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Part I. Ordinary Differential Eqations: 1. Euler's method and beyond 2. Multistep methods 3. Runge-Kutta methods 4. Stiff equations 5. Error control 6. Nonlinear algebraic systems Part II. The Possion Equation: 7. Finite difference schemes 8. The finite element method 9. Gaussian elimination for sparse linear equations 10. Iterative methods for sparse linear equations 11. Multigrid techniques 12. Fast Poisson solvers Part III. Partial Differential Equations of Evolution: 13. The diffusion equation 14. Hyperbolic equations Appendix: a bluffer's guide to useful mathematics.