MAS.864
The
Nature of Mathematical Modeling
Neil
Gershenfeld
Surveys the range of levels of description useful for the mathematical description of real and virtual worlds, including: analytical solutions and approximations for difference and differential equations; finite difference, finite element and cellular automata numerical models; and stochastic processes, nonlinear function fitting and observational model inference. Emphasis on efficient practical implementation of these ideas.
A bouncing ball in many languages
Java Applet with sound | link |
Java Application with more physics | link |
Open GL 3D version | link |
X-Windows version running from a Unix server | link |
Postscript file to print | link |
Max/MSP with real-time sound synthesis | link |
Ordinary Differential Equations
A simple Harmonic Oscillator : Euler, Runge-Kutta and Numerov methods | link |
Fourth-order Runge-Kutta algorithm and Adaptative Variable Stepper | link |
Partial Differential Equations
Waves : a damped string model in a Java Applet | link |
Diffusion : a model in one dimension | link |
Cellular Automata and Lattice Gases
HPP and FHP Models of Gases or Fluids | link |
Random Systems & Random Number Generators
Random Walker in one dimension | link |
Transforms
Inverse Discrete Wavelet Transformation | link |
Optimization & Search
Simulated Annealing | link |
Genetic Algorithm | link |
Clustering and Density Estimation
Cluster-Weighted Modeling | link |
Final class project
Modelization of the Mathematics for a Parametric EQ (dropped idea) | link |
Modelization of the Noise of Acoustic Instruments | link |