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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 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.

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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: 2.134

AuthorTable of Contents

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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