Mathematical Methods for Physicists

7th Edition

A Comprehensive Guide

Authors: George Arfken Hans Weber Frank E. Harris
Hardcover ISBN: 9780123846549
eBook ISBN: 9780123846556
Imprint: Academic Press
Published Date: 17th January 2012
Page Count: 1220
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Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.

Key Features

  • Revised and updated version of the leading text in mathematical physics
  • Focuses on problem-solving skills and active learning, offering numerous chapter problems
  • Clearly identified definitions, theorems, and proofs promote clarity and understanding

New to this edition:

  • Improved modular chapters
  • New up-to-date examples
  • More intuitive explanations


Graduate students and advanced undergraduates in Physics, Engineering, Applied Mathematics, Chemistry, and Environmental Science/Geophysics; also practitioners and researchers in these fields.

Table of Contents

  • Preface
    • To the Student
    • What’s New
    • Pathways through the Material
    • Acknowledgments
  • Chapter 1. Mathematical Preliminaries
    • 1.1 Infinite Series
    • 1.2 Series of Functions
    • 1.3 Binomial Theorem
    • 1.4 Mathematical Induction
    • 1.5 Operations on Series Expansions of Functions
    • 1.6 Some Important Series
    • 1.7 Vectors
    • 1.8 Complex Numbers and Functions
    • 1.9 Derivatives and Extrema
    • 1.10 Evaluation of Integrals
    • 1.11 Dirac Delta Function
    • Additional Readings
  • Chapter 2. Determinants and Matrices
    • 2.1 Determinants
    • 2.2 Matrices
    • Additional Readings
  • Chapter 3. Vector Analysis
    • 3.1 Review of Basic Properties
    • 3.2 Vectors in 3-D Space
    • 3.3 Coordinate Transformations
    • 3.4 Rotations in ℝ3
    • 3.5 Differential Vector Operators
    • 3.6 Differential Vector Operators: Further Properties
    • 3.7 Vector Integration
    • 3.8 Integral Theorems
    • 3.9 Potential Theory
    • 3.10 Curvilinear Coordinates
    • Additional Readings
  • Chapter 4. Tensors and Differential Forms
    • 4.1 Tensor Analysis
    • 4.2 Pseudotensors, Dual Tensors
    • 4.3 Tensors in General Coordinates
    • 4.4 Jacobians
    • 4.5 Differential Forms
    • 4.6 Differentiating Forms
    • 4.7 Integrating Forms
    • Additional Readings
  • Chapter 5. Vector Spaces
    • 5.1 Vectors in Function Spaces
    • 5.2 Gram-Schmidt Orthogonalization
    • 5.3 Operators
    • 5.4 Self-Adjoint Operators
    • 5.5 Unitary Operators
    • 5.6 Transformations of Operators
    • 5.7 Invariants
    • 5.8 Summary—Vector Space Notation
    • Additional Readings
  • Chapter 6. Eigenvalue Problems
    • 6.1 Eigenvalue Equations


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© Academic Press 2012
Academic Press
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About the Author

George Arfken

Affiliations and Expertise

Miami University, Oxford, Ohio, USA

Hans Weber

Affiliations and Expertise

University of Virginia, USA

Frank E. Harris

Affiliations and Expertise

University of Florida, USA


"...a thorough handbook about mathematics that is useful in physics.", Mathematical Methods for Physicists, 7th Edition

"This volume is a great collection of essential mathematical tools and techniques used to solve problems in physics, very useful to any student of physics or research professional in the field. It is concentrated to problem-solving art and offers a large amount of problems and exercises."--Zentralblatt MATH 1239