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E-raamat: Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition

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(Mathematics Department, Cornell University)
  • Formaat: 935 pages
  • Ilmumisaeg: 21-Sep-2018
  • Kirjastus: Westview Press Inc
  • Keel: eng
  • ISBN-13: 9780429680168
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Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering, Second EditionSuurem pilt
  • Formaat: 935 pages
  • Ilmumisaeg: 21-Sep-2018
  • Kirjastus: Westview Press Inc
  • Keel: eng
  • ISBN-13: 9780429680168
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Steven H. Strogatz’s Nonlinear Dynamics and Chaos, second edition, is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

The Student Solutions Manual, by Mitchal Dichter, includes solutions to the odd-numbered exercises featured in Nonlinear Dynamics and Chaos, second edition. Complete with graphs and worked-out solutions, the Student Solutions Manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects explored in Strogatz’s popular book.

Arvustused

"The new edition has a friendly yet clear technical style . . . One of the book's biggest strengths is that it explains core concepts through practical examples drawn from various fields and from real-world systems . . . the author's excellent use of geometric and graphical techniques greatly clarifies what can be amazingly complex behavior." Physics Today

"Nonlinear Dynamics and Chaos is an excellent book that effectively demonstrates the power and beauty of the theory of dynamical systems. Its readers will want to learn more." Mathematical Association of America "The new edition has a friendly yet clear technical style . . . One of the book's biggest strengths is that it explains core concepts through practical examples drawn from various fields and from real-world systems . . . the author's excellent use of geometric and graphical techniques greatly clarifies what can be amazingly complex behavior." Physics Today

"Nonlinear Dynamics and Chaos is an excellent book that effectively demonstrates the power and beauty of the theory of dynamical systems. Its readers will want to learn more." Mathematical Association of America

