Partial differential equations: 1 Basic theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [und andere]
Springer
[2010]
|
| Edition: | Second edition |
| Series: | Applied mathematical sciences
volume 115 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxii, 654 Seiten |
| ISBN: | 9781441970541 9781461427261 |
Staff View
MARC
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| 008 | 100816s2010 xxu |||| 00||| eng d | ||
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| 020 | |a 9781461427261 |c softcover |9 978-1-4614-2726-1 | ||
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| 035 | |a (DE-599)BVBBV036617490 | ||
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| 100 | 1 | |a Taylor, Michael Eugene |d 1946- |e Verfasser |0 (DE-588)123980119 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations |n 1 |p Basic theory |c Michael E. Taylor |
| 250 | |a Second edition | ||
| 264 | 1 | |a New York [und andere] |b Springer |c [2010] | |
| 300 | |a xxii, 654 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v volume 115 | |
| 490 | 0 | |a Applied mathematical sciences | |
| 773 | 0 | 8 | |w (DE-604)BV010899159 |g 1 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4419-7055-8 |
| 830 | 0 | |a Applied mathematical sciences |v volume 115 |w (DE-604)BV000005274 |9 115 | |
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Record in the Search Index
| _version_ | 1805066157106921472 |
|---|---|
| adam_text |
Contents
Contents
of Volumes II
and III
. xi
Preface
. xiii
1
Basic Theory of ODE and Vector Fields
.
I
1 The derivative
. 3
2
Fundamental local existence theorem for ODK
. 9
3
Inverse function and implicit function theorems
. 12
4
Constant-coefficient linear systems; exponentiation of matrices
_ 16
5
Variable-coefficient linear systems
ofODl·: Duhameľs
principle
26
6
Impendence of solutions on initial data and on other parameters
З І
7
Rows and vector fields
.
VS
8
Lie brackets
. 40
9
Commuting flows; Frobenius's theorem
. 43
10
Hamiltonian systems
. 47
I I Geodesies
.
S
I
12
Variational problems and the stationary· action principle
. 59
13
Differential forms
. 70
14
The symplectic form and canonical transformations
. 83
15
First-order, scalar, nonlinear PDE
. 89
16
Completely
integrable
hamiltonian systems
. 96
17
Examples of
integrable
systems; central force problems
. 101
18
Relativislic motion
. 105
19
Topologica]
applications of differential forms
. 110
20
Critical points and index of a vector field
. 118
A Nonsmooth vector fields
. 122
References
. 125
2
The Laplace
Equation
and Wave Equation
. 127
1
Vibrating strings and membranes
. 129
2
The divergence of a vector field
. 140
3
The
cevariam
derivative and divergence of tensor fields
. 145
4
The Laplace operator on a Riemannian manifold
. 153
5
The wave equation on a product manifold and energy conservation
156
6
Uniqueness and finite propagation speed
. 162
7
Lorentz
manifolds and stress-energy tensors
. 166
8
More general hyperbolic equations; energy estimates
. 172
Contents
9
The symbol of a differential operator and a genera]
Green- Stokes formula
. 176
10
The Hodge Laplacian on
к
-forms
. 180
11
Maxwell's equations
. 184
References
. 194
Fourier Analysis, Distributions,
and Constant-Coefficient Linear PDE
. 197
1
Fourier series
. 198
2
Harmonic functions and bolomorphic functions in the plane
.209
3
The Fourier transform
.222
4
Distributions and tempered distributions
.230
5
The classical evolution equations
.244
6
Radial
distributions,
polar coordinates, and Bessel functions
.263
7
The method of images and Poisson's summation formula
.273
8
Homogeneous distributions and principal value distributions
.278
9
Elliptic operators
.286
10
Local solvability of constant-coefficient PDE
.289
11
The discrete Fourier transform
.292
12
The fast Fourier transform
.301
A The mighty Gaussian and the sublime gamma function
.306
References
.312
Sobolev Spaces
.315
1
Sobolev spaces
ont"
.315
2
The complex interpolation method
.321
3
Sobolev spaces on compact manifolds
.328
4
Sobolev spaces on bounded domains
.331
5
The Sobolev spaces H$
(Ω)
.338
6
The Schwartz kernel theorem
.345
7
Sobolev spaces on rough domains
.349
References
.351
Linear Elliptic Equations
.353
1
