The Classical Theory of Integral Equations: A Concise Treatment

ISBN-13: 9780817683481 / Angielski / Twarda / 2012 / 344 str.

Stephen M. Zemyan

Opis

The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter;Thorough discussions of the analytical methods used to solve many types of integral equations;An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations;Over 80 illustrative examples that are explained in meticulous detail;
Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts;
Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.

Recenzje

From the reviews:

"The textbook under review is a concise introduction to the classical theory of integral equations. The textbook is written for an advanced undergraduate student or an early graduate student; it is essentially self-contained. Comprehensive examples are presented that reinforce underlying theories and illustrate computational procedures. The textbook consists of eight chapters and two appendices ... . Each chapter begins with a section titled 'Tools of the trade' that contains all the necessary prerequisites. ... Each section ends with a list of 5-15 exercises." (Alexei Yu. Karlovich, Mathematical Reviews, April, 2013)

"This book covers the classical theory of linear, scalar Fredholm and Volterra equations. ... All chapters include numerous simple examples ... . useful for engineering students wishing to learn the fundamentals of integral equation theory." (Stig-Olof Londen, zbMATH, Vol. 1270, 2013)

Spis treści

Preface.- Introduction.- Fredholm Integral Equations of the Second Kind (Separable Kernel).- Fredholm Integral Equations of the Second Kind (General Kernel).- Volterra Integral Equations.- Differential and Integrodifferential Equations.- Nonlinear Integral Equations.- Singular Integral Equations.- Systems of Integral Equations.- Appendix A 2010 Mathematics Subject Classification 45-XX Integral Equations.- Appendix B Specialized Vocabularies and Sample Translations.- Bibliography.- Index.