Boundary Value Problems (eBook)

and Partial Differential Equations

David L. Powers (Autor)

eBook Download: EPUB

2009 | 6. Auflage
520 Seiten
Elsevier Science (Verlag)
978-0-08-088441-7 (ISBN)

Infos

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

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Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods.The book contains nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises.Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems.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- Student Solution Manual for Sixth Edition - https://www.elsevier.com/books/student-solutions-manual-boundary-value-problems/powers/978-0-12-375664-0- 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

Inhalt

Front Cover 
1 
Boundary Value Problems and Partial Differential Equations 3
Copyright Page 5
Contents 
6 
Preface 
10 
Chapter 0: Ordinary Differential Equations 13
Homogeneous Linear Equations 
13 
Nonhomogeneous Linear Equations 
26 
Boundary Value Problems 
37 
Singular Boundary Value Problems 50
Chapter Review 
56 
Miscellaneous Exercises 
56 
Chapter 1: Fourier Series and Integrals 63
Periodic Functions and Fourier Series 63
Arbitrary Period and Half-Range Expansions 
68 
Convergence of Fourier Series 
77 
Uniform Convergence 
84 
Operations on Fourier Series 
90 
Mean Error and Convergence in Mean 
96 
Proof of Convergence 
100 
Numerical Determination of Fourier Coefficients 
106 
Fourier Integral 
111 
Complex Methods 
118 
Applications of Fourier Series and Integrals 
122 
Comments and References 
129 
Chapter Review 
130 
Miscellaneous Exercises 
130 
Chapter 2: The Heat Equation 139
Derivation and Boundary Conditions 139
Steady-State Temperatures 
147 
Example: Fixed End Temperatures 
154 
Example: Insulated Bar 
162 
Example: Different Boundary Conditions 
169 
Example: Convection 
176 
Sturm-Liouville Problems 
182 
Expansion in Series of Eigenfunctions 
188 
Generalities on the Heat Conduction Problem 
191 
Semi-Infinite Rod 
195 
Infinite Rod 
201 
The Error Function 
208 
Comments and References 
215 
Chapter Review 
217 
Miscellaneous Exercises 
217 
Chapter 3: The Wave Equation 227
The Vibrating String 227
Solution of the Vibrating String Problem 
231 
D'Alembert's Solution 
241 
One-Dimensional Wave Equation: Generalities 
248 
Estimation of Eigenvalues 
251 
Wave Equation in Unbounded Regions 
255 
Comments and References 
263 
Chapter Review 
264 
Miscellaneous Exercises 
264 
Chapter 4: The Potential Equation 273
Potential Equation 273
Potential in a Rectangle 276
Further Examples for a Rectangle 
282 
Potential in Unbounded Regions 
290 
Potential in a Disk 
299 
Classification of Partial Differential Equations and Limitations of the Product Method 306
Comments and References 
309 
Chapter Review 
311 
Miscellaneous Exercises 
311 
Chapter 5: Higher Dimensions and Other Coordinates 321
Two-Dimensional Wave Equation: Derivation 321
Three-Dimensional Heat Equation: Vector 
324 
Two-Dimensional Heat Equation: Double Series 
329 
Problems in Polar Coordinates 
334 
Bessel’s Equation 
337 
Temperature in a Cylinder 
343 
Vibrations of a Circular Membrane 
349 
Some Applications of Bessel Functions 
357 
Spherical Coordinates Legendre Polynomials
364 
Some Applications of Legendre Polynomials 
374 
Comments and References 
381 
Chapter Review 
382 
Miscellaneous Exercises 
383 
Chapter 6: Laplace Transform 391
Definition and Elementary Properties 
391 
Partial Fractions and Convolutions 
397 
Partial Differential Equations 
404 
Some Nontrivial Examples 
411 
Comments and References 
418 
Miscellaneous Exercises 
418 
Chapter 7: Numerical Methods 425
Boundary Value Problems 425
Heat Problems 
431 
Wave Equation 
435 
Potential Equation 
441 
Comments and References 
447 
Miscellaneous Exercises 
448 
Bibliography 
453 
Appendix: Mathematical References 
455 
Answers to Odd-Numbered Exercises 
461 
Index 
515 

Produkt-Details

• Erscheint lt. Verlag: 1.9.2009
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• ISBN-10: 0-08-088441-5 / 0080884415
• ISBN-13: 978-0-08-088441-7 / 9780080884417