1 INTRODUCTION

• 1.1 About this course
  • 1.1.1 Motivation
  • 1.1.2 How to study
  
  
• 1.2 Differential Equations
  • 1.2.1 Ordinary differential equations
  • 1.2.2 Partial differential equations
  • 1.2.3 Boundary / initial conditions
  • 1.2.4 Characteristics and dispersion relations
  • 1.2.5 Moments and conservation laws
  
  
• 1.3 Prototype problems
  • 1.3.1 Advection
  • 1.3.2 Diffusion
  • 1.3.3 Dispersion
  • 1.3.4 Wave-breaking
  • 1.3.5 Schrödinger
  
  
• 1.4 Numerical discretization
  • 1.4.1 Convergence, Richardson extrapolation
  • 1.4.2 Sampling on a regular grid
  • 1.4.3 Finite elements
  • 1.4.4 Splines
  • 1.4.5 Harmonic functions
  • 1.4.6 Wavelets
  • 1.4.7 Sampling with quasi-particles
  
  
• 1.5 Computer quiz
• 1.6 Exercises
• 1.7 Further reading
• 1.8 Interactive evaluation form