James G. Uber

Lecture notes & References

HW & exams

Algs. & Links

Ex. Problems

Review

• lecture 1 - vector fields & sketching solutions
• lecture 2 - linear algebra and calculus

Intro. to Numerical Methods

• lecture 3 - Intro. to Simulink
• lecture 4 - Simulink Tutorial
• lecture 5 - Runge-Kutta

Dynamical Systems Stability

• lecture 6 - 1-D linear stability analysis
• lecture 7 - higher-order linear stability analysis
• lecture 8 - Dimensional Analysis

Biological Growth Dynamics

• lecture 9 - CSTR Biological Growth/Substrate Util. Model
  handout
• lecture 10 - Linear Stability Analysis
  handout
• CSTR Biological Growth with Recycle Model Handout

Parameter Estimation

• Introduction
• Numerical Methods
• Interpreting the estimates
• Chlorine Dynamics Estimation Handout
  • M-Files

Space-Time (PDEs)

• 1-D Advective-Dispersive Model
• Method of Finite Differences

Space-Time (Discrete-Time)

• Cellular Automata
• Sorting and MIxing
  • M-Files
• Predator-Prey
•  
• Analysis of Bistable Behavior
• Fishing Dynamics Handout
• Bistability in Chemical Reaction Dynamics Handout 1
• Bistability in Chemical Reaction Dyanimcs Handout 2

Take Home

• Statement
• Data

Sample Examinations

• Mid-Term 99
• Final 99

Matlab

• Simple Prog.
  • input
  • analyze.m
  • isitstable.m
  • maxeig.m
• Linear systems
  • ploteig.m
  • plotsolution.m
  • linode.m
• Documentation
• Getting Started
• ode45
• ode file
• ode set
• optim set

Strogatz

• Chapter 2
• Chapter 3