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Full Description
Numerical mathematics proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations.
This book provides the mathematical foundations of numerical methods and demonstrate 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. The attention to applications and software development makes it valuable also for users in a wide variety of professional fields.
In this second edition, 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 added.
Contents
Series Preface.- Preface.- I Getting Started.- 1. Foundations of Matrix Analysis.- 2 Principles of Numerical Mathematics.- 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.- III Around Functions and Functionals.- 6 Rootfinding for Nonlinear Equations.- 7 Nonlinear Systems and Numerical Optimization.- 8 Polynomial Interpolation.- 9 Numerical Integration.- 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.
