All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook starts with a short introduction to functional analysis, including a review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of the Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations.
After a few remarks on the historical development, the second part gives an introduction to the calculus of Variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory.
Throughout the book, the author presents over 150 problems and exercises. Detailed solutions are give, supplementing the material discussed in the main text, allowing problems to be solved by making direct use of the method illustrated. The result is a complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians.
Intended for senior undergraduates and first-year graduates in science and engineering, this textbook is equally useful as reference and self-study guide.
Applied Mathematical Methods in Theoretical Physics
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