A Guided Tour of Mathematical Methods

In this book mathematics for university students is presented in an integrated fashion with its applications in the physical sciences. In this way the mathematical insights acquired are driven by physical insight. The material is presented as a set of problems, many of which are playful and applied in character.

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Mathematical methods are essential tools for all physical scientists. This novel textbook provides a comprehensive guided tour of the mathematical knowledge and techniques needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are very well integrated. In this way the mathematical insights that the students acquire are driven by their physical insight. Topics that are covered include vector calculus (div, grad, curl, Laplacian), linear algebra, Fourier analysis, scale analysis, Green's functions, normal modes, tensor calculus and perturbation theory. This book can be used by undergraduates or by lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. This guided tour of mathematical techniques is instructive, applied, and even fun.