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Mathematical analysis of physical problems. Corrected reprint of the 1972 original. (English) Zbl 1092.00501

Mineola, NY: Dover Publications (ISBN 0-486-64676-9). xix, 616 p. (1984).
This book will be generally useful to students of theoretical or mathematical physics. In his preface the author makes the underlying philosophy of his approach quite clear: it is not a book on mathematics per se, and therefore not a rigorous treatise. Although mathematical structures (such as linear vector spaces) are featured, at all times the mathematics is subservient to the physics, insofar as it is comprehended at any given time. Thus mathematical modelling uses mathematics as a tool to describe the physical (or biological, or economic, etc.) world around us. This is not, therefore, a book for the budding applied mathematician who (according to the reviewer’s definition of that subject) would wish to see something of the mathematical structure present in a model (“distilled” from the “real world”) for its own sake.
The book is well-organized, and there is a prelude to each chapter which outlines the topics contained within the chapter, and the mathematical background assumed. There is no treatment of group theory, perhaps more of an omission now than when the book was first published. Contents include chapters on the vibrating string, linear vector spaces, the potential equation, Fourier and Laplace transforms (and applications, including considerable detail on special functions), wave propagation/scattering, diffusion problems, probability/stochastic processes, and quantum mechanics (including many-body problems).

MSC:

00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
00A69 General applied mathematics

Citations:

Zbl 1092.00500
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