Differential equations, mechanics, and computation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc. [u.a.]
2009
|
| Series: | Student mathematical library
51 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 313 S. graph. Darst. |
| ISBN: | 9780821821381 |
Staff View
MARC
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| 100 | 1 | |a Palais, Richard S. |d 1931- |e Verfasser |0 (DE-588)141996048 |4 aut | |
| 245 | 1 | 0 | |a Differential equations, mechanics, and computation |c Richard S. Palais ; Robert A. Palais |
| 264 | 1 | |a Providence, RI |b American Math. Soc. [u.a.] |c 2009 | |
| 300 | |a XIII, 313 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Student mathematical library |v 51 | |
| 650 | 4 | |a Evolution equations | |
| 650 | 4 | |a Differential equations, Linear |x Numerical solutions | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
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Record in the Search Index
| _version_ | 1804140854298804224 |
|---|---|
| adam_text | Contents
IAS/Park City Mathematics Institute
ix
Preface
xi
Acknowledgments
xiii
Introduction
1
Chapter
1.
Differential Equations and Their Solutions
5
1.1.
First-Order ODE: Existence and Uniqueness
5
1.2.
Euler s Method
16
1.3.
Stationary Points and Closed Orbits
19
1.4.
Continuity with Respect to Initial Conditions
22
1.5.
Chaos
—
Or a Butterfly Spoils Laplace s Dream
25
1.6.
Analytic ODE and Their Solutions
31
1.7.
Invariance
Properties of Flows
33
Chapter
2.
Linear Differential Equations
37
2.1.
First-Order Linear ODE
37
2.2.
Nonautonomous First-Order Linear ODE
48
2.3.
Coupled and Uncoupled Harmonic Operators
50
2.4.
Inhomogeneous Linear Differential Equations
52
2.5.
Asymptotic Stability of Nonlinear ODE
53
2.6.
Forced Harmonic Oscillators
55
2.7.
Exponential Growth and Ecological Models
56
VI
Contents
Chapter
3.
Second-Order ODE and the Calculus of Variations
63
3.1.
Tangent Vectors and the Tangent Bundle
63
3.2.
Second-Order Differential Equations
66
3.3.
The Calculus of Variations
68
3.4.
The Euler-Lagrange Equations
70
3.5.
Conservation Laws for Euler-Lagrange Equations
73
3.6.
Two Classic Examples
75
3.7.
Derivation of the Euler-Lagrange Equations
78
3.8.
More General Variations
80
3.9.
The Theorem of E. Noether
81
3.10.
Lagrangians Defining the Same Functionals
82
3.11.
Riemannian Metrics and Geodesies
85
3.12.
A Preview of Classical Mechanics
86
Chapter
4.
Newtonian Mechanics
91
4.1.
Introduction
91
4.2.
Newton s Laws of Motion
92
4.3.
Newtonian Kinematics
96
4.4.
Classical Mechanics as a Physical Theory
99
4.5.
Potential Functions and Conservation of Energy
106
4.6.
One-Dimensional Systems
Ш
4.7.
The Third Law and Conservation Principles
118
4.8.
Synthesis and Analysis of Newtonian Systems
122
4.9.
Linear Systems and Harmonic Oscillators
124
4.10.
Small Oscillations about Equilibrium
126
Chapter
5.
Numerical Methods
133
5.1.
Introduction
133
5.2.
Fundamental Examples and Their Behavior
144
Contents
vii
5.3.
Summary of Method Behavior on Model Problems
169
5.4.
Paired Methods: Error, Step-Size, Order Control
177
5.5.
Behavior of Example Methods on a Model
2x2
System
180
5.6.
Stiff Systems and the Method of Lines
187
5.7.
Convergence Analysis: Euler s Method
213
Appendix A. Linear Algebra and Analysis
225
A.I. Metric and Normed Spaces
225
A.2. Inner-Product Spaces
227
Appendix B. The Magic of Iteration
233
B.I. The Banach Contraction Principle
233
B.2. Newton s Method
238
B.3. The Inverse Function Theorem
240
B.4. The Existence and Uniqueness Theorem for ODE
241
Appendix C. Vector Fields as Differential Operators
243
Appendix D. Coordinate Systems and Canonical Forms
247
D.I.
Local Coordinates
247
D.2. Some Canonical Forms
250
Appendix E. Parametrized Curves and Arclength
255
Appendix F. Smoothness with Respect to Initial Conditions
257
Appendix G. Canonical Form for Linear Operators
259
G.I. The Spectral Theorem
259
Appendix H. Runge-Kutta Methods
263
viii
Contents
Appendix
I. Multistep Methods
281
Appendix J. Iterative Interpolation and Its Error
303
Bibliography
307
Index
311
|
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| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.6 |
| dewey-search | 518/.6 |
| dewey-sort | 3518 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035876907 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:35Z |
| institution | BVB |
| isbn | 9780821821381 |
| language | English |
| lccn | 2009011294 |
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| physical | XIII, 313 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Math. Soc. [u.a.] |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Palais, Richard S. 1931- Verfasser (DE-588)141996048 aut Differential equations, mechanics, and computation Richard S. Palais ; Robert A. Palais Providence, RI American Math. Soc. [u.a.] 2009 XIII, 313 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 51 Evolution equations Differential equations, Linear Numerical solutions Differential equations Numerical solutions Mechanics Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Lineare Differentialgleichung (DE-588)4206889-7 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Palais, Robert A. Sonstige oth Student mathematical library 51 (DE-604)BV013184751 51 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734575&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Palais, Richard S. 1931- Differential equations, mechanics, and computation Student mathematical library Evolution equations Differential equations, Linear Numerical solutions Differential equations Numerical solutions Mechanics Lineare Differentialgleichung (DE-588)4206889-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4206889-7 (DE-588)4128130-5 (DE-588)4129061-6 |
| title | Differential equations, mechanics, and computation |
| title_auth | Differential equations, mechanics, and computation |
| title_exact_search | Differential equations, mechanics, and computation |
| title_full | Differential equations, mechanics, and computation Richard S. Palais ; Robert A. Palais |
| title_fullStr | Differential equations, mechanics, and computation Richard S. Palais ; Robert A. Palais |
| title_full_unstemmed | Differential equations, mechanics, and computation Richard S. Palais ; Robert A. Palais |
| title_short | Differential equations, mechanics, and computation |
| title_sort | differential equations mechanics and computation |
| topic | Evolution equations Differential equations, Linear Numerical solutions Differential equations Numerical solutions Mechanics Lineare Differentialgleichung (DE-588)4206889-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Evolution equations Differential equations, Linear Numerical solutions Differential equations Numerical solutions Mechanics Lineare Differentialgleichung Numerisches Verfahren Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734575&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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