Beginning partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2008
|
| Edition: | 2. ed. |
| Series: | Pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erg. dazu : O'Neil, Peter: Solutions manual to accompany beginning partial differnetial equations. |
| Physical Description: | IX, 477 S. graph. Darst. |
| ISBN: | 9780470133903 |
Staff View
MARC
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| 100 | 1 | |a O'Neil, Peter V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Beginning partial differential equations |c Peter V. O'Neil |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2008 | |
| 300 | |a IX, 477 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 500 | |a Erg. dazu : O'Neil, Peter: Solutions manual to accompany beginning partial differnetial equations. | ||
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804137568806109184 |
|---|---|
| adam_text | Contents
First-Order Equations
1
1.1
Notation and Terminology
1
1.2
The Linear First-Order Equation
4
1.3
The Significance of Characteristics
12
1.4
The Quasi-Linear Equation
16
Linear Second-Order Equations
23
2.1
Classification
23
2.2
The Hyperbolic Canonical Form
25
2.3
The Parabolic Canonical Form
30
2.4
The Elliptic Canonical Form
33
2.5
Some Equations of Mathematical Physics
38
2.6
The Second-Order Cauchy Problem
46
2.7
Characteristics and the Cauchy Problem
49
2.8
Characteristics as Carriers of Discontinuities
56
Elements of Fourier Analysis
59
3.1
Why Fourier Series?
59
3.2
The Fourier Series of a Function
60
3.3
Convergence of Fourier Series
63
3.4
Sine and Cosine Expansions
81
3.5
The Fourier Integral
89
3.6
The Fourier Transform
95
3.7
Convolution
101
3.8
Fourier Sine and Cosine Transforms
106
CONTENTS
The Wave Equation
109
4.1
d Alembert Solution of the Cauchy Problem
109
4.2
ďAlemberťs
Solution as a Sum of Waves
117
4.3
The Characteristic Triangle
126
4.4
The Wave Equation on a Half-Line
131
4.5
A Half-Line with Moving End
134
4.6
A Nonhomogeneous Problem on the Real Line
137
4.7
A General Problem on a Closed Interval
141
4.8
Fourier Series Solutions on a Closed Interval
150
4.9
A Nonhomogeneous Problem on a Closed Interval
159
4.10
The Cauchy Problem by Fourier Integral
168
4.11
A Wave Equation in Two Space Dimensions
173
4.12
The Kirchhoff-Poisson Solution
177
4.13
Hadamard s Method of Descent
182
The Heat Equation
185
5.1
The Cauchy Problem and Initial Conditions
185
5.2
The Weak Maximum Principle
188
5.3
Solutions on Bounded Intervals
192
5.4
The Heat Equation on the Real Line
210
5.5
The Heat Equation on the Half-Line
218
5.6
The Debate Over the Age of the Earth
224
5.7
The Nonhomogeneous Heat Equation
227
5.8
The Heat Equation in Two Space Variables
234
Dirichlet and Neumann Problems
239
6.1
The Setting of the Problems
239
6.2
Some Harmonic Functions
247
6.3
Representation Theorems
251
6.4
Two Properties of Harmonic Functions
257
6.5
Is the Dirichlet Problem Well Posed?
263
6.6
Dirichlet Problem for a Rectangle
266
6.7
Dirichlet Problem for a Disk
269
6.8
Poisson s Integral Representation for a Disk
272
6.9
Dirichlet Problem for the Upper Half-Plane
276
6.10
Dirichlet Problem for the Right Quarter-Plane
279
6.11
Dirichlet Problem for a Rectangular Box
282
6.12
The Neumann Problem
285
6.13
Neumann Problem for a Rectangle
288
6.14
Neumann Problem for a Disk
290
6.15
Neumann Problem for the Upper Half-Plane
294
6.16
Green s Function for a Dirichlet Problem
296
6.17
Conformai
Mapping Techniques
303
6.17.1
Conformai
Mappings
303
6.17.2
Bilinear Transformations
308
6.17.3
Construction of
Conformai
Mappings between Domains
313
6.17.4
An Integral Solution of the Dirichlet Problem for a Disk
320
6.17.5
Solution of Dirichlet Problems by
Conformai
Mapping
323
Vil
Existence
Theorems 327
7.1
A Classical Existence Theorem
327
7.2
A Hubert Space Approach
336
7.3
Distributions and an Existence Theorem
344
Additional Topics
351
8.1
Solutions by Eigenfunction Expansions
351
8.2
Numerical Approximations of Solutions
370
8.3
Burger s Equation
377
8.4
The Telegraph Equation
383
8.5
Poisson s Equation
390
End Materials
395
9.1
Historical Notes
395
9.2
Glossary
398
9.3
Answers to Selected Problems
399
Index
473
|
| adam_txt |
Contents
First-Order Equations
1
1.1
Notation and Terminology
1
1.2
The Linear First-Order Equation
4
1.3
The Significance of Characteristics
12
1.4
The Quasi-Linear Equation
16
Linear Second-Order Equations
23
2.1
Classification
23
2.2
The Hyperbolic Canonical Form
25
2.3
The Parabolic Canonical Form
30
2.4
The Elliptic Canonical Form
33
2.5
Some Equations of Mathematical Physics
38
2.6
The Second-Order Cauchy Problem
46
2.7
Characteristics and the Cauchy Problem
49
2.8
Characteristics as Carriers of Discontinuities
56
Elements of Fourier Analysis
59
3.1
Why Fourier Series?
59
3.2
The Fourier Series of a Function
60
3.3
Convergence of Fourier Series
63
3.4
Sine and Cosine Expansions
81
3.5
The Fourier Integral
89
3.6
The Fourier Transform
95
3.7
Convolution
101
3.8
Fourier Sine and Cosine Transforms
106
CONTENTS
The Wave Equation
109
4.1
d'Alembert Solution of the Cauchy Problem
109
4.2
ďAlemberťs
Solution as a Sum of Waves
117
4.3
The Characteristic Triangle
126
4.4
The Wave Equation on a Half-Line
131
4.5
A Half-Line with Moving End
134
4.6
A Nonhomogeneous Problem on the Real Line
137
4.7
A General Problem on a Closed Interval
141
4.8
Fourier Series Solutions on a Closed Interval
150
4.9
A Nonhomogeneous Problem on a Closed Interval
159
4.10
The Cauchy Problem by Fourier Integral
168
4.11
A Wave Equation in Two Space Dimensions
173
4.12
The Kirchhoff-Poisson Solution
177
4.13
Hadamard's Method of Descent
182
The Heat Equation
185
5.1
The Cauchy Problem and Initial Conditions
185
5.2
The Weak Maximum Principle
188
5.3
Solutions on Bounded Intervals
192
5.4
The Heat Equation on the Real Line
210
5.5
The Heat Equation on the Half-Line
218
5.6
The Debate Over the Age of the Earth
224
5.7
The Nonhomogeneous Heat Equation
227
5.8
The Heat Equation in Two Space Variables
234
Dirichlet and Neumann Problems
239
6.1
The Setting of the Problems
239
6.2
Some Harmonic Functions
247
6.3
Representation Theorems
251
6.4
Two Properties of Harmonic Functions
257
6.5
Is the Dirichlet Problem Well Posed?
263
6.6
Dirichlet Problem for a Rectangle
266
6.7
Dirichlet Problem for a Disk
269
6.8
Poisson's Integral Representation for a Disk
272
6.9
Dirichlet Problem for the Upper Half-Plane
276
6.10
Dirichlet Problem for the Right Quarter-Plane
279
6.11
Dirichlet Problem for a Rectangular Box
282
6.12
The Neumann Problem
285
6.13
Neumann Problem for a Rectangle
288
6.14
Neumann Problem for a Disk
290
6.15
Neumann Problem for the Upper Half-Plane
294
6.16
Green"s Function for a Dirichlet Problem
296
6.17
Conformai
Mapping Techniques
303
6.17.1
Conformai
Mappings
303
6.17.2
Bilinear Transformations
308
6.17.3
Construction of
Conformai
Mappings between Domains
313
6.17.4
An Integral Solution of the Dirichlet Problem for a Disk
320
6.17.5
Solution of Dirichlet Problems by
Conformai
Mapping
323
Vil
Existence
Theorems 327
7.1
A Classical Existence Theorem
327
7.2
A Hubert Space Approach
336
7.3
Distributions and an Existence Theorem
344
Additional Topics
351
8.1
Solutions by Eigenfunction Expansions
351
8.2
Numerical Approximations of Solutions
370
8.3
Burger's Equation
377
8.4
The Telegraph Equation
383
8.5
Poisson's Equation
390
End Materials
395
9.1
Historical Notes
395
9.2
Glossary
398
9.3
Answers to Selected Problems
399
Index
473 |
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| index_date | 2024-07-02T20:31:47Z |
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| institution | BVB |
| isbn | 9780470133903 |
| language | English |
| lccn | 2007039327 |
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| physical | IX, 477 S. graph. Darst. |
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| spelling | O'Neil, Peter V. Verfasser aut Beginning partial differential equations Peter V. O'Neil 2. ed. Hoboken, NJ Wiley 2008 IX, 477 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Erg. dazu : O'Neil, Peter: Solutions manual to accompany beginning partial differnetial equations. Differential equations, Partial 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=016445669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Neil, Peter V. Beginning partial differential equations Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Beginning partial differential equations |
| title_auth | Beginning partial differential equations |
| title_exact_search | Beginning partial differential equations |
| title_exact_search_txtP | Beginning partial differential equations |
| title_full | Beginning partial differential equations Peter V. O'Neil |
| title_fullStr | Beginning partial differential equations Peter V. O'Neil |
| title_full_unstemmed | Beginning partial differential equations Peter V. O'Neil |
| title_short | Beginning partial differential equations |
| title_sort | beginning partial differential equations |
| topic | Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations, Partial Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016445669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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