Solutions manual to accompany beginning partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2008
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Erg. zu O'Neil, Peter: Beginning partial differential equations. |
| Beschreibung: | IX, 180 S. graph. Darst. |
| ISBN: | 9780470133897 |
Internformat
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| 100 | 1 | |a O'Neil, Peter V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Solutions manual to accompany 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, 180 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Erg. zu O'Neil, Peter: Beginning partial differential equations. | ||
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137805127876608 |
|---|---|
| adam_text | Contents
First-Order Equations
1
1.1
Notation and Terminology
1
1.2
The Linear First Order Equation
3
1.3
The Significance of Characteristics
6
1.4
The Quasi-Linear Equation
11
Linear Second-Order Equations
17
2.1
Classification
17
2.2
The Hyperbolic Canonical Form
17
2.3
The Parabolic Canonical Form
20
2.4
The Elliptic Canonical Form
21
Problems for Sections
2.1 - 2.4 23
2.5
Some Equations of Mathematical Physics
31
2.6
The Second Order Cauchy Problem
31
2.7
Characteristics and the Cauchy Problem
33
Elements of Fourier Analysis
37
3.1
Why Fourier Series?
37
3.2
The Fourier Series of a Function
37
3.3
Convergence of Fourier Series
38
3.4
Sine and Cosine Expansions
50
3.5
The Fourier Integral
65
3.6
The Fourier Transform
66
3.7
Convolution
72
3.8
Fourier Sine and Cosine Transforms
74
vi
CONTENTS
4
The Wave Equation
11
4.1
The Cauchy Problem and d Alembert s Solution
77
4.2
d Alembert s Solution As a Sum of Waves
78
4.3
The Characteristic Triangle 78
4.4
The Wave Equation on a Half-Line
79
4.5
A Problem on a Half-Line With Moving End
82
4.6
A Nonhomogeneous Problem on the Real Line
84
4.7
A General Problem on a Closed Interval
87
4.8
Fourier Series Solutions on a Closed Interval
94
4.9
A Nonhomogeneous Problem on a Closed Interval
106
4.10
The Cauchy Problem by Fourier Integral
109
4.11
A Wave Equation in Two Space Dimensions
112
4.12
The Kirchhoff-Poisson Solution
112
4.13
Hadamard s Method of Descent
ИЗ
5
The Heat Equation I15
5.1
The Cauchy Problem and Initial Conditions
115
5.3
Solutions on Bounded Intervals
116
5.4
The Heat Equation on the Real Line
121
5.5
The Heat Equation on the Half-Line
124
5.7
The Nonhomogeneous Heat Equation
125
5.8
The Heat Equation In Several Space Variables
129
6
Dirichlet and Neumann Problems
133
6.1
The Setting of the Problems
133
6.2
Some Harmonic Functions
133
6.3
Representation Theorems
134
6.4
Two Properties of Harmonic Functions
136
6.6
Dirichlet Problem for a Rectangle
138
6.7
Dirichlet Problem for a Disk
141
6.8
Poisson s Integral Representation for a Disk
144
6.9
Dirichlet Problem for the Upper Half-Plane
146
6.10
Dirichlet. Problem for the Right Quarter-Plane
147
6.11
Dirichlet Problem for a Rectangular Box
148
6.12
The Neumann Problem
148
6.13
Neumann Problem for a Rectangle
149
6.14
Neumann Problem for a Disk
151
6.15
Neumann Problem for the Upper Half-Plane
153
6.16
Green s Function for a Dirichlet Problem
153
6.17
Conformai
Mapping Techniques
157
6.17.1
Conformai
Mappings
157
6.17.2
Bilinear Transformations
157
6.17.3
Construction of
Conformai
Mappings Between Domains
159
6.17.5
Solution of Dirichlet Problems by
Conformai
Mapping
161
Existence
Theorems
165
7.1
A
Classical
Existence
Theorem
165
7.2
A
Hubert Space Approach
165
7.3
Distributions and an Existence Theorem
166
Additional Topics
167
8.1
Solutions by Eigenftmction Expansions
167
8.2
Numerical Approximations of
Solutions
173
8.3
Burger s Equation
176
8.4
The Telegraph Equation
178
8.5
Poisson
s Equation
179
|
| adam_txt |
Contents
First-Order Equations
1
1.1
Notation and Terminology
1
1.2
The Linear First Order Equation
3
1.3
The Significance of Characteristics
6
1.4
The Quasi-Linear Equation
11
Linear Second-Order Equations
17
2.1
Classification
17
2.2
The Hyperbolic Canonical Form
17
2.3
The Parabolic Canonical Form
20
2.4
The Elliptic Canonical Form
21
Problems for Sections
2.1 - 2.4 23
2.5
Some Equations of Mathematical Physics
31
2.6
The Second Order Cauchy Problem
31
2.7
Characteristics and the Cauchy Problem
33
Elements of Fourier Analysis
37
3.1
Why Fourier Series?
37
3.2
The Fourier Series of a Function
37
3.3
Convergence of Fourier Series
38
3.4
Sine and Cosine Expansions
50
3.5
The Fourier Integral
65
3.6
The Fourier Transform
66
3.7
Convolution
72
3.8
Fourier Sine and Cosine Transforms
74
vi
CONTENTS
4
The Wave Equation
11
4.1
The Cauchy Problem and d'Alembert's Solution
77
4.2
d'Alembert's Solution As a Sum of Waves
78
4.3
The Characteristic Triangle 78
4.4
The Wave Equation on a Half-Line
79
4.5
A Problem on a Half-Line With Moving End
82
4.6
A Nonhomogeneous Problem on the Real Line
84
4.7
A General Problem on a Closed Interval
87
4.8
Fourier Series Solutions on a Closed Interval
94
4.9
A Nonhomogeneous Problem on a Closed Interval
106
4.10
The Cauchy Problem by Fourier Integral
109
4.11
A Wave Equation in Two Space Dimensions
112
4.12
The Kirchhoff-Poisson Solution
112
4.13
Hadamard's Method of Descent
ИЗ
5
The Heat Equation I15
5.1
The Cauchy Problem and Initial Conditions
115
5.3
Solutions on Bounded Intervals
116
5.4
The Heat Equation on the Real Line
121
5.5
The Heat Equation on the Half-Line
124
5.7
The Nonhomogeneous Heat Equation
125
5.8
The Heat Equation In Several Space Variables
129
6
Dirichlet and Neumann Problems
133
6.1
The Setting of the Problems
133
6.2
Some Harmonic Functions
133
6.3
Representation Theorems
134
6.4
Two Properties of Harmonic Functions
136
6.6
Dirichlet Problem for a Rectangle
138
6.7
Dirichlet Problem for a Disk
141
6.8
Poisson's Integral Representation for a Disk
144
6.9
Dirichlet Problem for the Upper Half-Plane
146
6.10
Dirichlet. Problem for the Right Quarter-Plane
147
6.11
Dirichlet Problem for a Rectangular Box
148
6.12
The Neumann Problem
148
6.13
Neumann Problem for a Rectangle
149
6.14
Neumann Problem for a Disk
151
6.15
Neumann Problem for the Upper Half-Plane
153
6.16
Green's Function for a Dirichlet Problem
153
6.17
Conformai
Mapping Techniques
157
6.17.1
Conformai
Mappings
157
6.17.2
Bilinear Transformations
157
6.17.3
Construction of
Conformai
Mappings Between Domains
159
6.17.5
Solution of Dirichlet Problems by
Conformai
Mapping
161
Existence
Theorems
165
7.1
A
Classical
Existence
Theorem
165
7.2
A
Hubert Space Approach
165
7.3
Distributions and an Existence Theorem
166
Additional Topics
167
8.1
Solutions by Eigenftmction Expansions
167
8.2
Numerical Approximations of
Solutions
173
8.3
Burger's Equation
176
8.4
The Telegraph Equation
178
8.5
Poisson
\s Equation
179 |
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| ctrlnum | (OCoLC)263455240 (DE-599)BVBBV023415150 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV023415150 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:29:05Z |
| indexdate | 2024-07-09T21:18:07Z |
| institution | BVB |
| isbn | 9780470133897 |
| language | English |
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| physical | IX, 180 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | Wiley |
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| spelling | O'Neil, Peter V. Verfasser aut Solutions manual to accompany beginning partial differential equations Peter V. O'Neil 2. ed. Hoboken, NJ Wiley 2008 IX, 180 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Erg. zu O'Neil, Peter: Beginning partial differential equations. 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=016597693&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Neil, Peter V. Solutions manual to accompany beginning partial differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Solutions manual to accompany beginning partial differential equations |
| title_auth | Solutions manual to accompany beginning partial differential equations |
| title_exact_search | Solutions manual to accompany beginning partial differential equations |
| title_exact_search_txtP | Solutions manual to accompany beginning partial differential equations |
| title_full | Solutions manual to accompany beginning partial differential equations Peter V. O'Neil |
| title_fullStr | Solutions manual to accompany beginning partial differential equations Peter V. O'Neil |
| title_full_unstemmed | Solutions manual to accompany beginning partial differential equations Peter V. O'Neil |
| title_short | Solutions manual to accompany beginning partial differential equations |
| title_sort | solutions manual to accompany beginning 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=016597693&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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