Boundary value problems : and partial differential equations / David L. Powers.

Format:

Book

Author/Creator:

Powers, David L.

Language:

English

Subjects (All):

Boundary value problems--Textbooks.

Boundary value problems.

Differential equations, Partial--Textbooks.

Differential equations, Partial.

Physical Description:

1 online resource (515 p.)

Edition:

5th ed.

Place of Publication:

Amsterdam ; Boston : Elsevier Academic Press, c2006.

Language Note:

English

Summary:

Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions

Contents:

Cover; Contents; Preface; Chapter 0. Ordinary Differential Equations; 0.1 Homogeneous Linear Equations; 0.2 Nonhomogeneous Linear Equations; 0.3 Boundary Value Problems; 0.4 Singular Boundary Value Problems; 0.5 Green's Functions; Chapter Review; Miscellaneous Exercises; Chapter 1. Fourier Series and Integrals; 1.1 Periodic Functions and Fourier Series; 1.2 Arbitrary Period and Half-Range Expansions; 1.3 Convergence of Fourier Series; 1.4 Uniform Convergence; 1.5 Operations on Fourier Series; 1.6 Mean Error and Convergence in Mean; 1.7 Proof of Convergence

1.8 Numerical Determination of Fourier Coefficients1.9 Fourier Integral; 1.10 Complex Methods; 1.11 Applications of Fourier Series and Integrals; 1.12 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 2. The Heat Equation; 2.1 Derivation and Boundary Conditions; 2.2 Steady-State Temperatures; 2.3 Example: Fixed End Temperatures; 2.4 Example: Insulated Bar; 2.5 Example: Different Boundary Conditions; 2.6 Example: Convection; 2.7 Sturm-Liouville Problems; 2.8 Expansion in Series of Eigenfunctions; 2.9 Generalities on the Heat Conduction Problem; 2.10 Semi-Infinite Rod

2.11 Infinite Rod2.12 The Error Function; 2.13 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 3. The Wave Equation; 3.1 The Vibrating String; 3.2 Solution of the Vibrating String Problem; 3.3 d'Alembert's Solution; 3.4 One-Dimensional Wave Equation: Generalities; 3.5 Estimation of Eigenvalues; 3.6 Wave Equation in Unbounded Regions; 3.7 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 4. The Potential Equation; 4.1 Potential Equation; 4.2 Potential in a Rectangle; 4.3 Further Examples for a Rectangle; 4.4 Potential in Unbounded Regions

4.5 Potential in a Disk4.6 Classification and Limitations; 4.7 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 5. Higher Dimensions and Other Coordinates; 5.1 Two-Dimensional Wave Equation: Derivation; 5.2 Three-Dimensional Heat Equation; 5.3 Two-Dimensional Heat Equation: Solution; 5.4 Problems in Polar Coordinates; 5.5 Bessel's Equation; 5.6 Temperature in a Cylinder; 5.7 Vibrations of a Circular Membrane; 5.8 Some Applications of Bessel Functions; 5.9 Spherical Coordinates; Legendre Polynomials; 5.10 Some Applications of Legendre Polynomials

5.11 Comments and ReferencesChapter Review; Miscellaneous Exercises; Chapter 6. Laplace Transform; 6.1 Definition and Elementary Properties; 6.2 Partial Fractions and Convolutions; 6.3 Partial Differential Equations; 6.4 More Difficult Examples; 6.5 Comments and References; Miscellaneous Exercises; Chapter 7. Numerical Methods; 7.1 Boundary Value Problems; 7.2 Heat Problems; 7.3 Wave Equation; 7.4 Potential Equation; 7.5 Two-Dimensional Problems; 7.6 Comments and References; Miscellaneous Exercises; Bibliography; Mathematical References; Answers to Odd-Numbered Exercises; Chapter 0; Chapter 1

Chapter 2

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 433-434) and index.

ISBN:

9786610961450

9781280961458

1280961457

9780080470795

0080470793

OCLC:

437176588