Applied Mathematical Methods in Theoretical Physics || Singular Integral Equations of the Cauchy Type

✍ Scribed by Masujima, Michio

• Publisher: Wiley-VCH Verlag GmbH & Co. KGaA
• Year: 2009
• Tongue: German
• Weight: 205 KB
• Edition: 2
• Category: Article
• ISBN: 352740936X
• DOI: 10.1002/9783527627745.ch6

✦ Synopsis

All there is to know about functional analysis, integral equations and calculus of variations in one handy volume, written for the specific needs of physicists and applied mathematicians.

The new edition of this handbook starts with a short introduction to functional analysis, including a review of complex analysis, before continuing a systematic discussion of different types of integral equations. After a few remarks on the historical development, the second part provides 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 a wealth of problems and examples, often with a physical background. He provides outlines of the solutions for each problem, while detailed solutions are also given, supplementing the materials discussed in the main text. The problems can be solved by directly applying the method illustrated in the main text, and difficult problems are accompanied by a citation of the original references.

Highly recommended as a textbook for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference or self-study guide.

From the contents:

• Function Spaces, Linear Operators and Green's Functions

  • Integral Equations and Green's Functions

    • Integral Equations of the Volterra Type

      • Integral Equations of the Fredholm Type

        • Hilbert-Schmidt Theory of Symmetric Kernel

          • Singular Integral Equations of the Cauchy Type

            • Wiener-Hopf Method and the Wiener-Hopf Integral Equation

              • Non-linear Integral Equations

                • Calculus of Variations: Fundamentals

                  • Calculus of Variations: Applications