Numerical Mathematics

The purpose of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties and to demonstrate their performances on examples and counterexamples. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified using the MATLAB software environment. Each chapter contains examples, exercises and applications of the theory discussed to the solution of real-life problems. While addressed to senior undergraduates and graduates in engineering, mathematics, physics and computer sciences, this text is also valuable for researchers and users of scientific computing in a large variety of professional fields.

Contenu

Preface Part I: Getting Started 1. Foundations of Matrix Analysis 2. Principles of Numerical Mathematics Part II. Numerical Linear Algebra 3. Direct Methods for the Solution of Linear Systems 4. Iterative Methods for Solving Linear Systems 5. Approximation of Eigenvalues and Eigenvectors Part III: Around Functions and Functionals 6. Rootfinding for Nonlinear Equations 7. Nonlinear Systems and Numerical Optimization 8. Polynomial Interpolation 9. Numerical Integration Part IV: 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 References Index of MATLAB Programs Index