Dynamical systems with applications using MAPLE:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2001
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 398 S. graph. Darst. |
| ISBN: | 0817641505 3764341505 |
Internformat
MARC
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| 245 | 1 | 0 | |a Dynamical systems with applications using MAPLE |c Stephen Lynch |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XIII, 398 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 630 | 0 | 4 | |a Maple (Computer file) |
| 650 | 7 | |a Análise matemática |2 larpcal | |
| 650 | 4 | |a Dynamique différentiable - Informatique | |
| 650 | 7 | |a Equações diferenciais ordinárias |2 larpcal | |
| 650 | 7 | |a Teoria da bifurcação (sistemas dinâmicos) |2 larpcal | |
| 650 | 7 | |a Teoria qualitativa |2 larpcal | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Differentiable dynamical systems |x Data processing | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maple |g Programm |0 (DE-588)4209397-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
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Datensatz im Suchindex
| _version_ | 1807954137902481408 |
|---|---|
| adam_text |
STEPHEN LYNCH DYNAMICAL SYSTEMS WITH APPLICATIONS USING MAPLE BIRKHAEUSER
BOSTON * BASEL * BERLIN CONTENTS PREFACE XI 0 A TUTORIAL INTRODUCTION TO
MAPLE 1 0.1 TUTORIAL ONE: THE BASICS (ONE HOUR) 2 0.2 TUTORIAL TWO:
PLOTS AND DIFFERENTIAL EQUATIONS (ONE HOUR) . 4 0.3 SIMPLE MAPLE
PROGRAMS 6 0.4 COMMON ERRORS 8 0.5 MAPLE EXERCISES 9 1 DIFFERENTIAL
EQUATIONS 13 1.1 SIMPLE DIFFERENTIAL EQUATIONS AND APPLICATIONS 14 1.2
APPLICATIONS TO CHEMICAL KINETICS 21 1.3 APPLICATIONS TO ELECTRIC
CIRCUITS 23 1.4 EXISTENCE AND UNIQUENESS THEOREM 27 1.5 MAPLE COMMANDS
30 1.6 EXERCISES 31 2 LINEAR SYSTEMS IN THE PLANE 35 2.1 CANONICAL FORMS
35 2.2 EIGENVECTORS DEFINING STAHLE AND UNSTABLE MANIFOLDS 41 2.3 PHASE
PORTRAITS OF LINEAR SYSTEMS IN THE PLANE 43 2.4 MAPLE COMMANDS 47 2.5
EXERCISES 48 VI CONTENTS 3 NONLINEAR SYSTEMS IN THE PLANE 51 3.1
LINEARIZATION AND HARTMAN'S THEOREM 51 3.2 CONSTRUCTING PHASE PLANE
DIAGRAMS 53 3.3 MAPLE COMMANDS 61 3.4 EXERCISES 62 4 INTERACTING SPECIES
65 4.1 COMPETING SPECIES 65 4.2 PREDATOR-PREY MODELS 68 4.3 OTHER
CHARACTERISTICS AFFECTING INTERACTING SPECIES 74 4.4 MAPLE COMMANDS 74
4.5 EXERCISES 75 5 LIMIT CYCLES 77 5.1 HISTORICAL BACKGROUND 77 5.2
EXISTENCE AND UNIQUENESS OF LIMIT CYCLES IN THE PLANE 80 5.3
NONEXISTENCE OF LIMIT CYCLES IN THE PLANE 85 5.4 MAPLE COMMANDS 88 5.5
EXERCISES 88 6 HAMILTONIAN SYSTEMS, LYAPUNOV FUNCTIONS, AND STABILITY 91
6.1 HAMILTONIAN SYSTEMS IN THE PLANE 92 6.2 LYAPUNOV FUNCTIONS AND
STABILITY 97 6.3 MAPLE COMMANDS 101 6.4 EXERCISES 102 7 BIFURCATION
THEORY 105 7.1 BIFURCATIONS OF NONLINEAR SYSTEMS IN THE PLANE 106 7.2
MULTISTABILITY AND BISTABILITY 112 7.3 MAPLE COMMANDS 115 7.4 EXERCISES
115 8 THREE-DIMENSIONAL AUTONOMOUS SYSTEMS AND CHAOS 119 8.1 LINEAR
SYSTEMS AND CANONICAL FORMS 120 8.2 NONLINEAR SYSTEMS AND STABILITY 125
