Introduction to Mathematical Physics

ISBN-10: 3527406271
ISBN-13: 9783527406272
Edition: 2007
List price: $106.95
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Description: A comprehensive survey of all the mathematical methods that should be available to graduate students in physics. In addition to the usual topics of analysis, such as infinite series, functions of a complex variable and some differential equations as  More...

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Book details

List price: $106.95
Copyright year: 2007
Publisher: John Wiley & Sons, Incorporated
Publication date: 6/18/2007
Binding: Paperback
Pages: 543
Size: 6.50" wide x 9.25" long x 0.75" tall
Weight: 2.156
Language: English

A comprehensive survey of all the mathematical methods that should be available to graduate students in physics. In addition to the usual topics of analysis, such as infinite series, functions of a complex variable and some differential equations as well as linear vector spaces, this book includes a more extensive discussion of group theory than can be found in other current textbooks. The main feature of this textbook is its extensive treatment of geometrical methods as applied to physics. With its introduction of differentiable manifolds and a discussion of vectors and forms on such manifolds as part of a first-year graduate course in mathematical methods, the text allows students to grasp at an early stage the contemporary literature on dynamical systems, solitons and related topological solutions to field equations, gauge theories, gravitational theory, and even string theory.

Michael T. Vaughn is Professor of Physics at Northeastern University in Boston and well known in particle theory for his contributions to quantum field theory especially in the derivation of two loop renormalization group equations for the Yukowa and scalar quartic couplings in Yang-Mills gauge theories and in softly broken supersymmetric theories. Professor Vaughn has taught graduate courses in mathematical physics at the University of Pennsylvania, Indiana University and Texas A&M University as well as at Northeastern.

Infinite Sequences and Series
Real and Complex Numbers
Convergence of Infinite Series and Products
Sequences and Series of Functions
Asymptotic Series
Finite-Dimensional Vector Spaces
Linear Vector Spaces
Linear Operators
Eigenvectors and Eigenvalues
Functions of Operators
Linear Dynamical Systems
Geometry in Physics
Manifolds and Coordinates
Vectors, Differential Forms, and Tensors
Calculuson Manifolds
Metric Tensor and Distance
Dynamical Systems and Vector Fields
Fluid Mechanics
Functions of a Complex Variable
Elementary Properties of Analytic Functions
Integration in the Complex Plane
Analytic Functions
Calculus of Residues: Applications
Periodic Functions; Fourier Series
Differential Equations: Analytical Methods
Systems of Differential Equations
First-Order Differential Equations
Linear Differential Equations
Linear Second-Order Equations
Legendre's Equation
Bessel's Equation
Hilbert Spaces
Infinite-Dimensional Vector Spaces
Function Spaces; Measure Theory
Fourier Series
Fourier Integral; Integral Transforms
Orthogonal Polynomials
Haar Functions; Wavelets
Linear Operators on Hilbert Space
Some Hilbert Space Subtleties
General Properties of Linear Operators on Hilbert Space
Spectrum of Linear Operators on Hilbert Space
Linear Differential Operators
Linear Integral Operators; Green Functions
Partial Differential Equations
LinearFirst-OrderEquations
The Laplacian and Linear Second-Order Equations
Time-Dependent Partial Differential Equations
Nonlinear Partial Differential Equations
Finite Groups
General Properties of Groups
Some Finite Groups
The Symmetric Group SN
Group Representations
Representations of the Symmetric Group SN
Discrete Infinite Groups
Lie Groups and Lie Algebras
Lie Groups
Lie Algebras
Representationsof Lie Algebras
Index

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