Mathematics for the physical sciences
This nicely written text is based on lecture notes for courses in mathematical methods the author taught to undergraduate and graduate students over a period of more than thirty years. Professor Copley recalls that suggestion to write a book came from students in one of the courses back in 1982, but only retirement in 2005 ``finally removed professional distractions and slow but steady progress ensued.'' The fact that the text was intended for students in physical sciences shaped essentially the content which focuses on topics frequently used in physics courses or by physicists.NEWLINENEWLINEThe text contains a good deal of theoretical material; proofs of theorems are sometimes included in the text. The author classifies exposition as ``educational'' in the sense that only the proofs that provide ``some insight into how to apply the theory'' have been selected. Therefore, ``the (rigorous) proof of Cauchy's theorem is excluded but the proofs of its many corollaries are included.'' There are many carefully explained examples in the text but, unfortunately, no exercises for the independent study are provided.NEWLINENEWLINEThere are thirteen chapters in the book. It starts with the fundamentals of complex analysis (Cauchy's theorem and related results, calculus of residues, dispersion representations, analytic continuation). Then asymptotic expansions and Padé approximations are discussed, followed by the basic facts from transforms theory (trigonometric and Fourier series, Fourier and Laplace transforms). The topics covered in the final part of the text include linear ordinary differential equations, special functions, integral equations, fundamentals of partial differential equations, and solution of nonhomogeneous boundary value problems`for partial differential equations by using Green's functions.NEWLINENEWLINEThe book collects under one cover a good wealth of useful information related to applications of mathematics in physical sciences; the fact that it can be freely downloaded in pdf format chapter by chapter makes it a very attractive reference for students and professionals.
scientific article; zbMATH DE number 6353480