Introduction to Mathematical Physics Methods and Concepts

ISBN-10: 0199641390
ISBN-13: 9780199641390
Edition: 2nd 2012
Authors: Chun Wa Wong
List price: $48.99 Buy it from $31.53 Rent it from $36.70
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Description: 'Introduction to Mathematical Physics' explains why and how mathematics is needed in describing physical events in space. It helps physics undergraduates master the mathematical tools needed in physics core courses.

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Book details

List price: $48.99
Edition: 2nd
Copyright year: 2012
Publisher: Oxford University Press
Publication date: 1/24/2013
Binding: Hardcover
Pages: 520
Size: 7.00" wide x 10.00" long x 1.50" tall
Weight: 3.476
Language: English

'Introduction to Mathematical Physics' explains why and how mathematics is needed in describing physical events in space. It helps physics undergraduates master the mathematical tools needed in physics core courses.

Vectors and fields in space
Concepts of space
Vectors in space
Permutation symbols
Vector differentiation of a scalar field
Vector differentiation of a vector field
Path-dependent scalar and vector integrations
Flux, divergence and Gauss's theorem
Circulation, curl and Stokes's theorem
Helmholtz's theorem
Orthogonal curvilinear coordinate systems
Vector differential operators in orthogonal curvilinear coordinate systems
Tables of mathematical formulas
Transformations, matrices and operators
Transformations and the laws of physics
Rotations in space: Matrices
Determinant and matrix inversion
Homogeneous equations
The matrix eigenvalue problem
Generalized matrix eigenvalue problems
Eigenvalues and eigenvectors of Hermitian matrices
The wave equation
Displacement in time and translation in space: Infinitesimal generators
Rotation operators
Matrix groups
Tables of mathematical formulas
Relativistic square-root spaces*
Introduction
Special relativity and Lorentz transformations
Relativistic kinematics and the mass-energy equivalence
Quaternions
Dirac equation, spinors and matrices
Symmetries of the Dirac equation*
Weyl and Majorana spinors, symmetry violations*
Lorentz group
Cartan spinors and spin transformations in square-root space
Dyadics
Cartesian tensors
Tensor analysis
Tables of mathematical formulas
Fourier series and Fourier transforms
Wave-particle duality: Quantum mechanics
Fourier series
Fourier coefficients and Fourier-series representation
Complex Fourier series and the Dirac � function
Fourier transform
Green function and convolution
Heisenberg's uncertainty principle
Conjugate variables and operators in wave mechanics
Generalized Fourier series and Legendre polynomials
Orthogonal functions and orthogonal polynomials
Mean-square error and mean-square convergence
Convergence of Fourier series
Maxwell equations in Fourier spaces
3D Fourier transforms: Helmholtz decomposition theorem
Short table of Fourier cosine series
Short table of Fourier sine series
Short table of Fourier transforms
Short table of 3D and 4D Fourier transforms
Tables of mathematical formulas
Differential equations in physics
Introduction
Linear differential equations
First-order differential equations
Second-order linear differential equations
The second homogeneous solution and an inhomogeneous solution
Green functions
Series solution of the homogeneous second-order linear differential equation
Differential eigenvalue equations and orthogonal functions
Partial differential equations of physics
Separation of variables and eigenfunction expansions
Boundary and initial conditions
Separation of variables for the Laplacian
Green functions for partial differential equations
Tables of mathematical formulas
Nonlinear systems*
Introduction
Nonlinear instabilities
Logistic map and chaos
Strange attractor
Driven dissipative linear pendula
Chaos in parametrically driven dissipative nonlinear pendula
Solitons
Traveling kinks
Nonlinear superposition of solitons
More general methods for multi-solitons*
Tables of mathematical formulas
Special functions
Introduction
Generating function for Legendre polynomials
Hermite polynomials and the quantum oscillator
Orthogonal polynomials
Classical orthogonal polynomials*
Associated Legendre polynomials and spherical harmonics
Bessel functions
Sturm-Liouville equation and eigenfunction expansions
Tables of mathematical formulas
Functions of a complex variable
Introduction
Functions of a complex variable
Multivalued functions and Riemann surfaces
Complex differentiation: Analytic functions and singularities
Complex integration: Cauchy integral theorem and integral formula
Harmonic functions in the plane
Taylor series and analytic continuation
Laurent series
Residues
Complex integration: Calculus of residues
Poles on the contour and Green functions
Laplace transform
Inverse Laplace transform
Construction of functions and dispersion relations
Asymptotic expansions*
Tables of mathematical formulas
Tutorials
Complex algebra
Vectors
Simple and partial differentiations
Simple and multiple integrals
Matrices and determinants
Infinite series
Exponential functions
Mathematica and other computer algebra systems
Computer algebra (CA) with Mathematica
Introduction to CA
Equation solvers
Drawing figures and graphs
Number-intensive calculations
Resources for students
Bibliography
Name index
Subject index

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