A student's guide to Fourier transforms

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Charles F. Stevens

The Six Core Theories of Modern Physics reviews all the key areas of physics in one place. It provides a brief, clear, and self-contained summary of the basic theoretical structures of classical mechanics, electricity and magnetism, quantum mechanics, statistical physics, special relativity, and quantum field theory. In addition, the mathematics required for these areas is conveniently summarized in the initial chapter. Advanced undergraduates or beginning graduate students can use The Six Core Theories of Modern Physics as a supplement to the standard texts or for an unclutterred, succinct review of the key areas. Professionals in such quantitative sciences as chemistry, engineering, computer science, applied mathematics, and biophysics who need to brush up on the essentials of a particular area will find most of the required background material, including the mathematics. Chapters may be read in any order, although the order in which they appear indicates roughly their level of difficulty and the extent to which a particular chapter depends on knowledge and sophistication gained in preceding ones. Each chapter consists of a main part, which gives the core theory, and optional sections which are more advanced and specialized.

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P.L. Christiansen, M.P. Sørensen, A.C. Scott, (eds

Nonlinear science is by now a well established field of research at the interface of many traditional disciplines and draws on the theoretical concepts developed in physics and mathematics. The present volume gathers the contributions of leading scientists to give the state of the art in many areas strongly influenced by nonlinear research, such as superconduction, optics, lattice dynamics, biology and biomolecular dynamics. While this volume is primarily intended for researchers working in the field care, has been taken that it will also be of benefit to graduate students or nonexpert scientist wishing to familiarize themselves with the current status of research.

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E.N. Economou

The main part of this book is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and boundlevel information. The bound-level treatment gives a clear physical understanding of "difficult" questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book.

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Michael Stone and Paul Goldbart

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics.