Lectures on partial differential equations:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English Russian |
Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
Schriftenreihe: | Universitext
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | X, 157 S. graph. Darst. |
ISBN: | 3540404481 9783540404484 |
Internformat
MARC
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245 | 1 | 0 | |a Lectures on partial differential equations |c Vladimir I. Arnold |
264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
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650 | 4 | |a Équations aux dérivées partielles | |
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Datensatz im Suchindex
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adam_text | Contents
Preface
to the Second Russian Edition
.........................
V
1.
The General Theory for One First-Order Equation
........ 1
Literature
................................................... 10
2.
The General Theory for One First-Order Equation
(Continued)
............................................... 11
Literature
................................................... 20
3.
Huygens Principle in the Theory of Wave Propagation
.... 21
4.
The Vibrating String (d Alembert s Method)
.............. 27
4.1.
The General Solution
.................................... 27
4.2.
Boundary-Value Problems and the Cauchy Problem
......... 28
4.3.
The Cauchy Problem for an Infinite String. d Alembert s
Formula
................................................ 29
4.4.
The Semi-Infinite String
.................................. 31
4.5.
The Finite String. Resonance
............................. 31
4.6.
The Fourier Method
..................................... 32
5.
The Fourier Method (for the Vibrating String)
............ 35
5.1.
Solution of the Problem in the Space of Trigonometric
Polynomials
............................................ 35
5.2.
A Digression
............................................ 36
5.3.
Formulas for Solving the Problem of Section
5.1............. 36
5.4.
The General Case
....................................... 36
5.5.
Fourier Series
........................................... 37
5.6.
Convergence of Fourier Series
............................. 37
5.7.
Gibbs Phenomenon
..................................... 39
X
Contents
6.
The Theory of Oscillations. The Variational Principle
...... 41
Literature
................................................... 50
7.
The Theory of Oscillations. The Variational Principle
(Continued)
............................................... 51
8.
Properties of Harmonic Functions
......................... 65
8.1.
Consequences of the Mean-Value Theorem
.................. 67
8.2.
The Mean-Value Theorem in the Multidimensional Case
...... 73
9.
The Fundamental Solution for the Laplacian. Potentials
... 77
9.1.
Examples and Properties
................................. 78
9.2.
A Digression. The Principle of Superposition
................ 79
9.3.
Appendix. An Estimate of the Single-Layer Potential
........ 89
10.
The Double-Layer Potential
............................... 93
10.1.
Properties of the Double-Layer Potential
................... 94
11.
Spherical Functions. Maxwell s Theorem. The Removable
Singularities Theorem
.....................................105
12.
Boundary-Value Problems for Laplace s Equation. Theory
of Linear Equations and Systems
..........................121
12.1.
Four Boundary-Value Problems for Laplace s Equation
.......121
12.2.
Existence and Uniqueness of Solutions
.....................125
12.3.
Linear Partial Differential Equations and Their Symbols
......127
A. The Topological Content of Maxwell s Theorem on the
Multifield Representation of Spherical Functions
...........135
A.I. The Basic Spaces and Groups
.............................136
A.
2.
Some Theorems of Real Algebraic Geometry
................137
A.3. From Algebraic Geometry to Spherical Functions
............139
A.4. Explicit Formulas
.......................................141
A.5. Maxwell s Theorem and CP2/conj
«
S4
....................144
A.6. The History of Maxwell s Theorem
........................145
Literature
...................................................146
B. Problems
..................................................149
B.I. Material from the Seminars
...............................149
B.2. Written Examination Problems
............................156
|
any_adam_object | 1 |
author | Arnolʹd, V. I. 1937-2010 |
author_GND | (DE-588)119540878 |
author_facet | Arnolʹd, V. I. 1937-2010 |
author_role | aut |
author_sort | Arnolʹd, V. I. 1937-2010 |
author_variant | v i a vi via |
building | Verbundindex |
bvnumber | BV017536721 |
callnumber-first | Q - Science |
callnumber-label | QA377 |
callnumber-raw | QA377 |
callnumber-search | QA377 |
callnumber-sort | QA 3377 |
callnumber-subject | QA - Mathematics |
classification_rvk | SK 540 |
classification_tum | MAT 350f |
ctrlnum | (OCoLC)53038209 (DE-599)BVBBV017536721 |
dewey-full | 515/.353 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515/.353 |
dewey-search | 515/.353 |
dewey-sort | 3515 3353 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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genre_facet | Lehrbuch |
id | DE-604.BV017536721 |
illustrated | Illustrated |
indexdate | 2024-07-09T19:19:05Z |
institution | BVB |
isbn | 3540404481 9783540404484 |
language | English Russian |
lccn | 2003060468 |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010557157 |
oclc_num | 53038209 |
open_access_boolean | |
owner | DE-91G DE-BY-TUM DE-824 DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-384 DE-706 DE-29T DE-634 DE-739 DE-11 DE-860 DE-83 |
owner_facet | DE-91G DE-BY-TUM DE-824 DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-384 DE-706 DE-29T DE-634 DE-739 DE-11 DE-860 DE-83 |
physical | X, 157 S. graph. Darst. |
publishDate | 2004 |
publishDateSearch | 2004 |
publishDateSort | 2004 |
publisher | Springer |
record_format | marc |
series2 | Universitext |
spelling | Arnolʹd, V. I. 1937-2010 Verfasser (DE-588)119540878 aut Lekcij ob uravnenijach s častnimi proizvodnimi Lectures on partial differential equations Vladimir I. Arnold Berlin [u.a.] Springer 2004 X, 157 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Análise numérica larpcal Equações diferenciais parciais larpcal Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010557157&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 |
spellingShingle | Arnolʹd, V. I. 1937-2010 Lectures on partial differential equations Análise numérica larpcal Equações diferenciais parciais larpcal Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
subject_GND | (DE-588)4044779-0 (DE-588)4123623-3 |
title | Lectures on partial differential equations |
title_alt | Lekcij ob uravnenijach s častnimi proizvodnimi |
title_auth | Lectures on partial differential equations |
title_exact_search | Lectures on partial differential equations |
title_full | Lectures on partial differential equations Vladimir I. Arnold |
title_fullStr | Lectures on partial differential equations Vladimir I. Arnold |
title_full_unstemmed | Lectures on partial differential equations Vladimir I. Arnold |
title_short | Lectures on partial differential equations |
title_sort | lectures on partial differential equations |
topic | Análise numérica larpcal Equações diferenciais parciais larpcal Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
topic_facet | Análise numérica Equações diferenciais parciais Partiële differentiaalvergelijkingen Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung Lehrbuch |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010557157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT arnolʹdvi lekcijoburavnenijachscastnimiproizvodnimi AT arnolʹdvi lecturesonpartialdifferentialequations |