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Boundary value problems play a significant role in modeling systems characterized by established conditions at their boundaries. On the other hand, initial value problems hold paramount importance in comprehending dynamic processes and foreseeing future behaviors. The fusion of these two types of problems yields profound insights into the intricacies of the conduct exhibited by many physical and mathematical systems regulated by linear partial differential equations. Boundary Value Problems for Linear Partial Differential Equations provides students with the opportunity to understand and exercise the benefits of this fusion, equipping them with realistic, practical tools to study solvable linear models of electromagnetism, fluid dynamics, geophysics, optics, thermodynamics and specifically, quantum mechanics. Emphasis is devoted to motivating the use of these methods by means of concrete examples taken from physical models.
The subject matter of this book has been taught for several years as a semester course at the undergraduate level Physics curriculum of the Physics Faculty at Complutense University of Madrid. The book has evolved from a set of lecture notes that we have been preparing for the last 20 years.
Features
No prerequisites apart from knowledge of differential and integral calculus and ordinary differential equations.
Provides students with practical tools and applications.
Contains numerous examples and exercises to help readers understand the concepts discussed in the book.
Preface.
About the authors.
Introduction.
Linear PDEs.
Separation of Variables Method.
Symmetric Differential Operators.
Fourier Analysis.
Eigenfunction Expansion Method.
Special Functions.
Cylindrical and Spherical BVPs.
Bibliography.
Subject Index.
Index of Capsule Biographies