Quasi-static state analysis of differential, difference, integral and gradient systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Courant Inst. of Mathematical Sciences [u.a.]
2010
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| Schriftenreihe: | Courant lecture notes in mathematics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 163 S. graph. Darst. |
| ISBN: | 9780821852699 |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: Quasi-static state analysis of differential, difference, integral, and gradient systems
Autor: Hoppensteadt, Frank C
Jahr: 2010
Contents Preface vii Part 1. Averaging Methods 1 Introduction 3 Time Scales 3 Oscillating Systems 5 Examples: Oscillatory Linear Systems 6 Overview 7 Chapter 1. Averaging Differential Equations 9 1.1. Averaging Nonlinear Systems 10 1.2. Highly Oscillatory Linear Systems 16 1.3. Perturbed Harmonic Systems 19 1.4. Rotation Numbers and Vectors 26 1.5. Pendulum Array in an Oscillatory Environment 35 1.6. Canonical Models in Weakly Connected Networks 41 Exercises 43 Chapter 2. Difference Equations 49 2.1. Averaging Nonlinear Discrete-Time Systems 50 2.2. Linear Difference Equations 52 2.3. Examples 54 2.4. Analyzing Discrete-Time Signals 57 2.5. Examples 58 2.6. Averaging and Computer Simulations 61 Exercises 65 Chapter 3. Averaging over Random Noise 67 3.1. Diffusion Processes 68 3.2. Random Processes 70 3.3. Random Perturbations of Nonlinear Differential Equations 76 3.4. Difference Equations Perturbed by Random Noise 79 3.5. Volterra Integral Equations Perturbed by Random Noise 80 Exercises 82 V
vi CONTENTS Part 2. Boundary Layer Methods 83 Introduction 85 Chapter 4. Asymptotic Stability and Singular Perturbations 89 4.1. Linear Stability Theory for Nonlinear Systems 89 4.2. Stability and Perturbation 91 4.3. Gradientlike Systems: Lyapunov Functions 99 Exercises 102 Chapter 5. QSSA for Boundary Layer Problems 105 5.1. Quasi-Static Linear Problems 105 5.2. Nonlinear Initial Value Problems 111 Exercises 125 Chapter 6. Other Singular Perturbation Problems 129 6.1. Quasi-Static Oscillations 129 6.2. Relaxation Oscillations 133 6.3. Boundary Value Problems 140 6.4. Nonlinear Stability Analysis 142 6.5. Explosion Mode Analysis of Rapid Chemical Reactions 147 Exercises 150 Appendix. Circuit Theory 155 Bibliography 159 Index 161
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| id | DE-604.BV037226635 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:53:53Z |
| institution | BVB |
| isbn | 9780821852699 |
| language | English |
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| physical | XIII, 163 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Courant Inst. of Mathematical Sciences [u.a.] |
| record_format | marc |
| series | Courant lecture notes in mathematics |
| series2 | Courant lecture notes in mathematics |
| spelling | Hoppensteadt, Frank C. 1938- Verfasser (DE-588)11268792X aut Quasi-static state analysis of differential, difference, integral and gradient systems Frank C. Hoppensteadt New York, NY Courant Inst. of Mathematical Sciences [u.a.] 2010 XIII, 163 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Courant lecture notes in mathematics 21 Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Funktionalgleichung (DE-588)4018923-5 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Differenzengleichung (DE-588)4012264-5 s Funktionalgleichung (DE-588)4018923-5 s Integralgleichung (DE-588)4027229-1 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1764-2 Courant lecture notes in mathematics 21 (DE-604)BV012714106 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021140400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoppensteadt, Frank C. 1938- Quasi-static state analysis of differential, difference, integral and gradient systems Courant lecture notes in mathematics Differenzengleichung (DE-588)4012264-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Funktionalgleichung (DE-588)4018923-5 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4012264-5 (DE-588)4012249-9 (DE-588)4018923-5 (DE-588)4064324-4 (DE-588)4027229-1 |
| title | Quasi-static state analysis of differential, difference, integral and gradient systems |
| title_auth | Quasi-static state analysis of differential, difference, integral and gradient systems |
| title_exact_search | Quasi-static state analysis of differential, difference, integral and gradient systems |
| title_full | Quasi-static state analysis of differential, difference, integral and gradient systems Frank C. Hoppensteadt |
| title_fullStr | Quasi-static state analysis of differential, difference, integral and gradient systems Frank C. Hoppensteadt |
| title_full_unstemmed | Quasi-static state analysis of differential, difference, integral and gradient systems Frank C. Hoppensteadt |
| title_short | Quasi-static state analysis of differential, difference, integral and gradient systems |
| title_sort | quasi static state analysis of differential difference integral and gradient systems |
| topic | Differenzengleichung (DE-588)4012264-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Funktionalgleichung (DE-588)4018923-5 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Differenzengleichung Differentialgleichung Funktionalgleichung Wahrscheinlichkeitsrechnung Integralgleichung |
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