Problems And Methods In Mathematical Physics

This book is the second edition, whose original mission was to offer a new approach for students wishing to better understand the mathematical tenets that underlie the study of physics. This mission is retained in this book. The structure of the book is one that keeps pedagogical principles in mind at every level. Not only are the chapters sequenced in such a way as to guide the reader down a clear path that stretches throughout the book, but all individual sections and subsections are also laid out so that the material they address becomes progressively more complex along with the reader's ability to comprehend it. This book not only improves upon the first in many details, but it also fills in some gaps that were left open by this and other books on similar topics. The 350 problems presented here are accompanied by answers which now include a greater amount of detail and additional guidance for arriving at the solutions. In this way, the mathematical underpinnings of the relevant physics topics are made as easy to absorb as possible.

The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.

This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.

Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences.

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.