Boundary value problems and partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier Acad. Press
2006
|
| Edition: | 5. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Frühere Aufl. u.d.T.: Powers, David Leusch: Boundary value problems |
| Physical Description: | XI, 501 S. Ill., graph. Darst. CD-ROM (12 cm) |
| ISBN: | 0125637381 9780125637381 012563739x 9780125637398 |
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MARC
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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 |
| 246 | 1 | 3 | |a Boundary value problems |
| 250 | |a 5. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier Acad. Press |c 2006 | |
| 300 | |a XI, 501 S. |b Ill., graph. Darst. |e CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Frühere Aufl. u.d.T.: Powers, David Leusch: Boundary value problems | ||
| 650 | 4 | |a Boundary value problems |v Textbooks | |
| 650 | 4 | |a Differential equations, Partial |v Textbooks | |
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Record in the Search Index
| _version_ | 1804134163067961344 |
|---|---|
| adam_text | Contents
Preface ¡x
chapter
ο
Ordinary Differential Equations
1
0.1
Homogeneous Linear Equations
1
0.2
Nonhomogeneous Linear Equations
14
0.3
Boundary Value Problems
26
0.4
Singular Boundary Value Problems
38
0.5
Green s Functions
43
Chapter Review
51
Miscellaneous Exercises
51
CHAPTER l Fourier Series and Integrals
59
1.1
Periodic Functions and Fourier Series
59
1.2
Arbitrary Period and Half-Range Expansions
64
1.3
Convergence of Fourier Series
73
1.4
Uniform Convergence
79
1.5
Operationson
Fourier Series
85
1.6
Mean Error and Convergence in Mean
90
1.7
Proof of Convergence
95
.8
Numerical Determination of Fourier Coefficients
100
.9
Fourier Integral
106
.10
Complex Methods
113
.11
Applications of Fourier Series and Integrals
117
.12
Comments and References
124
Chapter Review
125
Miscellaneous Exercises
125
vi
Contents
CHAPTER
2
The Heat Equation
135
2.1
Derivation and Boundary Conditions
135
2.2
Steady-State Temperatures
143
2.3
Example: Fixed End Temperatures
149
2.4
Example: Insulated Bar
157
2.5
Example: Different Boundary Conditions
163
2.6
Example: Convection
170
2.7
Sturm-Liouville Problems
175
2.8
Expansion in Series of Eigenf unctions
181
2.9
Generalities on the Heat Conduction Problem
184
2.10
Semi-Infinite Rod
188
2.11
Infinite Rod
193
2.12
The Error Function
199
2.13
Comments and
Ref
erences
204
Chapter Review
206
Miscellaneous Exercises
206
chapter
з
The Wave Equation
215
3.1
The Vibrating String
215
3.2
Solution of the Vibrating String Problem
218
3.3
d Alembert s Solution
227
3.4
One-Dimensional Wave Equation: Generalities
233
3.5
Estimation of Eigenvalues
236
3.6
Wave Equation in Unbounded Regions
239
3.7
Comments and References
246
Chapter Review
247
Miscellaneous Exercises
247
chapter
4
The Potential Equation
255
4.1
Potential Equation
255
4.2
Potential in a Rectangle
259
4.3
Further Examples for a Rectangle
264
4.4
Potential in Unbounded Regions
270
4.5
Potential in a Disk
275
4.6
Classification and Limitations
280
4.7
Comments and References
283
Chapter Review
285
Miscellaneous Exercises
285
chapter
5
Higher Dimensions and Other Coordinates
295
5.1
Two-Dimensional Wave Equation: Derivation
295
5.2
Three-Dimensional Heat
Equation
298
5.3
Two-Dimensional Heat Equation: Solution
303
Contents
vii
5.4 Problems
¡η
Polar
Coordinates
308
5.5
Besseľs
Equation
311
5.6
Temperature
in a Cylinder
316
5.7
Vibrations of a Circular Membrane
321
5.8
Some Applications of Bessel Functions
329
5.9
Spherical Coordinates; Legendre Polynomials
335
5.10
Some Applications of Legendre Polynomials
345
5.11
Comments and References
353
Chapter Review
354
Miscellaneous Exercises
354
chapter
б
Laplace Transform
363
6.1
Definition and Elementary Properties
363
6.2
Partial Fractions and Convolutions
369
6.3
Partial Differential Equations
376
6.4
More Difficult Examples
383
6.5
Comments and References
389
Miscellaneous Exercises
389
chapter? Numerical Methods
397
7.1
Boundary Value Problems
397
7.2
Heat Problems
403
7.3
Wave Equation
408
7.4
Potential Equation
414
7.5
Two-Dimensional Problems
420
7.6
Comments and
Ref erences
428
Miscellaneous Exercises
428
Bibliography
433
Appendix: Mathematical References
435
Answers to Odd-Numbered Exercises
441
Index
495
|
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| discipline | Mathematik |
| edition | 5. ed. |
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| id | DE-604.BV020831295 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:20:14Z |
| institution | BVB |
| isbn | 0125637381 9780125637381 012563739x 9780125637398 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013836500 |
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| open_access_boolean | |
| owner | DE-824 DE-355 DE-BY-UBR DE-92 |
| owner_facet | DE-824 DE-355 DE-BY-UBR DE-92 |
| physical | XI, 501 S. Ill., graph. Darst. CD-ROM (12 cm) |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Elsevier Acad. Press |
| record_format | marc |
| spelling | Powers, David Leusch Verfasser aut Boundary value problems and partial differential equations David L. Powers Boundary value problems 5. ed. Amsterdam [u.a.] Elsevier Acad. Press 2006 XI, 501 S. Ill., graph. Darst. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Frühere Aufl. u.d.T.: Powers, David Leusch: Boundary value problems 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 Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013836500&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_alt | Boundary value problems |
| 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=013836500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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