Advanced Textbooks in Physics: A Guide to Mathematical Methods for Physicists (ePub)

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.Contents: Complex Analysis:IntroductionMapping Properties of Holomorphic FunctionsLaplace TransformAsymptotic ExpansionsDifferential Equations:IntroductionThe Cauchy Problem for Differential EquationsBoundary Value ProblemsGreen FunctionsPower Series MethodsHilbert Spaces:IntroductionCompact Operators and Integral EquationsHilbert Spaces and Quantum MechanicsAppendices:Review of Basic ConceptsSolutions of the ExercisesReadership: Students and professionals in the field.Mathematical Methods0Key Features:This book treats the chosen topics in depth, always keeping in mind physical applications and practical aspectsThe book contains many examples and exercises with solutions. This is of course of practical use for the students, and it is also meant to stress the main purpose of relating concrete physical examples with more formal mathematical aspects