Methods of Mathematical Physics (vol. 1)

Description

Since the first volume of this work came out in Germany in 1924, this book, together with its second 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 second and final revision of 1953.

This book is a welcome translation of the second edition of the well known "Methoden der mathematischen Physik'' [Springer, Berlin, 1931]. The text covers the following subjects: linear transformations and quadratic forms, development of arbitrary functions in series of orthogonal functions, linear integral equations, calculus of variations, eigenvalue and vibration problems, application of variational calculus to eigenvalue problems, and special functions, as in the German original. The main additions are an interesting appendix by W. Magnus, treating the transformation of linearly independent spherical harmonics in three variables under a rotation of the coordinate system and a paragraph entitled "Reciprocal quadratic variational problems'' (chapter 4, §\S11, pp. 252–257), which amplifies the discussion of upper and lower bounds of quadratic functionals and Friedrichs' analysis of Trefftz's method given in §\S9 (in this connection, a remark of J. B. Diaz and A. Weinstein [J. Math. Physics 26, 133–136 (1947); MR0022458] seems to have been overlooked). Reviewed by J. B. Diaz

Ibragimov's Practical Course cites this.