Numerical Approximation Methods

This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques.

Focuses on the methods and algorithms of computation Addresses concrete applications in science and engineering Includes plenty of illustrated examples, with separate index table for quick access Includes supplementary material: sn.pub/extras

Klappentext

This book presents numerical approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well-known methods, it contains a collection of non-standard approximation techniques that appear in the literature but are not otherwise well known. This text also contains original methods developed by the author. It includes an extensive treatment of approximate solutions to various types of integral equations. Examples are used extensively to illustrate the theory. Problems at the end of the chapters are provided for practice.

The book is suitable as a textbook or as a reference for students taking a course in numerical methods. Researchers in need of approximation methods in their work will also find this book useful.

Inhalt
Preface. -1 INTERPOLATION and CURVE FITTING. -2 ZEROS of a FUNCTION. -3 SERIES. -4 INTEGRATION. -5 DETERMINANTS and MATRICES. -6 ORDINARY FIRST ORDER DIFFERENTIAL EQUATIONS. -7 ORDINARY SECOND ORDER DIFFERENTIAL EQUATIONS. -8 PARTIAL DIFFERENTIAL EQUATIONS. -9 LINEAR INTEGRAL EQUATIONS IN ONE VARIABLE. -APPENDIX 1 PADE APPROXIMANTS. -APPENDIX 2 INFINITE SERIES CONVERGENCE TESTS. -APPENDIX 3 GAMMA and BETA FUNCTIONS. -APPENDIX 4 PROPERTIES OF DETERMINANTS. -APPENDIX 5 PROOF OF THE SINGULARITY OF A MATRIX. References. -INDEX.