An introduction to partial differential equations
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2004
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Texts in applied mathematics
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV016972750 | ||
| 003 | DE-604 | ||
| 005 | 20240522 | ||
| 007 | t| | ||
| 008 | 030311s2004 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 966479513 |2 DE-101 | |
| 020 | |a 0387004440 |9 0-387-00444-0 | ||
| 020 | |a 9780387004440 |c hbk |9 978-0-387-00444-0 | ||
| 020 | |a 9781441918208 |c pbk |9 978-1-4419-1820-8 | ||
| 035 | |a (OCoLC)51566394 | ||
| 035 | |a (DE-599)BVBBV016972750 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-29T |a DE-739 |a DE-703 |a DE-91G |a DE-355 |a DE-706 |a DE-19 |a DE-11 |a DE-188 |a DE-83 |a DE-573 |a DE-20 | ||
| 050 | 0 | |a QA374 | |
| 082 | 0 | |a 515/.353 |2 21 | |
| 082 | 0 | |a 515.353 | |
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a MAT 350f |2 stub | ||
| 084 | |a 35-01 |2 msc | ||
| 100 | 1 | |a Renardy, Michael |d 1955- |e Verfasser |0 (DE-588)142008257 |4 aut | |
| 245 | 1 | 0 | |a An introduction to partial differential equations |c Michael Renardy ; Robert C. Rogers |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2004 | |
| 300 | |a XIV, 434 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts in applied mathematics |v 13 | |
| 650 | 7 | |a Análise numérica |2 larpcal | |
| 650 | 7 | |a Equações diferenciais parciais |2 larpcal | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rogers, Robert C. |e Verfasser |0 (DE-588)128614854 |4 aut | |
| 830 | 0 | |a Texts in applied mathematics |v 13 |w (DE-604)BV002476038 |9 13 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010250160 | |
Datensatz im Suchindex
| DE-19_call_number | 1699/SK 540 R394(2)+4 1699/SK 540 R394(2)+5 1601/Zi 329 Ren 1601/SK 540 R394(2) 1699/SK 540 R394(2)+3 1601/SK 540 R394(2)=HB Numerik 1699/SK 540 R394(2)+2 |
|---|---|
| DE-19_location | 95 |
| DE-BY-TUM_call_number | 0202 MAT 350f 2007 A 5829(2) |
| DE-BY-TUM_katkey | 1594426 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020773399 |
| DE-BY-UBM_katkey | 4029481 |
| DE-BY-UBM_media_number | 99995526000 41610937750017 41610937710019 41610937720011 41610937740015 41610937730013 99995125962 |
| DE-BY-UBR_call_number | 00/SK 540 R394(2) 80/SK 540 R394(2) 8014/SK 540 R394(2) 803/SK 540 R394(2) 8071/SK 540 R394(2) |
| DE-BY-UBR_katkey | 3872618 |
| DE-BY-UBR_location | 00 80 |
| DE-BY-UBR_media_number | 069035624713 069035624735 069035624724 TEMP12314784 TEMP12438581 TEMP12038883 |
| _version_ | 1823054202663862272 |
| adam_text | Contents
Series
Preface v
Preface
vii
1
Introduction
1
1.1
Basic
Mathematical
Questions
............... 2
1.1.1
Existence
....................... 2
1.1.2
Multiplicity
..................... 4
1.1.3
Stability.......................
6
1.1.4
Linear
Systems
of ODEs and Asymptotic Stability
7
1.1.5
Well-Posed Problems
................ 8
1.1.6
Representations
...................
g
1.1.7
Estimation
......................
Ю
1.1.8
Smoothness
..................... 12
1.2
Elementary Partial Differential Equations
........ 14
1.2.1
Laplace s Equation
................. 15
1.2.2
The Heat Equation
................. 24
1.2.3
The Wave Equation
................. 30
2
Characteristics 3g
2.1
Classification and Characteristics
............. 3ß
2.1.1
The Symbol of a Differential Expression
..... 37
2.1.2
Scalar Equations of Second Order
.........