Existence and regularity of solutions to the Dinchlet problem
.354
2
The weak
ала
strong maximum principles
.364
3
The Dinchlet problem on the ball ml"
.373
4
The Riemann mapping theorem (smooth boundary)
.379
5
The Dinchlet problem on
a domam
with a rough boundary
.383
6
The Riemann mapping theorem (rough boundary)
.398
7
The Neumann boundary problem
.402
8
The Hodge decomposition and harmonic forms
.410
9
Natural boundary problems for the Hodge Laplacian
.421
10
Isothermal coordinates and
conformai
structures on surfaces
.438
11
General elliptic boundary problems
.441
12
Operator properties of regular boundary problems
.462
Contents
їх
A
Spaces
of generalized functions on manifolds with boundary
.471
В
The Mayer-Vietoris sequence in deRham cohomoiogy
.475
References
.478
6
Linear Evolution Equations
.48 ]
1
The heat equation and the wave equation on bounded domains
.482
2
The heat equation and wave equation on unbounded domains
.490
3
Maxwell's equations
.496
4
The Cauchy-Kowalewsky theorem
.499
5
Hyperbolic systems
.504
6
Geometrical optics
.510
7
The formation of caustics
. 518
8
Boundary layer phenomena for the heat semigroup
. 535
A Some Banach spaces of harmonic functions
. 541
В
The stationary phase method
. 543
References
.545
A Outline of Functional Analysis
. 549
1
Banach spaces
.549
2
Hubert spaces
. 556
3
Fréchet
spaces; locally convex spaces
.561
4
Duality
.564
5
Linear operators
.571
6
Compact operators
.579
7
Fredholm
operators
.593
8
Unbounded operators
.596
9
Semigroups
.603
References
.615
В
Manifolds, Vector Bundles, and Lie Groups
.617
1
Metric spaces and
topo
logical spaces
.617
2
Manifolds
.622
3
Vector bundles
.624
4
Sard's theorem
.626
5
Lie groups
.627
6
The Campbell-Hausdorff formula
.630
7
Representations of Lie groups and Lie algebras
.632
8
Representations of compact Lie groups
.636
9
Representations of SU(2) and related groups
.641
References
.647
Index
.649 |
| any_adam_object | 1 |
| author | Taylor, Michael Eugene 1946- |
| author_GND | (DE-588)123980119 |
| author_facet | Taylor, Michael Eugene 1946- |
| author_role | aut |
| author_sort | Taylor, Michael Eugene 1946- |
| author_variant | m e t me met |
| building | Verbundindex |
| bvnumber | BV036617490 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)705736945 (DE-599)BVBBV036617490 |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV036617490 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T03:13:53Z |
| institution | BVB |
| isbn | 9781441970541 9781461427261 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020537589 |
| oclc_num | 705736945 |
| open_access_boolean | |
| owner | DE-20 DE-11 DE-188 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-703 DE-706 |
| owner_facet | DE-20 DE-11 DE-188 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-703 DE-706 |
| physical | xxii, 654 Seiten |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Taylor, Michael Eugene 1946- Verfasser (DE-588)123980119 aut Partial differential equations 1 Basic theory Michael E. Taylor Second edition New York [und andere] Springer [2010] xxii, 654 Seiten txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences volume 115 Applied mathematical sciences (DE-604)BV010899159 1 Erscheint auch als Online-Ausgabe 978-1-4419-7055-8 Applied mathematical sciences volume 115 (DE-604)BV000005274 115 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020537589&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taylor, Michael Eugene 1946- Partial differential equations Applied mathematical sciences |
| title | Partial differential equations |
| title_auth | Partial differential equations |
| title_exact_search | Partial differential equations |
| title_full | Partial differential equations 1 Basic theory Michael E. Taylor |
| title_fullStr | Partial differential equations 1 Basic theory Michael E. Taylor |
| title_full_unstemmed | Partial differential equations 1 Basic theory Michael E. Taylor |
| title_short | Partial differential equations |
| title_sort | partial differential equations basic theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020537589&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010899159 (DE-604)BV000005274 |
| work_keys_str_mv | AT taylormichaeleugene partialdifferentialequations1 |