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MATHEMATICAL METHODS IN PHYSICS, VOLUME I

This book aims to develop methods for solving mathematical problems that primarily address Physics – as "Mathematics is the language of Physics" – but also a plethora of other natural sciences. The topics presented here cover fundamental areas of Mathematics, such as: theory of functions of a complex variable, theory of linear vector spaces, development of functions in complete systems (Fourier series, classical polynomials, etc.), basic elements of algebra and operator representation, study of some simple eigenvalue problems, Fourier and Laplace integral transforms and their applications, and finally, the study of the coordinate systems in which the Laplace operator is divided and applications in solving differential equations with partial derivatives. Each chapter is accompanied by a variety of examples and exercises.

The presentation of the methods, balanced between mathematical rigor and intuitive understanding, aims not only at solving certain categories of physical problems but, mainly, at developing general techniques that will be used in a wide variety of applications.

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