Differential equations: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2010
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zusatzmaterial unter http://extras.springer.com nach Eingabe der ISBN erhältlich |
| Beschreibung: | XIV, 626 S. graph. Darst. |
| ISBN: | 1441911626 9781441911629 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035783987 | ||
| 003 | DE-604 | ||
| 005 | 20101015 | ||
| 007 | t | ||
| 008 | 091022s2010 d||| |||| 00||| eng d | ||
| 020 | |a 1441911626 |9 1-4419-1162-6 | ||
| 020 | |a 9781441911629 |9 978-1-4419-1162-9 | ||
| 035 | |a (OCoLC)467779993 | ||
| 035 | |a (DE-599)BVBBV035783987 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-355 |a DE-11 |a DE-824 |a DE-91G | ||
| 050 | 0 | |a QA371.5.D37 | |
| 082 | 0 | |a 515.35 |2 22 | |
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 084 | |a MAT 340f |2 stub | ||
| 100 | 1 | |a Betounes, David |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential equations |b theory and applications |c David Betounes |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2010 | |
| 300 | |a XIV, 626 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Zusatzmaterial unter http://extras.springer.com nach Eingabe der ISBN erhältlich | ||
| 630 | 0 | 4 | |a Maple (Computer file) |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Dynamics | |
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 4 | |a Mechanics | |
| 650 | 4 | |a Vector fields | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4419-1163-6 |
| 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=018643444&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018643444 | ||
Datensatz im Suchindex
| _version_ | 1804140721045766144 |
|---|---|
| adam_text | Contents
1
Introduction
1
1.1
Examples of Dynamical Systems
................ 1
1.2
Vector Fields and Dynamical Systems
............. 16
1.3
Nonautonomous Systems
..................... 26
1.4
Fixed Points
........................... 29
1.5
Reduction to lst-Order, Autonomous
.............. 30
1.6
Summary
............................. 34
2
Techniques, Concepts and Examples
37
2.1
Euler s Numerical Method
.................... 38
2.1.1
The Geometric View
................... 38
2.1.2
The Analytical View
................... 40
2.2
Gradient Vector Fields
...................... 43
2.3
Fixed Points and Stability
.................... 50
2.4
Limit Cycles
........................... 55
2.5
The Two-Body Problem
..................... 60
2.5.1
Jacobi Coordinates
.................... 62
2.5.2
The Central Force Problem
............... 63
2.6
Summary
............................. 77
3
Existence and Uniqueness: The Flow Map
79
3.1
Picard
Iteration
.......................... 82
3.2
Existence and Uniqueness Theorems
.............. 86
3.3
Maximum Interval of Existence
................. 96
3.4
The Flow Generated by a Time-Dependent Vector Field
... 100
3.5
The Flow for Autonomous Systems
............... 108
3.6
Summary
............................. 117
xi
xii
CONTENTS
4 Linear Systems
4.1
Existence
and Uniqueness for Linear
Systems
..............................
124
4.2
The Fundamental Matrix and the Flow
............ 128
4.3
Homogeneous, Constant Coefficient Systems
.......... 154
4.4
The Geometry of the Integral Curves
.............. 161
4.4.1
Real Eigenvalues
..................... 163
4.4.2
Complex Eigenvalues
................... 174
4.5
Canonical Systems
........................ 201
4.5.1
Diagonalizable Matrices
................. 204
4.5.2
Complex Diagonalizable Matrices
............ 208
4.5.3
The Nondiagonalizable Case: Jordan Forms
...... 209
4.6
Summary
............................. 218
5
Linearization
&
Transformation
221
5.1
Linearization
...........................221
5.2
Transforming Systems of DEs
..................237
5.2.1
The Spherical Coordinate Transformation
.......243
5.2.2
Some Results on Diiferentiable Equivalence
......248
5.3
The Linearization and Flow Box Theorems
..........258
6
Stability Theory
267
6.1
Stability of Fixed Points
..................... 269
6.2
Linear Stability of Fixed Points
.................. 272
6.2.1
Computation of the Matrix Exponential for Jordan
Forms
........................... 272
6.3
Nonlinear Stability
........................ 283
6.4
Liapunov Functions
....................... 285
6.5
Stability of Periodic Solutions
.................. 296
7
Integrable
Systems
333
7.1
First Integrals (Constants of the Motion)
...........334
7.2
Integrable
Systems in the Plane
.................339
7.3
Integrable
Systems in
3-D....................345
7.4
Integrable
Systems in Higher Dimensions
...........359
8
Newtonian Mechanics
371
8.1
The N-Body Problem
............... . ...... 372
8.1.1
Fixed Points
.................... . . 375
CONTENTS xiii
8.1.2 Initial
Conditions.....................
