## 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 multi-dimensional iterative maps, matrix operations, Lindenmayer systems and some cellular automata. MathGrapher ranks between graphical calculators and full-fledged 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 Cross-sections 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 Cross-sections through Contour plots can be drawn in same way as 3D Functions. Some statistical tests (Chi-squared and Kolmogorov-Smirnov) are included.

## Curve fitting (linear and non-linear)

A number of least squares curve fitting methods can be selected:

You may choose the general and powerfull (non-linear) Levenberg-Marquardt 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 multi-dimensional 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 Adams-Bashforth variable order, variable step predictor-corrector 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.