Nonlinear Dynamics and Chaos
Preface to the Second Edition
ix
Preface to the First Edition
xi
1 Overview
1(14)
1.0 Chaos, Fractals, and Dynamics
1(1)
1.1 Capsule History of Dynamics
2(2)
1.2 The Importance of Being Nonlinear
4(5)
1.3 A Dynamical View of the World
9(6)
Part I One-Dimensional Flows
2 Flows on the Line
15(30)
2.0 Introduction
15(1)
2.1 A Geometric Way of Thinking
16(2)
2.2 Fixed Points and Stability
18(3)
2.3 Population Growth
21(3)
2.4 Linear Stability Analysis
24(2)
2.5 Existence and Uniqueness
26(2)
2.6 Impossibility of Oscillations
28(2)
2.7 Potentials
30(2)
2.8 Solving Equations on the Computer
32(4)
Exercises for
Chapter 2
36(9)
3 Bifurcations
45(50)
3.0 Introduction
45(1)
3.1 Saddle-Node Bifurcation
46(5)
3.2 Transcritical Bifurcation
51(3)
3.3 Laser Threshold
54(2)
3.4 Pitchfork Bifurcation
56(6)
3.5 Overdamped Bead on a Rotating Hoop
62(8)
3.6 Imperfect Bifurcations and Catastrophes
70(4)
3.7 Insect Outbreak
74(6)
Exercises for
Chapter 3
80(15)
4 Flows on the Circle
95(30)
4.0 Introduction
95(1)
4.1 Examples and Definitions
95(2)
4.2 Uniform Oscillator
97(1)
4.3 Nonuniform Oscillator
98(5)
4.4 Overdamped Pendulum
103(2)
4.5 Fireflies
105(4)
4.6 Superconducting Josephson Junctions
109(6)
Exercises for
Chapter 4
115(10)
Part II Two-Dimensional Flows
5 Linear Systems
125(21)
5.0 Introduction
125(1)
5.1 Definitions and Examples
125(6)
5.2 Classification of Linear Systems
131(8)
5.3 Love Affairs
139(3)
Exercises for
Chapter 5
142(4)
6 Phase Plane
146(52)
6.0 Introduction
146(1)
6.1 Phase Portraits
146(3)
6.2 Existence, Uniqueness, and Topological Consequences
149(2)
6.3 Fixed Points and Linearization
151(5)
6.4 Rabbits versus Sheep
156(4)
6.5 Conservative Systems
160(4)
6.6 Reversible Systems
164(4)
6.7 Pendulum
168(6)
6.8 Index Theory
174(7)
Exercises for
Chapter 6
181(17)
7 Limit Cycles
198(46)
7.0 Introduction
198(1)
7.1 Examples
199(2)
7.2 Ruling Out Closed Orbits
201(4)
7.3 Poincare—Bendixson Theorem
205(7)
7.4 Lienard Systems
212(1)
7.5 Relaxation Oscillations
213(4)
7.6 Weakly Nonlinear Oscillators
217(13)
Exercises for
Chapter 7
230(14)
8 Bifurcations Revisited
244(65)
8.0 Introduction
244(1)
8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations
244(7)
8.2 Hopf Bifurcations
251(6)
8.3 Oscillating Chemical Reactions
257(7)
8.4 Global Bifurcations of Cycles
264(4)
8.5 Hysteresis in the Driven Pendulum and Josephson Junction
268(8)
8.6 Coupled Oscillators and Quasiperiodicity
276(5)
8.7 Poincare Maps
281(6)
Exercises for
Chapter 8
287(22)
Part III Chaos
9 Lorenz Equations
309(46)
9.0 Introduction
309(1)
9.1 A Chaotic Waterwheel
310(9)
9.2 Simple Properties of the Lorenz Equations
319(6)
9.3 Chaos on a Strange Attractor
325(8)
9.4 Lorenz Map
333(4)
9.5 Exploring Parameter Space
337(5)
9.6 Using Chaos to Send Secret Messages
342(6)
Exercises for
Chapter 9
348(7)
10 One-Dimensional Maps
355(50)
10.0 Introduction
355(1)
10.1 Fixed Points and Cobwebs
356(4)
10.2 Logistic Map: Numerics
360(4)
10.3 Logistic Map: Analysis
364(4)
10.4 Periodic Windows
368(5)
10.5 Liapunov Exponent
373(3)
10.6 Universality and Experiments
376(10)
10.7 Renormalization
386(8)
Exercises for
Chapter 10
394(11)
11 Fractals
405(24)
11.0 Introduction
405(1)
11.1 Countable and Uncountable Sets
406(2)
11.2 Cantor Set
408(3)
11.3 Dimension of Self-Similar Fractals
411(5)
11.4 Box Dimension
416(2)
11.5 Pointwise and Correlation Dimensions
418(5)
Exercises for
Chapter 11
423(6)
12 Strange Attractors
429
12.0 Introduction
429(1)
12.1 The Simplest Examples
429(6)
12.2 Henon Map
435(5)
12.3 Rossler System
440(3)
12.4 Chemical Chaos and Attractor Reconstruction
443(4)
12.5 Forced Double-Well Oscillator
447(7)
Exercises for
Chapter 12
454(6)
Answers to Selected Exercises
460(10)
References
470(13)
Author Index
483(4)
Subject Index
487
Nonlinear Dynamics and Chaos: Student Solutions Manual
2 Flows on the Line
1(18)
2.1 A Geometric Way of Thinking
1(1)
2.2 Fixed Points and Stability
2(5)
2.3 Population Growth
7(2)
2.4 Linear Stability Analysis
9(2)
2.5 Existence and Uniqueness
11(2)
2.6 Impossibility of Oscillations
13(1)
2.7 Potentials
13(1)
2.8 Solving Equations on the Computer
14(5)
3 Bifurcations
19(46)
3.1 Saddle-Node Bifurcation
19(8)
3.2 Transcritical Bifurcation
27(4)
3.3 Laser Threshold
31(2)
3.4 Pitchfork Bifurcation
33(10)
3.5 Overdamped Bead on a Rotating Hoop
43(2)
3.6 Imperfect Bifurcations and Catastrophes
45(10)
3.7 Insect Outbreak
55(10)
4 Flows on the Circle
65(22)
4.1 Examples and Definitions
65(1)
4.2 Uniform Oscillator
66(1)
4.3 Nonuniform Oscillator
67(8)
4.4 Overdamped Pendulum
75(2)
4.5 Fireflies
77(3)
4.6 Superconducting Josephson Junctions
80(7)
5 Linear Systems
87(16)
5.1 Definitions and Examples
87(5)
5.2 Classification of Linear Systems
92(9)
5.3 Love Affairs
101(2)
6 Phase Plane
103(70)
6.1 Phase Portraits
103(6)
6.2 Existence, Uniqueness, and Topological Consequences
109(1)
6.3 Fixed Points and Linearization
110(7)
6.4 Rabbits versus Sheep
117(12)
6.5 Conservative Systems
129(16)
6.6 Reversible Systems
145(15)
6.7 Pendulum
160(4)
6.8 Index Theory
164(9)
7 Limit Cycles
173(46)
7.1 Examples
173(6)
7.2 Ruling Out Closed Orbits
179(9)
7.3 Poincare-Bendixson Theorem
188(9)
7.4 Lienard Systems
197(1)
7.5 Relaxation Oscillations
198(5)
7.6 Weakly Nonlinear Oscillators
203(16)
8 Bifurcations Revisited
219(54)
8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations
219(7)
8.2 Hopf Bifurcations
226(11)
8.3 Oscillating Chemical Reactions
237(4)
8.4 Global Bifurcations of Cycles
241(7)
8.5 Hysteresis in the Driven Pendulum and Josephson Junction
248(5)
8.6 Coupled Oscillators and Quasiperiodicity
253(14)
8.7 Poincare Maps
267(6)
9 Lorenz Equations
273(34)
9.1 A Chaotic Waterwheel
273(3)
9.2 Simple Properties of the Lorenz Equations
276(3)
9.3 Chaos on a Strange Attractor
279(13)
9.4 Lorenz Map
292(1)
9.5 Exploring Parameter Space
292(11)
9.6 Using Chaos to Send Secret Messages
303(4)
10 One-Dimensional Maps
307(52)
10.1 Fixed Points and Cobwebs
307(11)
10.2 Logistic Map: Numerics
318(5)
10.3 Logistic Map: Analysis
323(8)
10.4 Periodic Windows
331(8)
10.5 Liapunov Exponent
339(3)
10.6 Universality and Experiments
342(10)
10.7 Renormalization
352(7)
11 Fractals
359(12)
11.1 Countable and Uncountable Sets
359(1)
11.2 Cantor Set
360(2)
11.3 Dimension of Self-Similar Fractals
362(4)
11.4 Box Dimension
366(3)
11.5 Pointwise and Correlation Dimensions
369(2)
12 Strange Attractors
371
12.1 The Simplest Examples
371(10)
12.2 Henon Map
381(6)
12.3 Rossler System
387(2)
12.4 Chemical Chaos and Attractor Reconstruction
389(2)
12.5 Forced Double-Well Oscillator
391
Steven Strogatz is the Schurman Professor of Applied Mathematics at Cornell University. His honors include MIT's highest teaching prize, a lifetime achievement award for the communication of mathematics to the general public, and membership in the American Academy of Arts and Sciences. His research on a wide variety of nonlinear systems from synchronized fireflies to small-world networks has been featured in the pages of Scientific American, Nature, Discover, Business Week, and The New York Times.
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