A basic course in partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2011
|
| Schriftenreihe: | Graduate studies in mathematics
120 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. 289 - 290 |
| Beschreibung: | X, 293 S. graph. Darst. |
| ISBN: | 9780821852552 |
Internformat
MARC
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| 010 | |a 2010043189 | ||
| 020 | |a 9780821852552 |c alk. paper |9 978-0-8218-5255-2 | ||
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| 100 | 1 | |a Han, Qing |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A basic course in partial differential equations |c Qing Han |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2011 | |
| 300 | |a X, 293 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 120 | |
| 500 | |a Literaturverz. S. 289 - 290 | ||
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804147955632963584 |
|---|---|
| adam_text | Contents
Preface
ix
Chapter
1.
Introduction
1
§1.1.
Notation
1
§1.2.
Well-Posed Problems
3
§1.3.
Overview
5
Chapter
2.
First-Order Differential Equations
9
§2.1.
Noncharacteristic Hypersurfaces
10
§2.2.
The Method of Characteristics
16
§2.3.
A Priori Estimates
30
§2.4.
Exercises
43
Chapter
3.
An Overview of Second-Order PDEs
47
§3.1.
Classifications
48
§3.2.
Energy Estimates
58
§3.3.
Separation of Variables
67
§3.4.
Exercises
86
Chapter
4.
Laplace Equations
89
§4.1.
Fundamental Solutions
90
§4.2.
Mean-Value Properties
105
§4.3.
The Maximum Principle
112
§4.4.
Poisson
Equations
133
§4.5.
Exercises
143
vn
Chapter
5.
Heat Equations
147
§5.1.
Fourier Transforms
148
§5.2.
Fundamental Solutions
158
§5.3.
The Maximum Principle
175
§5.4.
Exercises
197
Chapter
6.
Wave Equations
201
§6.1.
One-Dimensional Wave Equations
202
§6.2.
Higher-Dimensional Wave Equations
213
§6.3.
Energy Estimates
237
§6.4.
Exercises
245
Chapter
7.
First-Order Differential Systems
249
§7.1.
Noncharacteristic Hypersurfaces
250
§7.2.
Analytic Solutions
259
§7.3.
Nonexistence of Smooth Solutions
270
§7.4.
Exercises
276
Chapter
8.
Epilogue
279
§8.1.
Basic Linear Differential Equations
279
§8.2.
Examples of Nonlinear Differential Equations
282
Bibliography
289
Index
291
This is a textbook for an introductory graduate course on partial differential
equations. Han focuses on linear equations of first and second order. An impor¬
tant feature of his treatment is that the majority of the techniques are applicable
more generally. In particular, Han emphasizes a priori estimates throughout the
text, even for those equations that can be solved explicitly. Such estimates are
indispensable tools for proving the existence and uniqueness of solutions to PDEs,
being especially important for nonlinear equations. The estimates are also crucial
to establishing properties of the solutions, such as the continuous dependence on
parameters.
Han s book is suitable for students interested in the mathematical theory of partial
differential equations, either as an overview of the subject or as an introduction
leading to further study.
|
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| indexdate | 2024-07-09T23:59:28Z |
| institution | BVB |
| isbn | 9780821852552 |
| language | English |
| lccn | 2010043189 |
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| publishDate | 2011 |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Han, Qing Verfasser aut A basic course in partial differential equations Qing Han Providence, RI American Math. Soc. 2011 X, 293 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 120 Literaturverz. S. 289 - 290 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Graduate studies in mathematics 120 (DE-604)BV009739289 120 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024142032&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024142032&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Han, Qing A basic course in partial differential equations Graduate studies in mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4123623-3 |
| title | A basic course in partial differential equations |
| title_auth | A basic course in partial differential equations |
| title_exact_search | A basic course in partial differential equations |
| title_full | A basic course in partial differential equations Qing Han |
| title_fullStr | A basic course in partial differential equations Qing Han |
| title_full_unstemmed | A basic course in partial differential equations Qing Han |
| title_short | A basic course in partial differential equations |
| title_sort | a basic course in partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Partielle Differentialgleichung Lehrbuch |
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