Contents

• 1 INTRODUCTION
  • 1.1 About this course
  • 1.2 Differential Equations
  • 1.3 Prototype problems
  • 1.4 Numerical discretization
  • 1.5 Computer quiz
  • 1.6 Exercises
  • 1.7 Further reading
  • 1.8 Interactive evaluation form
  
  
• 2 FINITE DIFFERENCES
  • 2.1 Explicit 2 levels
  • 2.2 Explicit 3 levels
  • 2.3 Lax-Wendroff
  • 2.4 Leap-frog, staggered grids
  • 2.5 Implicit Crank-Nicholson
  • 2.6 Computer quiz
  • 2.7 Exercises
  • 2.8 Further reading
  • 2.9 Interactive evaluation form
  
  
• 3 FINITE ELEMENT METHOD
  • 3.1 Mathematical background
  • 3.2 An engineer's formulation
  • 3.3 Numerical quadrature
  • 3.4 Implementation and solution
  • 3.5 Linear solvers
  • 3.6 Variational inequalities
  • 3.7 Computer quiz
  • 3.8 Exercises
  • 3.9 Further Reading
  • 3.10 Interactive evaluation form
  
  
• 4 FOURIER TRANSFORM
  • 4.1 FFT with the computer
  • 4.2 Linear equations.
  • 4.3 Aliasing, filters and convolution.
  • 4.4 Non-linear equations.
  • 4.5 Computer quiz
  • 4.6 Exercises
  • 4.7 Further Reading
  • 4.8 Interactive evaluation form
  
  
• 5 MONTE-CARLO METHOD
  • 5.1 Monte Carlo integration
  • 5.2 Stochastic theory
  • 5.3 Particle orbits
  • 5.4 A scheme for the advection diffusion equation
  • 5.5 When should you use Monte Carlo methods?
  • 5.6 Computer quiz
  • 5.7 Exercises
  • 5.8 Further Reading
  • 5.9 Interactive evaluation form
  
  
• 6 LAGRANGIAN METHOD
  • 6.1 Splitting advection from the rest
  • 6.2 Cubic-Interpolated Propagation (CIP)
  • 6.3 Non-Linear equations with CIP
  • 6.4 Quiz
  • 6.5 Exercises
  • 6.6 Further Reading
  • 6.7 Interactive evaluation form
  
  
• 7 WAVELETS
  • 7.1 Remain a matter of research
  
  
• 8 THE JBONE USER MANUAL
  • 8.1 Source code & installation
  • 8.2 Program execution
  • 8.3 Program structure & documentation
  • 8.4 An object-oriented example: Monte Carlo in JBONE
  • 8.5 Interactive evaluation form
  
  
• 9 PROBLEM BASED LEARNING ENVIRONEMENT
  • 9.1 Typesetting with TEX
  • 9.2 Programming in JAVA
  • 9.3 Parameters and switches in HTML
  • 9.4 Interactive evaluation form
  
  
• 10 COURSE EVALUATION AND PROJECTS
  • 10.1 Interactive evaluation form
  • 10.2 Suggestions for one-week projects