This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been

PARTⅠ: Getting Started 1. Foundations of Matrix Analysis 2. Principles of Numerical Mathematics PARTⅡ: Numerical Linear Algebra 3. Direct Methods for the Solution of Linear Systems 4. Iterative Methoed for Solving Linear Systems 5. Approximation of Eigenvalues and Eigenvectors PARTⅢ: Around Functions and Functionals 6. Rootfinding for Nonlinear Equations 7. Nonlinear Systems and Numerical Optimization 8. Polynomial Interpolation 9. Numerical Integration PARTⅣ: Transforms, Differentiation and Problem Discretization 10. Orthogonal Polynomials in Approximation Theory 11. Numerical Solution of Ordinary Differential Equations 12. Two-Point Boundary Value Problems 13. Parabolic and Hyperbolic Initial Boundary Value Problems

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