376
8.1.3
Conservation
Laws
....................377
8.1.4
Stability of Conservative Systems
............385
8.2
Euler s Method and the N-body Problem
...........394
8.2.1
Discrete Conservation Laws
...............403
8.3
The Central Force Problem Revisited
..............412
8.3.1
Effective Potentials
.................... 415
8.3.2
Qualitative Analysis
................... 416
8.3.3
Linearization and Stability
............... 420
8.3.4
Circular Orbits
...................... 421
8.3.5
Analytical Solution
.................... 423
8.4
Rigid-Body Motions
....................... 436
8.4.1
The Rigid-Body Differential Equations
......... 443
8.4.2
Kinetic Energy and Moments of Inertia
........ 450
8.4.3
The Degenerate Case
................... 458
8.4.4
Euler s Equation
..................... 459
8.4.5
The General Solution of Euler s Equation
....... 463
9
Hamiltonian Systems
475
9.1
1-Dimensional Hamiltonian Systems
.............. 478
9.1.1
Conservation of Energy
................. 481
9.2
Conservation Laws and
Poisson
Brackets
............ 489
9.3
Lie Brackets and Arnold s Theorem
............... 502
9.3.1
Arnold s Theorem
.................... 505
9.4
Liouville s Theorem
....................... 528
A Elementary Analysis
535
A.I
Multivariable
Calculus
...................... 535
A.2 The Chain Rule
.......................... 541
A.3 The Inverse and Implicit Function Theorems
......... 542
A.4 Taylor s Theorem and The Hessian
............... 548
A.5 The Change of Variables Formula
................ 552
В
Lipschitz Maps and Linearization
553
B.I Norms
...............................554
B.2 Lipschitz Functions
........................555
B.3 The Contraction Mapping Principle
..............559
B.4 The Linearization Theorem
...................565
xiv CONTENTS
С
Linear Algebra 579
Cl Vector
Spaces
and Direct Sums
................. 579
C.2 Bilinear Forms
.......................... 582
C.3 Inner Product Spaces
....................... 584
C.4 The Principal Axes Theorem
.................. 588
C.5 Generalized
Eigenspaces..................... 591
C.6 Matrix Analysis
.......................... 602
C.6.1 Power Series with Matrix Coefficients
......... 609
D
Electronic Contents
613
Bibliography
615
Index
621
|
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| dewey-raw | 515.35 |
| dewey-search | 515.35 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035783987 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:28Z |
| institution | BVB |
| isbn | 1441911626 9781441911629 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018643444 |
| oclc_num | 467779993 |
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| physical | XIV, 626 S. graph. Darst. |
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| spelling | Betounes, David Verfasser aut Differential equations theory and applications David Betounes 2. ed. New York, NY Springer 2010 XIV, 626 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zusatzmaterial unter http://extras.springer.com nach Eingabe der ISBN erhältlich Maple (Computer file) Differential equations Dynamics Hamiltonian systems Mechanics Vector fields Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4419-1163-6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018643444&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Betounes, David Differential equations theory and applications Maple (Computer file) Differential equations Dynamics Hamiltonian systems Mechanics Vector fields Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4123623-3 |
| title | Differential equations theory and applications |
| title_auth | Differential equations theory and applications |
| title_exact_search | Differential equations theory and applications |
| title_full | Differential equations theory and applications David Betounes |
| title_fullStr | Differential equations theory and applications David Betounes |
| title_full_unstemmed | Differential equations theory and applications David Betounes |
| title_short | Differential equations |
| title_sort | differential equations theory and applications |
| title_sub | theory and applications |
| topic | Maple (Computer file) Differential equations Dynamics Hamiltonian systems Mechanics Vector fields Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Maple (Computer file) Differential equations Dynamics Hamiltonian systems Mechanics Vector fields Gewöhnliche Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018643444&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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