A Guide to Mathematical Methods for Physicists

With Problems and Solutions

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.

Contents:

• Complex Analysis:

  • Holomorphic Functions
  • Integration
  • Taylor and Laurent Series
  • Residues

• Functional Spaces:

  • Vector Spaces
  • Spaces of Functions
  • Distributions
  • Fourier Analysis
  • Linear Operators in Hilbert Spaces I: The Finite-Dimensional Case
  • Linear Operators in Hilbert Spaces II: The Infinite-Dimensional Case

• Appendices:

  • Complex Numbers, Series and Integrals
  • Solutions of the Exercises

Readership: Students of undergraduate mathematics and postgraduate students of physics or engineering.
Key Features:

• Chosen topics are treated in depth, always keeping in mind physical applications and practical aspects
• Contains many examples and exercises with solutions for practical use for the students, emphasizing the main purpose of relating concrete physical examples with more formal mathematical aspects