9780321797063

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems

Richard Haberman

5th Edition

This edition features the exact same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value--this format costs significantly less than a new textbook. This text emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equation

5-3

Sturm-Liouville Eigenvalue Problems

Exercises

p.161

5-4

Worked Example: Heat Flow in a Nonuniform Rod without Sources

Exercises

p.166

5-5

Self-Adjoint Operators and Sturm-Liouville Eigenvalue Problems

Exercises

p.174

Appendix Exercises

p.183

5-6

Rayleigh Quotient

Exercises

p.188

5-7

Worked Example: Vibrations of a Nonuniform String

Exercises

p.192

5-8

Boundary Condition of the Third Kind

Exercises

p.204

5-9

Large Eigenvalues (Asymptotic Behavior)

Exercises

p.210

5-10

Approximation Properties

Exercises

p.215

7-2

Separation of the Time Variable

Exercises

p.272

7-3

Vibrating Rectangular Membrane

Exercises

p.278

7-4

Statements and Illustrations of Theorems for the Eigenvalue Problem ∇2φ+λφ= 0

Exercises

p.287

7-5

Green's Formula, Self-Adjoint Operators, and Multidimensional Eigenvalue Problems

Exercises

p.290

7-6

Rayleigh Quotient and Laplace's Equation

Exercises

p.295

7-7

Vibrating Circular Membrane and Bessel Functions

Exercises

p.308

7-8

More on Bessel Functions

Exercises

p.317

7-9

Laplace's Equation in a Circular Cylinder

Exercises

p.328

7-10

Spherical Problems and Legendre Polynomials

Exercises

p.338

8-2

Heat Flow with Sources and Nonhomogeneous Boundary Conditions

Exercises

p.346

8-3

Method of Eigenfunction Expansion with Homogeneous Boundary Condition (Differentiating Series of Eigenfunctions)

Exercises

p.352

8-4

Method of Eigenfunction Expansion Using Green's Formula (With or Without Homogeneous Boundary Conditions)

Exercises

p.357

8-5

Forced Vibrating Membranes and Resonance

Exercises

p.364

8-6

Poisson's Equation

Exercises

p.371

9-2

One-Dimensional Heat Equation (Optional)

Exercises

p.378

9-3

Green's Functions for Boundary Value Problems for Ordinary Differential Equations

Exercises

p.393

9-4

Fredholm Alternative and Generalized Green's Functions

Exercises

p.406

9-5

Green's Functions for Poisson's Equation

Exercises

p.426

9-6

Perturbed Eigenvalue Problems

Exercises

p.434

10-2

Heat Equation on an Infinite Domain

Exercises

p.441

10-3

Fourier Transform Pair

Exercises

p.447

10-4

Fourier Transform and the Heat Equation

Exercises

p.461

10-5

Fourier Sine and Cosine Transforms: The Heat Equation on Semi-Infinite Intervals

Exercises

p.471

10-6

Worked Examples Using Transforms

Exercises

p.491

10-7

Scattering and Inverse Scattering

Exercises

p.498

12-2

Characteristics for First-Order Wave Equations

Exercises

p.533

12-3

Method of Characteristics for the One-Dimensional Wave Equation

Exercises

p.541

12-4

Semi-Infinite Strings and Reflections

Exercises

p.546

12-5

Method of Characteristics for a Vibrating String of Fixed Length

Exercises

p.551

12-6

The Method of Characteristics for Quasilinear Partial Differential Equations

Exercises

p.572

12-7

First-Order Nonlinear Partial Differential Equations

Exercises

p.580

13-2

Properties of the Laplace Transform

Exercises

p.590

13-3

Green's Function for Initial Value Problems for Ordinary Differential Equations

Exercises

p.593

13-4

A Signal Problem for the Wave Equation

Exercises

p.596

13-5

A Signal Problem for a Vibrating String of Finite Length

Exercises

p.599

13-6

The Wave Equation and Its Green's Function

Exercises

p.602

13-7

Inversion of Laplace Transforms Using Contour Integrals in the Complex Plane

Exercises

p.607

13-8

Solving the Wave Equation Using Laplace Transforms (With Complex Variables)

Exercises

p.609

14-2

Dispersive Waves and Group Velocity

Exercises

p.616

14-3

Wave Guides

Exercises

p.622

14-4

Fiber Optics

Exercises

p.627

14-5

Group Velocity II and the Method of Stationary Phase

Exercises

p.632

14-6

Slowly Varying Dispersive Waves (Group Velocity and Caustics)

Exercises

p.641

14-7

Wave Envelope Equations (Concentrated Wave Number)

Exercises

p.655

14-8

Stability and Instability

Exercises

p.681

14-9

Singular Perturbation Methods: Multiple Scales

Exercises

p.699

14-10

Singular Perturbation Methods: Boundary Layers Method of Matched Asymptotic Expansions

Exercises

p.710