З8
2.1.3
Higher-Order Equations and Systems
....... 41
χ
Contents
2.1.4
Nonlinear Equations
................ 44
2.2
The Cauchy-Kovalevskaya Theorem
............ 46
2.2.1
Real Analytic Functions
.............. 46
2.2.2
Majorization
..................... 50
2.2.3
Statement and Proof of the Theorem
....... 51
2.2.4
Reduction of General Systems
........... 53
2.2.5
A PDE without Solutions
............. 57
2.3
Holmgren s Uniqueness Theorem
............. 61
2.3.1
An Outline of the Main Idea
............ 61
2.3.2
Statement and Proof of the Theorem
....... 62
2.3.3
The
Weierstraß
Approximation Theorem
..... 64
3
Conservation Laws and Shocks
67
3.1
Systems in One Space Dimension
............. 68
3.2
Basic Definitions and Hypotheses
............. 70
3.3
Blowup of Smooth Solutions
................ 73
3.3.1
Single Conservation Laws
............. 73
3.3.2
The
ρ
System
.................... 76
3.4
Weak Solutions
....................... 77
3.4.1
The Rankine-Hugoniot Condition
......... 79
3.4.2
Multiplicity
..................... 81
3.4.3
The Lax Shock Condition
............. 83
3.5
Riemann Problems
..................... 84
3.5.1
Single Equations
.................. 85
3.5.2
Systems
....................... 86
3.6
Other Selection Criteria
.................. 94
3.6.1
The Entropy Condition
............... 94
3.6.2
Viscosity Solutions
................. 97
3.6.3
Uniqueness
...................... 99
4
Maximum Principles
101
4.1
Maximum Principles of Elliptic Problems
......... 102
4.1.1
The Weak Maximum Principle
........... 102
4.1.2
The Strong Maximum Principle
.......... 103
4.1.3
A Priori Bounds
................... 105
4.2
An Existence Proof for the Dirichlet Problem
...... 107
4.2.1
The Dirichlet Problem on a Ball
.......... 108
4.2.2
Subharmonic Functions
............... 109
4.2.3
The Arzela-Ascoli Theorem
............ 110
4.2.4
Proof of Theorem
4.13............... 112
4.3
Radial Symmetry
...................... 114
4.3.1
Two Auxiliary Lemmas
............... 114
4.3.2
Proof of the Theorem
................ 115
4.4
Maximum Principles for Parabolic Equations
....... 117
4.4.1
The Weak Maximum Principle
........... 117
Contents xi
4.4.2
The Strong Maximum Principle
.......... 118
Distributions
122
5.1
Test Functions and Distributions
............. 122
5.1.1
Motivation
...................... 122
5.1.2
Test Functions
.................... 124
5.1.3
Distributions
.................... 126
5.1.4
Localization and Regularization
.......... 129
5.1.5
Convergence of Distributions
............ 130
5.1.6
Tempered Distributions
.............. 132
5.2
Derivatives and Integrals
.................. 135
5.2.1
Basic Definitions
.................. 135
5.2.2
Examples
...................... 136
5.2.3
Primitives and Ordinary Differential Equations
. 140
5.3
Convolutions and Fundamental Solutions
......... 143
5.3.1
The Direct Product of Distributions
....... 143
5.3.2
Convolution of Distributions
............ 145
5.3.3
Fundamental Solutions
............... 147
5.4
The Fourier Transform
................... 151
5.4.1
Fourier Transforms of Test Functions
....... 151
5.4.2
Fourier Transforms of Tempered Distributions
. . 153
5.4.3
The Fundamental Solution for the Wave Equation
156
5.4.4
Fourier Transform of Convolutions
........ 158
5.4.5
Laplace Transforms
................. 159
5.5
Green s Functions
...................... 163
5.5.1
Boundary-Value Problems and their
Adjoints
. . 163
5.5.2
Green s Functions for Boundary-Value Problems
. 167
5.5.3
Boundary Integral Methods
............ 170
Function Spaces
174
6.1
Banach Spaces and Hubert Spaces
............. 174
6.1.1
Banach Spaces
.................... 174
6.1.2
Examples of Banach Spaces
............ 177
6.1.3
Hubert Spaces
.................... 180
6.2
Bases in Hubert Spaces
................... 184
6.2.1
The Existence of a Basis
.............. 184
6.2.2
Fourier Series
.................... 188
6.2.3
Orthogonal Polynomials
.............. 190
6.3
Duality and Weak Convergence
.............. 194
6.3.1
Bounded Linear Mappings
............. 194
6.3.2
Examples of Dual Spaces
.............. 195
6.3.3
The Hahn-Banach Theorem
............ 197
6.3.4
The Uniform Boundedness Theorem
....... 198
6.3.5
Weak Convergence
................. 199
xii Contents
7 Sobolev Spaces 203
7.1 Basic
Definitions
...................... 204
7.2
Characterizations of
Sobolev Spaces............ 207
7.2.1
Some Comments on the Domain
Ω
........ 207
7.2.2
Sobolev Spaces and Fourier Transform
...... 208
7.2.3
The Sobolev Imbedding Theorem
......... 209
7.2.4
Compactness Properties
.............. 210
7.2.5
The Trace Theorem
................. 214
7-3
Negative Sobolev Spaces and Duality
........... 218
7.4
Technical Results
...................... 220
7.4.1
Density Theorems
.................. 220
7.4.2
Coordinate Transformations and Sobolev Spaces on
Manifolds
...................... 221
7.4.3
Extension Theorems
................ 223
7.4.4
Problems
....................... 225
8
Operator Theory
228
8.1
Basic Definitions and Examples
.............. 229
8.1.1
Operators
...................... 229
8.1.2
Inverse Operators
.................. 230
8.1.3
Bounded Operators, Extensions
.......... 230
8.1.4
Examples of Operators
............... 232
8.1.5
Closed Operators
.................. 237
8.2
The Open Mapping Theorem
............... 241
8.3
Spectrum and Resolvent
.................. 244
8.3.1
The Spectra of Bounded Operators
........ 246
8.4
Symmetry and Self-adjointness
............... 251
8.4.1
The Adjoint Operator
............... 251
8.4.2
The Hubert Adjoint Operator
........... 253
8.4.3
Adjoint Operators and Spectral Theory
...... 256
8.4.4
Proof of the Bounded Inverse Theorem for Hubert
Spaces
........................ 257
8.5
Compact Operators
..................... 259
8.5.1
The Spectrum of a Compact Operator
...... 265
8.6
Sturm-Liouville Boundary-Value Problems
........ 271
8.7
The
Fredholm
Index
.................... 279
9
Linear Elliptic Equations
283
9.1
Definitions
.......................... 283
9.2
Existence and Uniqueness of Solutions of the Dirichlet
Problem
........................... 287
9.2.1
The Dirichlet Problem—Types of Solutions
... 287
9.2.2
The Lax-Milgram Lemma
............. 290
9.2.3
Garding s Inequality
................ 292
9.2.4
Existence of Weak Solutions
............ 298
Contents xiii
9.3
Eigenfunction Expansions
................. 300
9.3.1
Fredholm
Theory
.................. 300
9.3.2
Eigenfunction Expansions
............. 302
9.4
General Linear Elliptic Problems
............. 303
9.4.1
The Neumann Problem
............... 304
9.4.2
The Complementing Condition for Elliptic Systems
306
9.4.3
The Adjoint Boundary-Value Problem
...... 311
9.4.4
Agmon s Condition and Coercive Problems
.... 315
9.5
Interior Regularity
..................... 318
9.5.1
Difference Quotients
................ 321
9.5.2
Second-Order Scalar Equations
.......... 323
9.6
Boundary Regularity
.................... 324
10
Nonlinear Elliptic Equations
335
10.1
Perturbation Results
.................... 335
10.1.1
The Banach Contraction Principle and the Implicit
Function Theorem
................. 336
10.1.2
Applications to Elliptic PDEs
........... 339
10.2
Nonlinear Variational Problems
.............. 342
10.2.1
Convex problems
.................. 342
10.2.2
Nonconvex Problems
................ 355
10.3
Nonlinear Operator Theory Methods
........... 359
10.3.1
Mappings on Finite-Dimensional Spaces
..... 359
10.3.2
Monotone Mappings on Banach Spaces
...... 363
10.3.3
Applications of Monotone Operators to Nonlinear
PDEs
......................... 366
10.3.4
Nemytskii Operators
................ 370
10.3.5
Pseudo-monotone Operators
............ 371
10.3.6
Application to PDEs
................ 374
11
Energy Methods for Evolution Problems
380
11.1
Parabolic Equations
..................... 380
11.1.1
Banach Space Valued Functions and Distributions
380
11.1.2
Abstract Parabolic Initial-Value Problems
.... 382
11.1.3
Applications
..................... 385
11.1.4
Regularity of Solutions
............... 386
11.2
Hyperbolic Evolution Problems
.............. 388
11.2.1
Abstract Second-Order Evolution Problems
... 388
11.2.2
Existence of a Solution
............... 389
11.2.3
Uniqueness of the Solution
............. 391
11.2.4
Continuity of the Solution
............. 392
12
Semigroup Methods
395
12.1
Semigroups and Infinitesimal Generators
......... 397
12.1.1
Strongly Continuous Semigroups
......... 397
xiv Contents
12.1.2 The Infinitesimal Generator............ 399
12.1.3
Abstract ODEs
................... 401
12.2 The Hille-Yosida Theorem................. 403
12.2.1 The Hille-Yosida Theorem............. 403
12.2.2 The Lumer-Phillips Theorem ........... 406
12.3 Applications
to PDEs
.................... 408
12.3.1 Symmetrie
Hyperbolic
Systems.......... 408
12.3.2
The Wave Equation.................
