2D and 3D
by Shaded surfaces, Contour plots and Crosssections through Contourplots. In the 3D viewer you may rapidly vary the
viewing angle, distance and shading of the 3D surface using your mouse.
Data in 2D and 3D
Edit and draw graphs of your 2D or 3D Data. Just select the Data in one of the Data grids and push the Draw button.
3D surfaces can be previewed in the 3D viewer (OpenGL). Shaded surfaces, Contour plots and
Crosssections through Contour plots can be drawn in same way as 3D Functions.
Some statistical tests (Chisquared and KolmogorovSmirnov) are included.
Curve fitting (linear and nonlinear)
A number of least squares curve fitting methods can be selected:
You may choose the general and powerfull (nonlinear) LevenbergMarquardt method to fit your data to
any continuous function you define. You may fit your data to a number of predefined functions such as
e.g. linear regression, polynomials, trigonometric polynomials or cubic splines. Finally you may fit the data
to a linear combination of Functions and Data sets provided by you.
Iterations
Calculate algebraic series or study iterative multidimensional maps. Several mathematical tools are
available to analyse the results (zie ODE's below): draw orbits, calculte power spectra,
bifurcation diagrams, Lyapunov exponents.
Ordinary Differential Equations (ODE's)
The evolution of dynamical systems in physics, chemistry, electronics, economics and population dynamics can often
be described with a set of coupled ODE's. Mathgrapher uses an
accurate AdamsBashforth variable order, variable step predictorcorrector algorithm to
integrate systems of up to 20 coupled ODE's. Several tools are available to analyse the
results of the integrations (and iterations) such as: Graph of the time evolution,
Projections in 2 or 3 dimensions, Phase portraits, Surfaces of Section, Power spectrum, Equilibrium points,
Lyapunov exponents.
Matrices
The most important matrix operations can be performed: addition, multiplication, tranposition, inversion,
solution of AX=B, calculation of eigenvalues, eigenvectors and determinants.
Lindenmayer systems
Experiment with iterative string rewriting methods (sometimes called turtle graphics) as
investigated by Lindenmayer.
Cellular Automata
Experiment with 1D and 2D cellular automata such as the Game of Life.
