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.

Review

"This book is intended for students, physicists or engineers, from the second or third year of their bachelor s degree. It differs from most of its competitors by the uncompromising rigour of mathematical processing, oriented more towards understanding and applications, rather than on the development of the theory itself. Thus, the more technical demonstrations are omitted or even dismissed in problems." -- Review of Scientific Questions

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