Chapter 1: Infinite Series, Power SeriesSection 1:

The Geometric Series

Section 2:

Definitions And Notation

Section 4:

Convergent And Divergent Series

Section 5:

Testing Series For Convergence; The Preliminary Test

Section 6:

Convergence Tests For Series Of Positive Terms; Absolute Convergence

Section 7:

Alternating Series

Section 9:

Useful Facts About Series

Section 10:

Power Series; Interval Of Convergence

Section 12:

Expanding Functions In Power Series

Section 13:

Techniques For Obtaining Power Series Expansions

Section 14:

Accuracy Of Series Approximations

Section 15:

Some Uses Of Series

Section 16:

Miscellaneous Problems

Chapter 2: Complex NumbersSection 4:

Terminology And Notation

Section 5:

Complex Algebra

Section 6:

Complex Infinite Series

Section 7:

Complex Power Series; Disk of Convergence

Section 8:

Elementary Functions of Complex Numbers

Section 9:

Euler’s Formula

Section 10:

Powers and Roots of Complex Numbers

Section 11:

The Exponential and Trigonometric Functions

Section 12:

Hyperbolic Functions

Section 14:

Complex Roots and Powers

Section 15:

Inverse Trigonometric and Hyperbolic Functions

Section 16:

Some Applications

Section 17:

Miscellaneous Problems

Section 2:

Matrices; Row Reduction

Section 3:

Determinants; Cramer’s Rule

Section 4:

Vectors

Section 5:

Lines and Planes

Section 6:

Complex Infinite Series

Section 7:

Linear Combinations, Linear Functions, Linear Operators

Section 8:

Linear Dependence and Independence

Section 9:

Special Matrices and Formulas

Section 10:

Linear Vector Spaces

Section 11:

Eigenvalues and Eigenvectors; Diagonalizing Matrices

Section 12:

Applications of Diagonalization

Section 13:

A Brief Introduction to Groups

Section 14:

General Vector Spaces

Section 15:

Miscellaneous Problems

Chapter 4: Partial DifferentiationSection 1:

Introduction and Notation

Section 2:

Power Series in Two Variables

Section 3:

Total DifferentialsSection 4:

Approximations using Differentials

Section 5:

Chain Rule or Differentiating a Function of a Function

Section 6:

Implicit Differentiation

Section 7:

More Chain Rule

Section 8:

Application of Partial Differentiation to Maximum and Minimum Problems

Section 9:

Maximum and Minimum Problems with Constraints; Lagrange Multipliers

Section 10:

Endpoint or Boundary Point Problems

Section 11:

Change of Variables

Section 12:

Differentiation of Integrals; Leibniz’ Rule

Section 13:

Miscellaneous Problems

Chapter 5: Multiple Integrals; Applications of IntegrationSection 1:

Introduction

Section 2:

Double and Triple Integrals

Section 3:

Applications of Integration; Single and Multiple Integrals

Section 4:

Change of Variables in Integrals; Jacobian's

Section 5:

Surface Integrals

Section 6:

Miscellaneous Problems

Chapter 6: Vector AnalysisSection 3:

Triple Products

Section 4:

Differentiation of Vectors

Section 6:

Directional Derivative; Gradient

Section 7:

Some other Expressions Involving ∇

Section 8:

Line Integrals

Section 9:

Green’s Theorem in the Plane

Section 10:

The Divergence and The Divergence Theorem

Section 11:

The Curl and Stokes’ Theorem

Section 12:

Miscellaneous Problems

Chapter 7: Fourier Series and TransformsSection 2:

Simple Harmonic Motion and Wave Motion; Periodic Functions

Section 3:

Applications of Fourier Series

Section 4:

Average Value of a Function

Section 5:

Fourier Coefficients

Section 6:

Dirichlet Conditions

Section 7:

Complex Form of Fourier Series

Section 8:

Other Intervals

Section 9:

Even and Odd Functions

Section 10:

An Application to Sound

Section 11:

Parseval’s Theorem

Section 12:

Fourier Transforms

Section 13:

Miscellaneous Problems

Chapter 8: Ordinary Differential EquationsSection 1:

Introduction

Section 2:

Separable Equations

Section 3:

Linear First-Order Equations

Section 4:

Other Methods for First-Order Equations

Section 5:

Second-Order Linear Equations with Constant Coefficients and Zero Right-Hand Side

Section 6:

Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero

Section 7:

Other Second-Order Equations

Section 8:

The Laplace Transform

Section 9:

Solution of Differential Equations by Laplace Transforms

Section 10:

Convolution

Section 11:

The Dirac Delta Function

Section 12:

A Brief Introduction to Green Functions

Section 13:

Miscellaneous Problems

Chapter 9: Calculus of VariationsSection 1:

Introduction

Section 2:

The Euler Equation

Section 3:

Using the Euler Equation

Section 4:

The Brachistochrone Problem; Cycloids

Section 5:

Several Dependent Variables; Lagrange’s Equations

Section 6:

Isoperimetric Problems

Section 8:

Miscellaneous Problems

Chapter 10: Tensor AnalysisSection 2:

Cartesian Tensors

Section 3:

Tensor Notation and Operations

Section 4:

Inertia Tensor

Section 5:

Kronecker Delta and Levi-Civita Symbol

Section 6:

Pseudovectors and Pseudotensors

Section 7:

More about Applications

Section 8:

Curvilinear Coordinates

Section 9:

Vector Operators in Orthogonal Curvilinear Coordinates

Section 10:

Non-Cartesian Tensors

Section 11:

Miscellaneous Problems

Chapter 11: Special FunctionsSection 2:

The Factorial Function

Section 3:

Definition of the Gamma Function; Recursion Relation

Section 5:

Some Important Formulas Involving Gamma Functions

Section 6:

Beta Functions

Section 7:

Beta Functions in Terms of Gamma Functions

Section 8:

The Simple Pendulum

Section 9:

The Error Function

Section 10:

Asymptotic Series

Section 11:

Stirling’s Formula

Section 12:

Elliptic Integrals and Functions

Section 13:

Miscellaneous Problems

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Chapter 12: Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre FunctionsSection 1:

Introduction

Section 2:

Legendre’s Equation

Section 3:

Leibniz’ Rule for Differentiating Products

Section 4:

Rodrigues’ Formula

Section 5:

Generating Function for Legendre Polynomials

Section 6:

Complete Sets of Orthogonal Functions

Section 7:

Orthogonality of The Legendre Polynomials

Section 8:

Normalization of The Legendre Polynomials

Section 9:

Legendre Series

Section 10:

The Associated Legendre Functions

Section 11:

Generalized Power Series or The Method of Frobenius

Section 12:

Bessel’s Equation

Section 13:

The Second Solution of Bessel’S Equation

Section 14:

Graphs and Zeros of Bessel Functions

Section 15:

Recursion Relations

Section 16:

Differential Equations with Bessel Function Solutions

Section 17:

Other Kinds of Bessel Functions

Section 18:

The Lengthening Pendulum

Section 19:

Orthogonality of Bessel Functions

Section 20:

Approximate Formulas for Bessel Functions

Section 21:

Series Solutions; Fuchs’S Theorem

Section 22:

Hermite Functions; Laguerre Functions; Ladder Operators

Section 23:

Miscellaneous Problems

Chapter 13: Partial Differential EquationsSection 1:

Introduction

Section 2:

Laplace’s Equation; Steady-State Temperature in a Rectangular Plate

Section 3:

The Diffusion or Heat Flow Equation; The Schrodinger Equation

Section 4:

The wave Equation; The Vibrating String

Section 5:

Steady-State Temperature in a Cylinder

Section 6:

Vibration of a Circular Membrane

Section 7:

Steady-State Temperature in a Sphere

Section 8:

Poisson’s Equation

Section 9:

Integral Transform Solutions of Partial Differential Equations

Section 10:

Miscellaneous Problems

Chapter 14: Functions of a Complex VariableSection 1:

Introduction

Section 2:

Analytic Functions

Section 3:

Contour Integrals

Section 4:

Laurent Series

Section 5:

The Residue Theorem

Section 6:

Methods of Finding Residues

Section 7:

Evaluation of Definite Integrals by Use of the Residue Theorem

Section 8:

The Point at Infinity; Residues at Infinity

Section 9:

Mapping

Section 10:

Some Applications of Conformal Mapping

Section 11:

Miscellaneous Problems

Chapter 15: Probability and StatisticsSection 1:

Introduction

Section 2:

Sample Space

Section 3:

Probability Theorems

Section 4:

Methods of Counting

Section 5:

Random Variables

Section 6:

Continuous Distributions

Section 7:

Binomial Distribution

Section 8:

The Normal or Gaussian Distribution

Section 9:

The Poisson Distribution

Section 10:

Statistics and Experimental Measurements

Section 11:

Miscellaneous Problems

At Quizlet, we’re giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Mathematical Methods in the Physical Sciences 3rd Edition, you’ll learn how to solve your toughest homework problems. Our resource for Mathematical Methods in the Physical Sciences includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence.