Introduction to applied partial differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
W.H. Freeman
2013
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 313 S. Ill., graph. Darst. |
| ISBN: | 9781429275927 1429275928 |
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MARC
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| 245 | 1 | 0 | |a Introduction to applied partial differential equations |c John M. Davis |
| 264 | 1 | |a New York, NY |b W.H. Freeman |c 2013 | |
| 300 | |a XII, 313 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
їх
1
Introduction
to PDEs
1
1.1
ODEs vs. PDEs
.......................... 1
1.2
How PDEs Are Born: Conservation Laws, Fluids, and Waves
..... 6
1.3
Boundary Conditions in One Space Dimension
............ 12
1.4
ODE Solution Methods
....................... 18
2
Fourier s Method: Separation of Variables
29
2.1
Linear Algebra Concepts
...................... 29
2.2
The General Solution via Eigenfunctions
............... 35
2.3
The Coefficients via Orthogonality
................. 42
2.4
Consequences of Orthogonality
................... 50
2.5
Robin Boundary Conditions
.................... 58
2.6
Nonzero Boundary Conditions: Steady-States and Transients*
..... 63
3
Fourier Series Theory
69
3.1
Fourier Series: Sine, Cosine, and Full
................ 69
3.2
Fourier Series vs. Taylor Series: Global vs. Local Approximations*
... 75
3.3
Error Analysis and Modes of Convergence
.............. 80
3.4
Convergence Theorems
....................... 87
3.5
Basic L2 Theory
.......................... 95
3.6
The Gibbs Phenomenon*
...................... 105
4
General Orthogonal Series Expansions
115
4.1
Regular and Periodic Sturm-Liouville Theory
............. 115
4.2
Singular Sturm-Liouville Theory
.................. 129
4.3
Orthogonal Expansions: Special Functions
.............. 135
4.4
Computing Bessel Functions: The Method of Frobenius
........ 145
4.5
The Gram-Schmidt Procedure*
................... 150
vi
Contents
5 PDEs in Higher
Dimensions
157
5.1
Nuggets from Vector Calculus
.................... 157
5.2
Deriving PDEs in Higher Dimensions
................ 166
5.3
Boundary Conditions in Higher Dimensions
............. 173
5.4
Well-Posed Problems: Good Models
................. 176
5.5
Laplace s Equation in 2D
...................... 181
5.6
The 2D Heat and Wave Equations
.................. 186
6
PDEs in Other Coordinate Systems
189
6.1
Laplace s Equation in Polar Coordinates
...............189
6.2
Poisson
s
Formula and Its Consequences*
..............200
6.3
The Wave Equation and Heat Equation in Polar Coordinates
.....204
6.4
Laplace s Equation in Cylindrical Coordinates
............210
6.5
Laplace s Equation in Spherical Coordinates
.............217
7
PDEs on Unbounded Domains
231
7.1
The Infinite String: d Alembert s Solution
..............231
7.2
Characteristic Lines
........................238
7.3
The Semi-infinite String: The Method of Reflections
.........242
7.4
The Infinite Rod: The Method of Fourier Transforms
.........248
Appendix
261
Selected Answers
263
Credits
307
Index
309
|
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| id | DE-604.BV041155307 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:40:51Z |
| institution | BVB |
| isbn | 9781429275927 1429275928 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026130699 |
| oclc_num | 859373679 |
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| physical | XII, 313 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | W.H. Freeman |
| record_format | marc |
| spelling | Davis, John M. Verfasser aut Introduction to applied partial differential equations John M. Davis New York, NY W.H. Freeman 2013 XII, 313 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 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=026130699&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davis, John M. Introduction to applied partial differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Introduction to applied partial differential equations |
| title_auth | Introduction to applied partial differential equations |
| title_exact_search | Introduction to applied partial differential equations |
| title_full | Introduction to applied partial differential equations John M. Davis |
| title_fullStr | Introduction to applied partial differential equations John M. Davis |
| title_full_unstemmed | Introduction to applied partial differential equations John M. Davis |
| title_short | Introduction to applied partial differential equations |
| title_sort | introduction to applied partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026130699&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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