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Mathematical Methods in the Physical Sciences, 3rd Edition

Mary L. Boas

ISBN: 978-1-118-04888-7 July 2018 864 Pages


Now in its third edition, Mathematical Concepts in the Physical Sciences, 3rd Edition provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

This book is intended for students who have had a two-semester or three-semester introductory calculus course.  Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering.  Students are given sufficient depth to gain a solid foundation (this is not a recipe book).  At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics.  The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.

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Chapter 1 Infinite Series, Power Series
Chapter 2 Complex Numbers
Chapter 3 Linear Algebra
Chapter 4 Partial Differentiation
Chapter 5 Multiple Integrals
Chapter 6 Vector Analysis
Chapter 7 Fourier Series and Transforms
Chapter 8 Ordinary Differential Equations
Chapter 9 Calculus of Variations
Chapter 10 Tensor Analysis
Chapter 11 Special Functions
Chapter 12 Legendre, Bessel, Hermite, and Laguerre functions
Chapter 13 Partial Differential Equations
Chapter 14 Functions of a Complex Variable
Chapter 15 Probability and Statistics
* Matrix diagonalization has been moved from Ch. 10 to Ch. 3 and the treatment of tensors in Ch. 10 has been expanded.

* Ch. 3 also includes more detail on linear vector spaces. The discussion of basis function is continued in Ch. 7 (Fourier Series), Ch. 8 (Differential Equations), Ch. 12 (Series Solutions) , and Chapter 13 (Partial Differential Equations).

* Fourier integrals have been moved to Ch. 7 (Fourier Series). The Laplace transform and an expanded treatment of the Dirac delta function have been moved to Ch. 8 (Differential Equations).

* Throughout the book, the usefulness and also the pitfall of computer algebra systems are pointed out.

“Bottom line: a good choice for a first methods course for physics majors. Serious students will want to follow this with specialized math courses in some of these topics.”  (MAA Reviews, 13 November 2015)