Mathematics for Physicists

ISBN-10: 0534379974
ISBN-13: 9780534379971
Edition: 2004
Authors: Susan M. Lea
List price: $246.95
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Description: This essential new text by Dr. Susan Lea will help physics undergraduate and graduate student hone their mathematical skills. Ideal for the one-semester course, MATHEMATICS FOR PHYSICISTS has been extensively class-tested at San Francisco State  More...

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Book details

List price: $246.95
Copyright year: 2004
Publisher: Brooks/Cole
Publication date: 4/14/2003
Binding: Hardcover
Pages: 625
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 2.552

This essential new text by Dr. Susan Lea will help physics undergraduate and graduate student hone their mathematical skills. Ideal for the one-semester course, MATHEMATICS FOR PHYSICISTS has been extensively class-tested at San Francisco State University--and the response has been enthusiastic from students and instructors alike. Because physics students are often uncomfortable using the mathematical tools that they learned in their undergraduate courses, MATHEMATICS FOR PHYSICISTS provides students with the necessary tools to hone those skills. Lea designed the text specifically for physics students by using physics problems to teach mathematical concepts.

Preface
Describing the Universe
A Universal Language
Scalar and Vector Fields
Curvilinear Coordinates
The Helmholtz Theorem
Vector Spaces
Matrices
Problems
Complex Variables
All About Numbers
Functions of Complex Variables
Complex Series
Complex Numbers and Laplace's Equation
Poles and Zeros
The Residue Theorem
Using the Residue Theorem
Conformal Mapping
The Gamma Function
Problems
Differential Equations
Some Definitions
Common Differential Equations Arising in Physics
Solution of Linear, Ordinary Differential Equations
Numerical Methods
Partial Differential Equations: Separation of Variables
Problems
Fourier Series
Fourier's Theorem
Finding the Coefficients
Fourier Sine and Cosine Series
Use of Fourier Series to Solve Differential Equations
Convergence of Fourier Series
Problems
Laplace Transforms
Definition of the Laplace Transform
Some Basic Properties of the Transform
Use of the Laplace Transform to Solve a Differential Equation
Some Additional Useful Tricks
Convolution
The General Inversion Procedure
Some More Physics
Problems
Generalized Functions in Physics
The Delta Function
Developing a Theory of Distributions
Properties of Distributions
Sequences and Series
Distributions in N Dimensions
Describing Physical Quantities Using Delta Functions
The Green's Function
Problems
Fourier Transforms
Definition of the Fourier Transform
Some Examples
Properties of the Fourier Transform
Causality
Use of Fourier Transforms in the Solution of Partial Differential Equations
Fourier Transforms and Power Spectra
Sine and Cosine Transforms
Problems
Sturm-Liouville Theory
The Sturm-Liouville Problem
Use of Sturm-Liouville Theory in Physics
Problems with Spherical Symmetry: Spherical Harmonics
Problems with Cylindrical Symmetry: Bessel Functions
Spherical Bessel Functions
The Classical Orthogonal Polynomials
Problems
Optional Topics
Tensors
Cartesian Tensors
Inner and Outer Products
Pseudo-tensors and Cross Products
General Tensor Calculus
The Metric Tensor
Contraction
Basis Vectors and Basis Forms
Derivatives
Problems
Group Theory
Definition of a Group
Examples of Groups
Classes
Subgroups
Cyclic Groups
Factor Groups and Direct Product Groups
Isomorphism
Representations
Generators of Groups
Lie Algebras
Problems
Green's Functions
Division-of-Region Method
Expansion in Eigenfunctions
Transform Methods
Extension to N Dimensions
Inhomogeneous Boundary Conditions
Green's Theorem
The Green's Function for Poisson's Equation in a Bounded Region
Problems
Approximate Evaluation of Integrals
The Method of Steepest Descent
The Method of Stationary Phase
Problems
Calculus of Variations
Integral Principles in Physics
The Euler Equation
Variation Subject to Constraints
Extension to Functions of More Than One Variable
Problems
Appendices
Transformation Properties of the Vector Cross Product
Proof of the Helmholtz Theorem
Proof by Induction: The Cauchy Formula
The Mean Value Theorem for Integrals
The Gibbs Phenomenon
The Laplace Transform and Convolution
Proof That P[superscript m subscript l]([mu]) = (-1)[superscript m](1 - [mu superscript 2])[superscript m/2]d[superscript m]/d[mu superscript m]P[subscript l]([mu])
Proof of the Relation [function of superscript infinity subscript 0] [rho]J[subscript m](k[rho])J[subscript m](k'[rho])d[rho] = 1/k[delta](k - k')
The Error Function
Classification of Partial Differential Equations
The Tangent Function: A Detailed Investigation of Series Expansions
Bibliography
Index

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