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 |