Table of contents : Cover Front Matter 1. Numerical Approximation of Model Partial Differential Equations 2. Nonlinear Differential Equations: Application to Chemical Kinetics 3. Fourier Approximation 4. Polynomial Approximation 5. Solving an Advection–Diffusion Equation by a Finite Element Method 6. Solving a Differential Equation by a Legendre Spectral Method 7. High-order finite difference methods 8. Signal Processing: Multiresolution Analysis 9. Elasticity: Elastic Deformation of a Thin Plate 10. Domain Decomposition Using a Schwarz Method 11. Geometrical Design: Bézier Curves and Surfaces 12. Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem 13. Optimization Applied to Model Fitting 14. Thermal Engineering: Optimization of an Industrial Furnace 15. Fluid Dynamics: Solving the 2D Navier–Stokes Equations Back Matter