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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 that are now formally collected as well as original methods developed by the author that do not appear in the literature.
This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text.
The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriatefor students taking courses in numerical approximation techniques.
List of contents
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.
Summary
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 that are now formally collected as well as original methods developed by the author that do not appear in the literature.
This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text.
The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriatefor students taking courses in numerical approximation techniques.
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From the reviews:
“This book is appropriate as a text for a course in computational methods as well as a reference for researchers who need such methods in their work. This book presents numerical approximation techniques for solving various types of mathematical problems that cannot be solved analytically. … This text also contains original methods developed by the author. Examples are used extensively to illustrate the theory.” (Michael M. Pahirya, Zentralblatt MATH, Vol. 1228, 2012)
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From the reviews:
"This book is appropriate as a text for a course in computational methods as well as a reference for researchers who need such methods in their work. This book presents numerical approximation techniques for solving various types of mathematical problems that cannot be solved analytically. ... This text also contains original methods developed by the author. Examples are used extensively to illustrate the theory." (Michael M. Pahirya, Zentralblatt MATH, Vol. 1228, 2012)
