Essential mathematical methods for physicists 1st Edition by Hans Weber, George Arfken 9780120598779 0120598779

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Product details:

ISBN 10: 0120598779

ISBN 13: 9780120598779

Author: Hans J. Weber; George B. Arfken

This new adaptation of Arfken and Weber’s bestselling Mathematical Methods for Physicists, Fifth Edition, is the most comprehensive, modern, and accessible reference for using mathematics to solve physics problems.

REVIEWERS SAY: “Examples are excellent. They cover a wide range of physics problems.” —Bing Zhou, University of Michigan

“The ideas are communicated very well and it is easy to understand…It has a more modern treatment than most, has a very complete range of topics and each is treated in sufficient detail….I’m not aware of another better book at this level…” —Gary Wysin, Kansas State University

• This is a more accessible version of Arken/Weber’s blockbuster reference, which already has more than 13,000 sales worldwide
• Many more detailed, worked-out examples illustrate how to use and apply mathematical techniques to solve physics problems
• More frequent and thorough explanations help readers understand, recall, and apply the theory
• New introductions and review material provide context and extra support for key ideas
• Many more routine problems reinforce basic, foundational concepts and computations

Table of contents:

Chapter 1: Vector Analysis
1.1 Elementary Approach
1.2 Scalar or Dot Product
1.3 Vector or Cross Product
1.4 Triple Scalar Product and Triple Vector Product
1.5 Gradient

Chapter 2: Vector Analysis in Curved Coordinates and Tensors
2.1 Special Coordinate Systems
2.2 Circular Cylinder Coordinates
2.3 Orthogonal Coordinates
2.4 Differential Vector Operators
2.5 Spherical Polar Coordinates
2.6 Tensor Analysis
2.7 Contraction and Direct Product
2.8 Quotient Rule
2.9 Dual Tensors

Chapter 3: Determinants and Matrices
3.1 Determinants
3.2 Matrices
3.3 Orthogonal Matrices
3.4 Hermitian Matrices and Unitary Matrices
3.5 Diagonalization of Matrices

Chapter 4: Group Theory
4.1 Introduction to Group Theory
4.2 Generators of Continuous Groups
4.3 Orbital Angular Momentum
4.4 Homogeneous Lorentz Group

Chapter 5: Infinite Series
5.1 Fundamental Concepts
5.2 Convergence Tests
5.3 Alternating Series
5.4 Algebra of Series
5.5 Series of Functions
5.6 Taylor’s Expansion
5.7 Power Series
5.8 Elliptic Integrals
5.9 Bernoulli Numbers and the Euler–Maclaurin Formula
5.10 Asymptotic Series

Chapter 6: Functions of a Complex Variable I — Analytic Properties and Mapping
6.1 Complex Algebra
6.2 Cauchy–Riemann Conditions
6.3 Cauchy’s Integral Theorem
6.4 Cauchy’s Integral Formula
6.5 Laurent Expansion
6.6 Mapping
6.7 Conformal Mapping

Chapter 7: Functions of a Complex Variable II — Calculus of Residues
7.1 Singularities
7.2 Calculus of Residues
7.3 Method of Steepest Descents

Chapter 8: Differential Equations
8.1 Introduction
8.2 First-Order ODEs
8.3 Second-Order ODEs
8.4 Singular Points
8.5 Series Solutions — Frobenius’s Method
8.6 A Second Solution
8.7 Numerical Solutions
8.8 Introduction to Partial Differential Equations
8.9 Separation of Variables

Chapter 9: Sturm–Liouville Theory — Orthogonal Functions
9.1 Self-Adjoint ODEs
9.2 Hermitian Operators
9.3 Gram–Schmidt Orthogonalization
9.4 Completeness of Eigenfunctions

Chapter 10: The Gamma Function (Factorial Function)
10.1 Definitions and Simple Properties
10.2 Digamma and Polygamma Functions
10.3 Stirling’s Series
10.4 The Incomplete Gamma Functions and Related Functions

Chapter 11: Legendre Polynomials and Spherical Harmonics
11.1 Introduction
11.2 Recurrence Relations and Special Properties
11.3 Orthogonality
11.4 Alternate Definitions of Legendre Polynomials
11.5 Associated Legendre Functions

Chapter 12: Bessel Functions
12.1 Bessel Functions of the First Kind, Jν(x)J_nu(x)Jν​(x)
12.2 Neumann Functions, Bessel Functions of the Second Kind
12.3 Asymptotic Expansions
12.4 Spherical Bessel Functions

Chapter 13: Hermite and Laguerre Polynomials
13.1 Hermite Polynomials
13.2 Laguerre Functions

Chapter 14: Fourier Series
14.1 General Properties
14.2 Advantages and Uses of Fourier Series
14.3 Complex Fourier Series
14.4 Properties of Fourier Series

Chapter 15: Integral Transforms
15.1 Introduction and Definitions
15.2 Fourier Transform
15.3 Development of the Inverse Fourier Transform
15.4 Fourier Transforms — Inversion Theorem
15.5 Fourier Transform of Derivatives
15.6 Convolution Theorem
15.7 Momentum Representation
15.8 Laplace Transforms
15.9 Laplace Transform of Derivatives
15.10 Other Properties
15.11 Convolution (Faltungs) Theorem
15.12 Inverse Laplace Transform

Chapter 16: Partial Differential Equations
16.1 Examples of PDEs and Boundary Conditions
16.2 Heat Flow or Diffusion PDE
16.3 Inhomogeneous PDE — Green’s Function

Chapter 17: Probability
17.1 Definitions and Simple Properties
17.2 Random Variables
17.3 Binomial Distribution
17.4 Poisson Distribution
17.5 Gauss’s Normal Distribution
17.6 Statistics

Chapter 18: Calculus of Variations
18.1 A Dependent and an Independent Variable
18.2 Several Dependent Variables
18.3 Several Independent Variables
18.4 Several Dependent and Independent Variables
18.5 Lagrangian Multipliers — Variation with Constraints
18.6 Rayleigh–Ritz Variational Technique

Chapter 19: Nonlinear Methods and Chaos
19.1 Introduction
19.2 The Logistic Map
19.3 Sensitivity to Initial Conditions and Parameters
19.4 Nonlinear Differential Equations

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