Powers Boundary Value Problems

and Partial Differential Equations
6. Auflage 2009
ISBN: 978-0-08-088441-7
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 520 Seiten

Ancillary list: * Online SSM- http://www.elsevierdirect.com/product.jsp?isbn=9780123747198 * Online ISM- http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123747198 * Companion site, Ebook- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747198 * SSM for 6e - http://store.elsevier.com/product.jsp?isbn=9780123756640&_requestid=59086&_requestid=59093
New animations and graphics of solutions, additional exercises and chapter review questions on the web   Nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises Many exercises based on current engineering applications An Instructor's Manual and Student Solutions Manual are available separately

Autoren/Hrsg.

Powers, David L.

Inhaltsverzeichnis

1;Front Cover
;1
2;Boundary Value Problems and Partial Differential Equations;3
3;Copyright Page;5
4;Contents
;6
5;Preface
;10
6;Chapter 0: Ordinary Differential Equations ;13
6.1;Homogeneous Linear Equations
;13
6.2;Nonhomogeneous Linear Equations
;26
6.3;Boundary Value Problems
;37
6.4;Singular Boundary Value Problems;50
6.5;Chapter Review
;56
6.6;Miscellaneous Exercises
;56
7;Chapter 1: Fourier Series and Integrals ;63
7.1;Periodic Functions and Fourier Series;63
7.2;Arbitrary Period and Half-Range Expansions
;68
7.3;Convergence of Fourier Series
;77
7.4;Uniform Convergence
;84
7.5;Operations on Fourier Series
;90
7.6;Mean Error and Convergence in Mean
;96
7.7;Proof of Convergence
;100
7.8;Numerical Determination of Fourier Coefficients
;106
7.9;Fourier Integral
;111
7.10;Complex Methods
;118
7.11;Applications of Fourier Series and Integrals
;122
7.12;Comments and References
;129
7.13;Chapter Review
;130
7.14;Miscellaneous Exercises
;130
8;Chapter 2: The Heat Equation ;139
8.1;Derivation and Boundary Conditions;139
8.2;Steady-State Temperatures
;147
8.3;Example: Fixed End Temperatures
;154
8.4;Example: Insulated Bar
;162
8.5;Example: Different Boundary Conditions
;169
8.6;Example: Convection
;176
8.7;Sturm-Liouville Problems
;182
8.8;Expansion in Series of Eigenfunctions
;188
8.9;Generalities on the Heat Conduction Problem
;191
8.10;Semi-Infinite Rod
;195
8.11;Infinite Rod
;201
8.12;The Error Function
;208
8.13;Comments and References
;215
8.14;Chapter Review
;217
8.15;Miscellaneous Exercises
;217
9;Chapter 3: The Wave Equation ;227
9.1;The Vibrating String;227
9.2;Solution of the Vibrating String Problem
;231
9.3;D'Alembert's Solution
;241
9.4;One-Dimensional Wave Equation: Generalities
;248
9.5;Estimation of Eigenvalues
;251
9.6;Wave Equation in Unbounded Regions
;255
9.7;Comments and References
;263
9.8;Chapter Review
;264
9.9;Miscellaneous Exercises
;264
10;Chapter 4: The Potential Equation ;273
10.1;Potential Equation;273
10.2;Potential in a Rectangle;276
10.3;Further Examples for a Rectangle
;282
10.4;Potential in Unbounded Regions
;290
10.5;Potential in a Disk
;299
10.6;Classification of Partial Differential Equations and Limitations of the Product Method;306
10.7;Comments and References
;309
10.8;Chapter Review
;311
10.9;Miscellaneous Exercises
;311
11;Chapter 5: Higher Dimensions and Other Coordinates ;321
11.1;Two-Dimensional Wave Equation: Derivation;321
11.2;Three-Dimensional Heat Equation: Vector
Derivation;324
11.3;Two-Dimensional Heat Equation: Double Series
Solution;329
11.4;Problems in Polar Coordinates
;334
11.5;Bessel’s Equation
;337
11.6;Temperature in a Cylinder
;343
11.7;Vibrations of a Circular Membrane
;349
11.8;Some Applications of Bessel Functions
;357
11.9;Spherical Coordinates; Legendre Polynomials
;364
11.10;Some Applications of Legendre Polynomials
;374
11.11;Comments and References
;381
11.12;Chapter Review
;382
11.13;Miscellaneous Exercises
;383
12;Chapter 6: Laplace Transform ;391
12.1;Definition and Elementary Properties
;391
12.2;Partial Fractions and Convolutions
;397
12.3;Partial Differential Equations
;404
12.4;Some Nontrivial Examples
;411
12.5;Comments and References
;418
12.6;Miscellaneous Exercises
;418
13;Chapter 7: Numerical Methods ;425
13.1;Boundary Value Problems;425
13.2;Heat Problems
;431
13.3;Wave Equation
;435
13.4;Potential Equation
;441
13.5;Comments and References
;447
13.6;Miscellaneous Exercises
;448
14;Bibliography
;453
15;Appendix: Mathematical References
;455
16;Answers to Odd-Numbered Exercises
;461
17;Index
;515