Mathematical Tools for Physicists, 2nd Edition

The new edition is significantly updated and expanded.
This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized.
While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Table of Contents

Part I: Probability
Chapter 1 Stochastic Processes
Chapter 2 Monte-Carlo Methods
Chapter 3 Stochastic Differential Equations

Part II: Discrete Mathematics, Geometry, Topology
Chapter 4 Graph and Network Theory
Chapter 5 Group Theory
Chapter 6 Algebraic Topology
Chapter 7 Special Functions
Chapter 8 Computer Algebra
Chapter 9 Differentiable Manifolds
Chapter 10 Topics in Differential Geometry

Part III: Analysis
Chapter 11 Dynamical Systems
Chapter 12 Perturbation Methods
Chapter 13 Functional Analysis
Chapter 14 Numerical Analysis
Chapter 15 Mathematical Transformations
Chapter 16 Partial Differential Equations
Chapter 17 Calculus of Variations