Symmetry and Separation of Variables

Erscheinungsjahr 2011
ISBN: 978-0-521-30224-1
Verlag: Cambridge University Press

Buch, Englisch, Band 4, 318 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 796 g

Reihe: Encyclopedia of Mathematics and its Applications

Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.

Autoren/Hrsg.

Miller, Willard

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Editor's statement; Section editor's statement; Preface; 1. The Helmholtz equation; 2. The Schrödinger and heat equations; 3. The three-variable Helmholtz and Laplace equations; 4. The wave equation; 5. The hypergeometric function and its generalizations; Appendices; References; Index.