Petrini M. A Guide To Mathematical Methods For Physicists...Solutions 2018

Textbook in PDF format

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 functions, distributions, Fourier analysis, linear operators, Hilbert spaces and eigenvalue problems. The different topics are organised into two main parts: Complex Analysis and Functional Spaces in order to stress how seemingly different mathematical tools, for instance the Fourier transform, eigenvalue problems or special functions, are all deeply interconnected.
This book originates from lectures given at the Ecole Normale Superieure and the Universite Pierre et Marie Curie in Paris, the University of Milano-Bicocca and the University of Rome Tor Vergata, and takes an intermediate approach. It keeps a rigorous mathematical level, but it uses examples to illustrate the general theory rather than showing long and complicated proofs. For the topics that involve advanced functional analysis, like the theory of linear operators in Hilbert spaces, we have emphasised the physicist point of view in spite of generality, with an eye to quantum mechanics. Each chapter contains fully worked-out exercises. Together with the examples, they are a central part of the book and illustrate the general theory. There are about 150 exercises with solutions. They range from very simple and basic exercises, which the readers are invited to solve by themselves, to more difficult or theoretical ones, denoted with a star. The latter sometimes provide proofs of theorems given in the main text.
Readership: Students of undergraduate mathematics and postgraduate students of physics or engineering