This book presents mathematical methods and tools which are useful for physicists and engineers: response functions, Kramers-Kronig relations, Green's functions, saddle point approximation. The derivations emphasize the underlying physical arguments and interpretations without any loss of rigor. General introductions describe the main features of the methods, while connections and analogies between a priori different problems are discussed. They are completed by detailed applications in many topics including electromagnetism, hydrodynamics, statistical physics, quantum mechanics, etc. Exercises are also proposed, and their solutions are sketched. A self-contained reading of the book is favored by avoiding too technical derivations, and by providing a short presentation of important tools in the appendices. It is addressed to undergraduate and graduate students in physics, but it can also be used by teachers, researchers and engineers.

Suitable for advanced undergraduate and graduate students, this new textbook contains an introduction to the mathematical concepts used in physics and engineering. The entire book is unique in that it draws upon applications from physics, rather than mathematical examples, to ensure students are fully equipped with the tools they need. This approach prepares the reader for advanced topics, such as quantum mechanics and general relativity, while offering examples, problems, and insights into classical physics. The book is also distinctive in the coverage it devotes to modelling, and to oft-neglected topics such as Green's functions.

Having the right answer doesn't guarantee understanding. This book helps physics students learn to take an informed and intuitive approach to solving problems. It assists undergraduates in developing their skills and provides them with grounding in important mathematical methods.Starting with a review of basic mathematics, the author presents a thorough analysis of infinite series, complex algebra, differential equations, and Fourier series. Succeeding chapters explore vector spaces, operators and matrices, multi-variable and vector calculus, partial differential equations, numerical and complex analysis, and tensors. Additional topics include complex variables, Fourier analysis, the calculus of variations, and densities and distributions. An excellent math reference guide, this volume is also a helpful companion for physics students as they work through their assignments.

This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the reader has an adequate preparation in general physics and calculus. The book bridges the gap between an introductory physics course and more advanced courses in classical mechanics, electricity and magnetism, quantum mechanics, and thermal and statistical physics. The text contains a large number of worked examples to illustrate the mathematical techniques developed and to show their relevance to physics. The book is designed primarily for undergraduate physics majors, but could also be used by students in other subjects, such as engineering, astronomy and mathematics.

Mathematics plays a fundamental role in the formulation of physical theories. This textbook provides a self-contained and rigorous presentation of the main mathematical tools needed in many fields of Physics, both classical and quantum. It covers topics treated in mathematics courses for final-year undergraduate and graduate physics programmes, including complex function: distributions, Fourier analysis, linear operators, Hilbert spaces and eigenvalue problems. The different topics are organised into two main parts — complex analysis and vector spaces — in order to stress how seemingly different mathematical tools, for instance the Fourier transform, eigenvalue problems or special functions, are all deeply interconnected. Also contained within each chapter are fully worked examples, problems and detailed solutions. A companion volume covering more advanced topics that enlarge and deepen those treated here is also available.

This book provides a self-contained and rigorous presentation of the main mathematical tools needed to approach many courses at the last year of undergraduate in Physics and MSc programs, from Electromagnetism to Quantum Mechanics. It complements A Guide to Mathematical Methods for Physicists with advanced topics and physical applications. The different arguments are organised in three main sections: Complex Analysis, Differential Equations and Hilbert Spaces, covering most of the standard mathematical method tools in modern physics.One of the purposes of the book is to show how seemingly different mathematical tools like, for instance, Fourier transforms, eigenvalue problems, special functions and so on, are all deeply interconnected. It contains a large number of examples, problems and detailed solutions, emphasising the main purpose of relating concrete physical examples with more formal mathematical aspects.