Table of Content

1. Getting Started.
2. Rootfinding.
3. Systems of Equations.
4. Eigenvalues and Eigenvectors.
5. Interpolation and Curve Fitting.
6. Numerical Differentiation and Integration.
7. Numerical Methods for Initial Value Problems of Ordinary Differential Equations.
8. Second-Order One-Dimensional Two-Point Boundary Value Problems.
9. Finite Difference Method for Elliptic Partial Differential Equations.
10. Finite Difference Method for Parabolic Partial Differential Equations.
11. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation.

Salient Features

• A theme of comparing/ contrasting numerical methods for accuracy, error, boundaries, and speed of convergence
• Chapters organized thematically around mathematical problems—Each chapter is devoted to a single type of problem. Within each chapter, the presentation begins with the simplest, most basic methods and progresses gradually to more advanced topics.
• Exercise Sets—Features roughly 1000 numbered exercises (many with multiple parts). An appropriate balance of theoretical, applications, and coding questions.