Preface 1. Solving Equations 2. Systems of Equations 3. Interpolation 4. Least Squares 5. Numerical Differentiation and Integration 6. Ordinary Differential Equations 7. Boundary Value Problems 8. Partial Differential Equations 9. Random Numbers and Applications 10. Trigonometric Interpolation and the FFT 11. Compression 12. Eigenvalues and Singular Values References

Chapter 0 (optional) provides students with the fundamental building blocks they will need in later chapters. The entire text is designed to move from elementary ideas to more sophisticated concepts to avoid sudden jumps in level.Spotlights throughout the text highlight the five major ideas of numerical analysis—convergence, complexity, conditioning, compression, and orthogonality. These spotlights comment on the topic at hand and make informal connections to other expressions of the same concept elsewhere in the book, helping students synthesise new material with what they already know.Reality Checks appear in each chapter to provide extended examples of the way numerical methods lead to solutions of important technological problems, making the topics immediately relevant.MATLAB® expositions appear throughout the text, giving students and instructors guidance on using this important software tool.Appendix B is a short MATLAB tutorial that can be used as a first introduction to students who have not used MATLAB, or as a reference to students already familiar with the software.

Coverage updates include: Chapter 2: Expansion of topics in the second half of the chapter. Cholesky factorization (section 2.6.2) is new, along with preconditioning techniques for iterative methods (section 2.6.4)Chapter 4: Added topics include the Modified Gram-Schmidt method (4.3.2), Levenberg-Marquardt optimization (4.5.3), and the GMRES method for solving linear systems (4.4).Chapter 8: New section 8.4 on nonlinear PDEs.MATLAB® code updates keep this text current with recent MATLAB changes.Improved exposition and examples throughout the text were based on feedback from reviewers and users.Significant content updates by section: 0.5: New figure illustrating the calculus refresher.1.5: New example with figure on Failure of Newton Method.2.6: Completely revised section on symmetric matrices; new subsection on Cholesky method; new subsection on Preconditioning.2.7: Revised subsection on Broyden's Method.Reality Check 2: Completely revised with new emphasis on clamped-free beam, i.e. diving board.3.2.2: New proof of Newton form of interpolating polynomial.4.3: New figure for Gram-Schmidt orthogonalizaton.4.3.2: New subsection on Modified Gram-Schmidt.4.4: New section on GMRES method.4.5.3: New subsection on Levenberg-Marquardt method.8.1: Two added figures, new examples of reaction-diffusion equations8.3: Revised bookkeeping system for 2-dimensional elliptic equations; revised Finite Element Method presentation with added figures.8.4: New section on nonlinear PDEs.Appendix B: Updated MATLAB function handling, added description on making QuickTime files.