Description
The material covered in this ebook includes intermediate topics in linear algebra, tensors,
curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace
transforms, differential equations, Dirac delta-functions, and solutions to Laplace’s
equation. In addition, we introduce the more advanced topics of contravariance and covariance in nonorthogonal systems, multi-valued complex functions described with
branch cuts and Riemann sheets, the method of steepest descent, and group theory.
These topics are presented in a unique way, with a generous use of illustrations and graphs and an informal writing style, so that students at the junior level can grasp and understand them. Throughout the text we attempt to strike a healthy balance between mathematical completeness and readability by keeping the number of formal proofs and theorems to a minimum. Applications for solving real, physical problems are stressed. There are many examples throughout the text and exercises for the students at the end of each chapter.
Unlike many text books that cover these topics, we have used an organization that is fundamentally pedagogical. We consider the book to be primarily a teaching tool, although we have attempted to also make it acceptable as a reference.
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