410
12.3.3 The Schrödinger
Equation
............. 411
12.4
Analytic Semigroups
.................... 413
12.4.1
Analytic Semigroups and Their Generators
.... 413
12.4.2
Fractional Powers
.................. 416
12.4.3
Perturbations of Analytic Semigroups
....... 419
12.4.4
Regularity of Mild Solutions
............ 422
A References
426
A.I Elementary Texts
...................... 426
A.2 Basic Graduate Texts
.................... 427
A.3 Specialized or Advanced Texts
............... 427
A.4
Multivolume
or Encyclopedic Works
............ 429
A.5 Other References
...................... 429
Index
431
|
| any_adam_object | 1 |
| author | Renardy, Michael 1955- Rogers, Robert C. |
| author_GND | (DE-588)142008257 (DE-588)128614854 |
| author_facet | Renardy, Michael 1955- Rogers, Robert C. |
| author_role | aut aut |
| author_sort | Renardy, Michael 1955- |
| author_variant | m r mr r c r rc rcr |
| building | Verbundindex |
| bvnumber | BV016972750 |
| callnumber-first | Q - Science |
| callnumber-label | QA374 |
| callnumber-raw | QA374 |
| callnumber-search | QA374 |
| callnumber-sort | QA 3374 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 |
| classification_tum | MAT 350f |
| ctrlnum | (OCoLC)51566394 (DE-599)BVBBV016972750 |
| dewey-full | 515/.353 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 515.353 |
| dewey-search | 515/.353 515.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02113nam a2200529 cb4500</leader><controlfield tag="001">BV016972750</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240522 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">030311s2004 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">966479513</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387004440</subfield><subfield code="9">0-387-00444-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387004440</subfield><subfield code="c">hbk</subfield><subfield code="9">978-0-387-00444-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441918208</subfield><subfield code="c">pbk</subfield><subfield code="9">978-1-4419-1820-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)51566394</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV016972750</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-573</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA374</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.353</subfield><subfield code="2">21</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.353</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 350f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">35-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Renardy, Michael</subfield><subfield code="d">1955-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)142008257</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An introduction to partial differential equations</subfield><subfield code="c">Michael Renardy ; Robert C. Rogers</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 434 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Texts in applied mathematics</subfield><subfield code="v">13</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Análise numérica</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Equações diferenciais parciais</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Partiële differentiaalvergelijkingen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Partial</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rogers, Robert C.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)128614854</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Texts in applied mathematics</subfield><subfield code="v">13</subfield><subfield code="w">(DE-604)BV002476038</subfield><subfield code="9">13</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-010250160</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV016972750 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T17:14:18Z |
| institution | BVB |
| isbn | 0387004440 9780387004440 9781441918208 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010250160 |
| oclc_num | 51566394 |
| open_access_boolean | |
| owner | DE-29T DE-739 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-706 DE-19 DE-BY-UBM DE-11 DE-188 DE-83 DE-573 DE-20 |
| owner_facet | DE-29T DE-739 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-706 DE-19 DE-BY-UBM DE-11 DE-188 DE-83 DE-573 DE-20 |
| physical | XIV, 434 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spellingShingle | Renardy, Michael 1955- Rogers, Robert C. An introduction to partial differential equations Texts in applied mathematics Análise numérica larpcal Equações diferenciais parciais larpcal Partiële differentiaalvergelijkingen gtt Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4123623-3 |
| title | An introduction to partial differential equations |
| title_auth | An introduction to partial differential equations |
| title_exact_search | An introduction to partial differential equations |
| title_full | An introduction to partial differential equations Michael Renardy ; Robert C. Rogers |
| title_fullStr | An introduction to partial differential equations Michael Renardy ; Robert C. Rogers |
| title_full_unstemmed | An introduction to partial differential equations Michael Renardy ; Robert C. Rogers |
| title_short | An introduction to partial differential equations |
| title_sort | an introduction to partial differential equations |
| topic | Análise numérica larpcal Equações diferenciais parciais larpcal Partiële differentiaalvergelijkingen gtt Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Análise numérica Equações diferenciais parciais Partiële differentiaalvergelijkingen Differential equations, Partial Partielle Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT renardymichael anintroductiontopartialdifferentialequations AT rogersrobertc anintroductiontopartialdifferentialequations |