Boundary value problems and partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier [u.a.]
2010
|
| Edition: | 6. ed |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 506 S. Ill., graph. Darst. |
| ISBN: | 9780123747198 0123747198 |
Staff View
MARC
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| 020 | |a 0123747198 |c (hbk.) £44.99 |9 0-12-374719-8 | ||
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| 100 | 1 | |a Powers, David Leusch |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boundary value problems and partial differential equations |c David L. Powers |
| 250 | |a 6. ed | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier [u.a.] |c 2010 | |
| 300 | |a XI, 506 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Boundary value problems |v Textbooks | |
| 650 | 4 | |a Differential equations, Partial |v Textbooks | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018651409 | ||
Record in the Search Index
| _version_ | 1804140733458808832 |
|---|---|
| adam_text | Contents
Preface
ix
CHAPTER
0
Ordinary Differential Equations
1
0.1.
Homogeneous Linear Equations
1
0.2.
Nonhomogeneous Linear Equations
14
0.3.
Boundary Value Problems
25
0.4.
Singular Boundary Value Problems
38
Chapter Review
44
Miscellaneous Exercises
44
CHAPTER
1
Fourier Series and Integrals
51
1.1.
Periodic Functions and Fourier Series
51
1.2.
Arbitrary Period and Half-Range Expansions
56
1.3.
Convergence of Fourier Series
65
1.4.
Uniform Convergence
72
1.5.
Operations on Fourier Series
78
1.6.
Mean Error and Convergence in Mean
84
1.7.
Proof of Convergence
88
1.8.
Numerical Determination of Fourier Coefficients
94
1.9.
Fourier Integral
99
1.10.
Complex Methods
106
1.11.
Applications of Fourier Series and Integrals
110
1.12.
Comments and References
117
Chapter Review
118
Miscellaneous Exercises
118
CHAPTER
2
The Heat Equation
127
2.1.
Derivation and Boundary Conditions
127
2.2.
Steady-State Temperatures
135
2.3.
Example: Fixed End Temperatures
142
2.4.
Example: Insulated Bar
150
2.5.
Example: Different Boundary Conditions
157
2.6.
Example: Convection
164
2.7.
Sturm-Liouville Problems
170
2.8.
Expansion in Series of Eigenfunctions
176
2.9.
Generalities on the Heat Conduction Problem
179
2.10.
Semi-Infinite Rod
183
2.11.
Infinite Rod
189
2.12.
The Error Function
196
2.13.
Comments and
Ref
erences
203
Chapter Review
205
Miscellaneous Exercises
205
CHAPTERS The Wave Equation
215
3.1.
The Vibrating String
215
3.2.
Solution of the Vibrating String Problem
219
3.3.
D Alembert s Solution
229
3.4.
One-Dimensional Wave Equation: Generalities
236
3.5.
Estimation of Eigenvalues
239
3.6.
Wave Equation in Unbounded Regions
243
3.7.
Comments and References
251
Chapter Review
252
Miscellaneous Exercises
252
CHAPTER
4
The Potential Equation
261
4.1.
Potential Equation
261
4.2.
Potential in a Rectangle
264
4.3.
Further Examples for a Rectangle
270
4.4.
Potential in Unbounded Regions
278
4.5.
Potential in a Disk
287
4.6.
Classification and Limitations
294
4.7.
Comments and References
297
Chapter Review
299
Miscellaneous Exercises
299
CHAPTER
5
Higher Dimensions and Other Coordinates
309
5.1.
Two-Dimensional Wave Equation: Derivation
309
5.2.
Three-Dimensional Heat Equation: Vector Derivation
312
5.3.
Two-Dimensional Heat Equation: Double Series Solution
317
5.4.
Problems in Polar Coordinates
322
5.5.
Bessel s Equation
325
5.6.
Temperature in a Cylinder
331
5.7.
Vibrations
of
α
Circular
Membrane 337
5.8.
Some
Applications
of Bessel Functions
345
5.9.
Spherical Coordinates; Legendre Polynomials
352
5.10.
Some Applications of Legendre Polynomials
362
5.11.
Comments and References
369
Chapter Review
370
Miscellaneous Exercises
371
CHAPTER
6
Laplace Transform
379
6.1.
Definition and Elementary Properties
379
6.2.
Partial Fractions and Convolutions
385
6.3.
Partial Differential Equations
392
6.4.
Some
Nontrivial
Examples
399
6.5.
Comments and References
406
Miscellaneous Exercises
406
CHAPTER
7
Numerical Methods
413
7.1.
Boundary Value Problems
413
7.2.
Heat Problems
419
7.3.
Wave Equation
423
7.4.
Potential Equation
429
7.5.
Comments and References
435
Miscellaneous Exercises
436
Bibliography
441
Appendix: Mathematical References
443
Answers to Odd-Numbered Exercises
449
Index
503
|
| any_adam_object | 1 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| edition | 6. ed |
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| id | DE-604.BV035792090 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:40Z |
| institution | BVB |
| isbn | 9780123747198 0123747198 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018651409 |
| oclc_num | 319940138 |
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| owner | DE-92 DE-739 DE-29T |
| owner_facet | DE-92 DE-739 DE-29T |
| physical | XI, 506 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Elsevier [u.a.] |
| record_format | marc |
| spelling | Powers, David Leusch Verfasser aut Boundary value problems and partial differential equations David L. Powers 6. ed Amsterdam [u.a.] Elsevier [u.a.] 2010 XI, 506 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018651409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Powers, David Leusch Boundary value problems and partial differential equations Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | Boundary value problems and partial differential equations |
| title_auth | Boundary value problems and partial differential equations |
| title_exact_search | Boundary value problems and partial differential equations |
| title_full | Boundary value problems and partial differential equations David L. Powers |
| title_fullStr | Boundary value problems and partial differential equations David L. Powers |
| title_full_unstemmed | Boundary value problems and partial differential equations David L. Powers |
| title_short | Boundary value problems and partial differential equations |
| title_sort | boundary value problems and partial differential equations |
| topic | Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018651409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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