Mathematical Methods in the Physical Sciences Wie

by Boas, Mary L.

• ISBN13: 9780471365808
• ISBN10: 0471365807
• Edition: 3rd
• Format: Hardcover
• Copyright: 2003-03-01
• Publisher: John Wiley & Sons Inc

Summary

Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

Table of Contents

Infinite Series, Power Series

The Geometric Series

Definitions and Notation

Applications of Series

Convergent and Divergent Series

Convergence Tests

Convergence Tests for Series of Positive Terms

Alternating Series

Conditionally Convergent Series

Useful Facts about Series

Power Series; Interval of Convergence

Theorems about Power Series

Expanding Functions in Power Series

Expansion Techniques

Accuracy of Series Approximations

Some Uses of Series

Complex Numbers

Introduction

Real and Imaginary Parts of a Complex Number

The Complex Plane

Terminology and Notation

Complex Algebra

Complex Infinite Series

Complex Power Series; Disk of Convergence

Elementary Functions of Complex Numbers

Euler's Formula

Powers and Roots of Complex Numbers

The Exponential and Trigonometric Functions

Hyperbolic Functions

Logarithms

Complex Roots and Powers

Inverse Trigonometric and Hyperbolic Functions

Some Applications

Linear Algebra

Introduction

Matrices; Row Reduction

Determinants; Cramer's Rule

Vectors

Lines and Planes

Matrix Operations

Linear Combinations, Functions, Operators

Linear Dependence and Independence

Special Matrices and Formulas

Linear Vector Spaces

Eigenvalues and Eigenvectors

Applications of Diagonalization

A Brief Introduction to Groups

General Vector Spaces

Partial Differentiation

Introduction and Notation

Power Series in Two Variables

Total Differentials

Approximations using Differentials

Chain Rule

Implicit Differentiation

More Chain Rule

Maximum and Minimum Problems

Constraints; Lagrange Multipliers

Endpoint or Boundary Point Problems

Change of Variables

Differentiation of Integrals

Multiple Integrals

Introduction

Double and Triple Integrals

Applications of Integration

Change of Variables in Integrals; Jacobians

Surface Integrals

Vector Analysis

Introduction

Applications of Vector Multiplication

Triple Products

Differentiation of Vectors

Fields

Directional Derivative; Gradient

Some Other Expressions Involving V. Line Integrals

Green's Theorems in the Plane

The Divergence and the Divergence Theorem

The Curl and Stokes' Theorem

Fourier Series and Transforms

Introduction

Simple Harmonic Motion and Wave Motion

Periodic Functions

Applications of Fourier Series

Average Value of a Function

Fourier Coefficients

Complex Form of Fourier Series

Other Intervals

Even and Odd Functions

An Application to Sound

Parseval's Theorem

Fourier Transforms

Ordinary Differential Equations

Introduction

Separable Equations

Linear First-Order Equations

Other Methods for First-Order Equations

Linear Equations (Zero Right-Hand Side)

Linear Equations (Nonzero Right-Hand Side)

Other Second-Order Equations

The Laplace Transform

Laplace Transform Solutions

Convolution

The Dirac Delta Function

A Brief Introduction to Green's Functions

Calculus of Variations

Introduction

The Euler Equation

Using the Euler Equation

The Brachistochrone Problem; Cycloids

Several Dependent Variables

Lagrange's Equations

Isoperimetric Problems

Variational Notation

Tensor Analysis

Introduction

Cartesian Tensors

Tensor Notation and Operations

Inertia Tensor

Kronecker Delta and Levi-Civita Symbol

Pseudovectors and Pseudotensors

More about Applications

Curvilinear Coordinates

Vector Operators

Non-Cartesian Tensors

Special Functions

Introduction

The Factorial Function

Gamma Function; Recursion Relation

The Gamma Function of Negative Numbers

Formulas Involving Gamma Functions

Beta Functions

Beta Functions in Terms of Gamma Functions

The Simple Pendulum

The Error Function

Asymptot

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