Partial differential equations: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
2008
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Ergänzung dazu: Levandosky, J. L.: Solutions manual for partial differential equations ... |
| Beschreibung: | X, 454 S. graph. Darst. |
| ISBN: | 9780470054567 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV023219837 | ||
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| 008 | 080318s2008 d||| |||| 00||| eng d | ||
| 020 | |a 9780470054567 |9 978-0-470-05456-7 | ||
| 035 | |a (OCoLC)488639007 | ||
| 035 | |a (DE-599)BVBBV023219837 | ||
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| 100 | 1 | |a Strauss, Walter A. |d 1937- |e Verfasser |0 (DE-588)111767504 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations |b an introduction |c Walter A. Strauss |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 2008 | |
| 300 | |a X, 454 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Ergänzung dazu: Levandosky, J. L.: Solutions manual for partial differential equations ... | ||
| 650 | 4 | |a differentialligninger | |
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Datensatz im Suchindex
| _version_ | 1804137506566832128 |
|---|---|
| adam_text | CONTENTS
(lhe
starred sections form the basic part of the book.)
Chapter
1
/Where PDEs Come From
1.1*
What is a Partial Differential Equation?
1
1.2*
First-Order Linear Equations
б
1.3*
Flows
,
Vibrations
,
and Diffusions
10
1.4*
Initial and Boundary Conditions
20
1.5
Well-Posed Problems
25
1.6
Types of Second-Order Equations
28
Chapter
2
/Waves and Diffusions
2.1*
The Wave Equation
33
2.2*
Causality and Energy
39
2.3*
The Diffusion Equation
42
2.4*
Diffusion on the Whole Line
46
2.5*
Comparison of Waves and Diffusions
54
Chapter
З
/Reflections
and Sources
3.1
Diffusion on the Half-Line
57
3.2
Reflections of Waves
61
3.3
Diffusion with a Source
67
3.4
Waves with a Source
71
3.5
Diffusion Revisited
80
Chapter 4/Boundarv Problems
4.1*
Separation of Variables
,
The Dirichlet Condition
84
4.2*
The Neumann Condition
89
4.3*
The Robin Condition
92
viii
CONTENTS ix
Chapter
5/
Fourier Series
5.1*
The Coefficients
104
5.2*
Even, Odd, Periodic, and Complex Functions
113
5.3*
Orthogonality and General Fourier Series
118
5.4*
Completeness
124
5.5
Completeness and the Gibbs Phenomenon
136
5.6
Inhomogeneous Boundary Conditions
147
Chapter
б/Нагтопіс
Functions
6.1*
Laplace s Equation
152
6.2*
Rectangles and Cubes
161
6.3*
Poisson s Formula
165
6.4
Circles
,
Wedges
,
and
Annuli 172
(The next four chapters may be studied in any order.)
Chapter 7/Green s Identities and Green s Functions
7.1
Green
s
First Identity
178
7.2
Green s Second Identity
185
7.3
Green s Functions
188
7.4
Half-Space and Sphere
191
Chapter
8/Computation of Solutions
8.1
Opportunities and Dangers
199
8.2
Approximations of Diffusions
203
8.3
Approximations of Waves
211
8.4
Approximations of Laplace s Equation
218
8.5
Finite Element Method
222
Chapter
9
/Waves in Space
9.1
Energy and Causality
228
9.2
The Wave Equation in Space-Time
234
9.3
Rays, Singularities, and Sources
242
9.4
The Diffusion and
Schrödinger
Equations
248
9.5
The Hydrogen Atom
254
Chapter
10/Boundaries in the Plane and in Space
10.1
Fouríeťs
Method, Revisited
258
10.2
Vibrations of a Drumhead
264
10.3
Solid Vibrations in a Ball
270
10.4
Nodes
278
10.5
Bessel Functions
282
χ
CONTENTS
10.6 Legendre
Functions
289
10.7
Angular Momentum in Quantum Mechanics
294
Chapter
11
/General Eigenvalue Problems
11.1
The Eigenvalues Are Minima of the Potential Energy
299
11.2
Computation of Eigenvalues
304
11.3
Completeness
310
11.4
Symmetric Differential Operators
314
11.5
Completeness and Separation of Variables
318
11.6
Asymptotics of the Eigenvalues
322
Chapter
12
/Distributions and Transforms
12.1
Distributions
331
12.2
Green s Functions, Revisited
338
12.3
Fourier Transforms
343
12.4
Source Functions
349
12.5
Laplace Transform Techniques
353
Chapter 13/PDE Problems from Physics
13.1
Electromagnetism
358
13.2
Fluids and Acoustics
361
13.3
Scattering
366
13.4
Continuous Spectrum
370
13.5
Equations of Elementary Particles
373
Chapter 14/Nonlinear PDEs
14.1
ShockWaves
380
14.2 Solitons 390
14.3
Calculus of Variations
397
14.4
Bifurcation Theory
401
14.5
Water Waves
406
Appendix
A.
1
Continuous and Differentiable Functions
414
A.
2
Infinite Series of Functions
418
A.3 Differentiation and Integration
420
A.
4
Differential Equations
423
A.5 The Gamma Function
425
References
427
Answers and Hints to Selected Exercises
431
Index
445
|
| adam_txt |
CONTENTS
(lhe
starred sections form the basic part of the book.)
Chapter
1
/Where PDEs Come From
1.1*
What is a Partial Differential Equation?
1
1.2*
First-Order Linear Equations
б
1.3*
Flows
,
Vibrations
,
and Diffusions
10
1.4*
Initial and Boundary Conditions
20
1.5
Well-Posed Problems
25
1.6
Types of Second-Order Equations
28
Chapter
2
/Waves and Diffusions
2.1*
The Wave Equation
33
2.2*
Causality and Energy
39
2.3*
The Diffusion Equation
42
2.4*
Diffusion on the Whole Line
46
2.5*
Comparison of Waves and Diffusions
54
Chapter
З
/Reflections
and Sources
3.1
Diffusion on the Half-Line
57
3.2
Reflections of Waves
61
3.3
Diffusion with a Source
67
3.4
Waves with a Source
71
3.5
Diffusion Revisited
80
Chapter 4/Boundarv Problems
4.1*
Separation of Variables
,
The Dirichlet Condition
84
4.2*
The Neumann Condition
89
4.3*
The Robin Condition
92
viii
CONTENTS ix
Chapter
5/
Fourier Series
5.1*
The Coefficients
104
5.2*
Even, Odd, Periodic, and Complex Functions
113
5.3*
Orthogonality and General Fourier Series
118
5.4*
Completeness
124
5.5
Completeness and the Gibbs Phenomenon
136
5.6
Inhomogeneous Boundary Conditions
147
Chapter
б/Нагтопіс
Functions
6.1*
Laplace's Equation
152
6.2*
Rectangles and Cubes
161
6.3*
Poisson's Formula
165
6.4
Circles
,
Wedges
,
and
Annuli 172
(The next four chapters may be studied in any order.)
Chapter 7/Green's Identities and Green's Functions
7.1
Green
s
First Identity
178
7.2
Green's Second Identity
185
7.3
Green's Functions
188
7.4
Half-Space and Sphere
191
Chapter
8/Computation of Solutions
8.1
Opportunities and Dangers
199
8.2
Approximations of Diffusions
203
8.3
Approximations of Waves
211
8.4
Approximations of Laplace's Equation
218
8.5
Finite Element Method
222
Chapter
9
/Waves in Space
9.1
Energy and Causality
228
9.2
The Wave Equation in Space-Time
234
9.3
Rays, Singularities, and Sources
242
9.4
The Diffusion and
Schrödinger
Equations
248
9.5
The Hydrogen Atom
254
Chapter
10/Boundaries in the Plane and in Space
10.1
Fouríeťs
Method, Revisited
258
10.2
Vibrations of a Drumhead
264
10.3
Solid Vibrations in a Ball
270
10.4
Nodes
278
10.5
Bessel Functions
282
χ
CONTENTS
10.6 Legendre
Functions
289
10.7
Angular Momentum in Quantum Mechanics
294
Chapter
11
/General Eigenvalue Problems
11.1
The Eigenvalues Are Minima of the Potential Energy
299
11.2
Computation of Eigenvalues
304
11.3
Completeness
310
11.4
Symmetric Differential Operators
314
11.5
Completeness and Separation of Variables
318
11.6
Asymptotics of the Eigenvalues
322
Chapter
12
/Distributions and Transforms
12.1
Distributions
331
12.2
Green's Functions, Revisited
338
12.3
Fourier Transforms
343
12.4
Source Functions
349
12.5
Laplace Transform Techniques
353
Chapter 13/PDE Problems from Physics
13.1
Electromagnetism
358
13.2
Fluids and Acoustics
361
13.3
Scattering
366
13.4
Continuous Spectrum
370
13.5
Equations of Elementary Particles
373
Chapter 14/Nonlinear PDEs
14.1
ShockWaves
380
14.2 Solitons 390
14.3
Calculus of Variations
397
14.4
Bifurcation Theory
401
14.5
Water Waves
406
Appendix
A.
1
Continuous and Differentiable Functions
414
A.
2
Infinite Series of Functions
418
A.3 Differentiation and Integration
420
A.
4
Differential Equations
423
A.5 The Gamma Function
425
References
427
Answers and Hints to Selected Exercises
431
Index
445 |
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| id | DE-604.BV023219837 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:15:32Z |
| indexdate | 2024-07-09T21:13:23Z |
| institution | BVB |
| isbn | 9780470054567 |
| language | English |
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| physical | X, 454 S. graph. Darst. |
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| publisher | Wiley |
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| spelling | Strauss, Walter A. 1937- Verfasser (DE-588)111767504 aut Partial differential equations an introduction Walter A. Strauss 2. ed. New York [u.a.] Wiley 2008 X, 454 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ergänzung dazu: Levandosky, J. L.: Solutions manual for partial differential equations ... differentialligninger partielle differentialligninger Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content 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=016405765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Strauss, Walter A. 1937- Partial differential equations an introduction differentialligninger partielle differentialligninger Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Partial differential equations an introduction |
| title_auth | Partial differential equations an introduction |
| title_exact_search | Partial differential equations an introduction |
| title_exact_search_txtP | Partial differential equations an introduction |
| title_full | Partial differential equations an introduction Walter A. Strauss |
| title_fullStr | Partial differential equations an introduction Walter A. Strauss |
| title_full_unstemmed | Partial differential equations an introduction Walter A. Strauss |
| title_short | Partial differential equations |
| title_sort | partial differential equations an introduction |
| title_sub | an introduction |
| topic | differentialligninger partielle differentialligninger Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | differentialligninger partielle differentialligninger Partielle Differentialgleichung Einführung Lehrbuch |
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