8.3 THE ROESSLER SYSTEM AND CHAOS 128 8.4 THE LORENZ EQUATIONS, CHUA'S
CIRCUIT, AND THE BELOUSOV-ZHABOTINSKI REACTION 132 8.5 MAPLE COMMANDS
139 8.6 EXERCISES 140 9 POINCARE MAPS AND NONAUTONOMOUS SYSTEMS IN THE
PLANE 143 9.1 POINCARE MAPS 144 9.2 HAMILTONIAN SYSTEMS WITH TWO DEGREES
OF FREEDOM 150 CONTENTS VII 9.3 NONAUTONOMOUS SYSTEMS IN THE PLANE 152
9.4 MAPLE COMMANDS 163 9.5 EXERCISES 165 10 LOCAL AND GLOBAL
BIFURCATIONS 169 10.1 SMALL-AMPLITUDE LIMIT CYCLE BIFURCATIONS 170 10.2
MELNIKOV INTEGRALS AND BIFURCATING LIMIT CYCLES FROM A CENTER 174 10.3
HOMOCLINIC BIFURCATIONS 176 10.4 MAPLE COMMANDS 177 10.5 EXERCISES 179
11 THE SECOND PART OF DAVID HILBERT'S SIXTEENTH PROBLEM 181 11.1
STATEMENT OF PROBLEM AND MAIN RESULTS 181 11.2 POINCARE COMPACTIFICATION
183 11.3 MAPLE COMMANDS 190 11.4 EXERCISES 191 12 LIMIT CYCLES OF
LIENARD SYSTEMS 193 12.1 GLOBAL RESULTS 193 12.2 LOCAL RESULTS 201 12.3
EXERCISES 202 13 LINEAR DISCRETE DYNAMICAL SYSTEMS 205 13.1 RECURRENCE
RELATIONS 206 13.2 THE LESLIE MODEL 210 13.3 HARVESTING AND CULLING
POLICIES 214 13.4 MAPLE COMMANDS 218 13.5 EXERCISES 219 14 NONLINEAR
DISCRETE DYNAMICAL SYSTEMS 223 14.1 THE TENT MAP AND GRAPHICAL
ITERATIONS 224 14.2 FIXED POINTS AND PERIODIC ORBITS 231 14.3 THE
LOGISTIC MAP, BIFURCATION DIAGRAM, AND FEIGENBAUM NUMBER 236 14.4
GAUSSIAN AND HENON MAPS 244 14.5 MAPLE COMMANDS 249 14.6 EXERCISES 251
15 COMPLEX ITERATIVE MAPS 255 15.1 JULIA SETS AND THE MANDELBROT SET 256
15.2 BOUNDARIES OF PERIODIC ORBITS 259 15.3 MAPLE COMMANDS 263 15.4
EXERCISES 264 VIII CONTENTS 16 ELECTROMAGNETIC WAVES AND OPTICAL
RESONATORS 267 16.1 MAXWELL'S EQUATIONS AND ELECTROMAGNETIC WAVES 268
16.2 HISTORICAL BACKGROUND OF OPTICAL RESONATORS 270 16.3 THE NONLINEAR
SIMPLE FIBER RING RESONATOR 273 16.4 CHAOTIC ATTRACTORS AND BISTABILITY
276 16.5 MAPLE COMMANDS 279 16.6 EXERCISES 280 17 ANALYSIS OF NONLINEAR
OPTICAL RESONATORS 283 17.1 LINEAR STABILITY ANALYSIS 284 17.2
INSTABILITIES AND BISTABILITY 286 17.3 MAPLE COMMANDS 291 17.4 EXERCISES
293 18 FRACTALS 295 18.1 CONSTRUCTION OF SIMPLE EXAMPLES 295 18.2
CALCULATING FRACTAL DIMENSIONS 301 18.3 MAPLE COMMANDS 307 18.4
EXERCISES 310 19 MULTIFRACTALS 313 19.1 A MULTIFRACTAL FORMALISM 314
19.2 MULTIFRACTALS IN THE REAL WORLD AND SOME SIMPLE EXAMPLES . . . 317
19.3 MAPLE COMMANDS 326 19.4 EXERCISES 326 20 CONTROLLING CHAOS 329 20.1
HISTORICAL BACKGROUND 330 20.2 CONTROLLING CHAOS IN THE LOGISTIC MAP 334
20.3 CONTROLLING CHAOS IN THE HENON MAP 336 20.4 MAPLE COMMANDS 341 20.5
EXERCISES 343 21 EXAMINATION-TYPE QUESTIONS 347 21.1 DYNAMICAL SYSTEMS
WITH APPLICATIONS 347 21.2 DYNAMICAL SYSTEMS WITH APPLICATIONS USING
MAPLE 350 22 SOLUTIONS TO EXERCISES 353 22.0 CHAPTERO 353 22.1 CHAPTERL
355 22.2 CHAPTER2 356 22.3 CHAPTER3 357 22.4 CHAPTER4 359 22.5 CHAPTER5
360 CONTENTS IX 22.6 CHAPTER6 361 22.7 CHAPTER7 361 22.8 CHAPTER8 363
22.9 CHAPTER9 364 22.10 CHAPTER 10 365 22.11 CHAPTER 11 365 22.12
CHAPTER 12 367 22.13 CHAPTER 13 367 22.14 CHAPTER 14 369 22.15 CHAPTER
15 370 22.16 CHAPTER 16 371 22.17 CHAPTER 17 371 22.18 CHAPTER 18 371
22.19 CHAPTER 19 372 22.20 CHAPTER 20 373 REFERENCES 375 TEXTBOOKS 375
RESEARCH PAPERS 379 INDEX 385 |
| any_adam_object | 1 |
| author | Lynch, Stephen 1964- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-08-21T00:17:06Z |
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| isbn | 0817641505 3764341505 |
| language | English |
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| spelling | Lynch, Stephen 1964- Verfasser (DE-588)122765052 aut Dynamical systems with applications using MAPLE Stephen Lynch Boston [u.a.] Birkhäuser 2001 XIII, 398 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Maple (Computer file) Análise matemática larpcal Dynamique différentiable - Informatique Equações diferenciais ordinárias larpcal Teoria da bifurcação (sistemas dinâmicos) larpcal Teoria qualitativa larpcal Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System (DE-588)4013396-5 gnd rswk-swf Maple Programm (DE-588)4209397-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Maple Programm (DE-588)4209397-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009302458&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lynch, Stephen 1964- Dynamical systems with applications using MAPLE Maple (Computer file) Análise matemática larpcal Dynamique différentiable - Informatique Equações diferenciais ordinárias larpcal Teoria da bifurcação (sistemas dinâmicos) larpcal Teoria qualitativa larpcal Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System (DE-588)4013396-5 gnd Maple Programm (DE-588)4209397-1 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4209397-1 |
| title | Dynamical systems with applications using MAPLE |
| title_auth | Dynamical systems with applications using MAPLE |
| title_exact_search | Dynamical systems with applications using MAPLE |
| title_full | Dynamical systems with applications using MAPLE Stephen Lynch |
| title_fullStr | Dynamical systems with applications using MAPLE Stephen Lynch |
| title_full_unstemmed | Dynamical systems with applications using MAPLE Stephen Lynch |
| title_short | Dynamical systems with applications using MAPLE |
| title_sort | dynamical systems with applications using maple |
| topic | Maple (Computer file) Análise matemática larpcal Dynamique différentiable - Informatique Equações diferenciais ordinárias larpcal Teoria da bifurcação (sistemas dinâmicos) larpcal Teoria qualitativa larpcal Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System (DE-588)4013396-5 gnd Maple Programm (DE-588)4209397-1 gnd |
| topic_facet | Maple (Computer file) Análise matemática Dynamique différentiable - Informatique Equações diferenciais ordinárias Teoria da bifurcação (sistemas dinâmicos) Teoria qualitativa Datenverarbeitung Differentiable dynamical systems Data processing Dynamisches System Maple Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009302458&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lynchstephen dynamicalsystemswithapplicationsusingmaple |