Introduction to differential equations with dynamical systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 430 S. graph. Darst. |
Internformat
MARC
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| 020 | |z 9780691124742 |9 978-0-691-12474-2 | ||
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| 100 | 1 | |a Campbell, Stephen L. |d 1945- |e Verfasser |0 (DE-588)129968188 |4 aut | |
| 245 | 1 | 0 | |a Introduction to differential equations with dynamical systems |c Stephen L. Campbell and Richard Haberman |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2008 | |
| 300 | |a XIII, 430 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Dynamique différentiable | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differential equations | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Haberman, Richard |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804137534361436160 |
|---|---|
| adam_text | CONTENTS
I·········!
Preface
ix
CHAPTER
1
First-Order Differential Equations and Their Applications
1
1.1
Introduction to Ordinary Differential Equations
1
1.2
The Definite Integral and the Initial Value Problem
4
1.2.1
The Initial Value Problem and the Indefinite Integral
5
1.2.2
The Initial Value Problem and the Definite Integral
6
1.2.3
Mechanics I: Elementary Motion of a Particle with Gravity Only
8
1.3
First-Order Separable Differential Equations
13
1.3.1
Using Definite Integrals for Separable Differential Equations
16
1.4
Direction Fields
19
1.4.1
Existence and Uniqueness
25
1.5
Euler s Numerical Method (optional)
31
1.6
First-Order Linear Differential Equations
37
1.6.1
Form of the General Solution
37
1.6.2
Solutions of Homogeneous First-Order Linear Differential
Equations
39
1.6.3
Integrating Factors for First-Order Linear Differential Equations
42
1.7
Linear First-Order Differential Equations with Constant
Coefficients and Constant Input
48
1.7.1
Homogeneous Linear Differential Equations with Constant
Coefficients
48
1.7.2
Constant Coefficient Linear Differential Equations with Constant
Input
50
1.7.3
Constant Coefficient Differential Equations with Exponential
Input
52
1.7.4
Constant Coefficient Differential Equations with Discontinuous
Input
52
1.8
Growth and Decay Problems
59
1.8.1
A First Model of Population Growth
59
1.8.2
Radioactive Decay
65
1.8.3
Thermal Cooling
68
1.9
Mixture Problems
74
1.9.1
Mixture Problems with a Fixed Volume
74
1.9.2
Mixture Problems with Variable Volumes
77
1.10
Electronic Circuits
82
1.11
Mechanics II: Including Air Resistance
88
1.12
Orthogonal Trajectories (optional)
92
Vi
CONTENTS
CHAPTER
2
Linear Second- and Higher-Order Differential Equations
96
2.1
General Solution of Second-Order Linear Differential
Equations
96
2.2
Initial Value Problem (for Homogeneous Equations)
100
2.3
Reduction of Order
107
2.4
Homogeneous Linear Constant Coefficient Differential Equations
(Second Order)
112
2.4.1
Homogeneous Linear Constant Coefficient Differential Equations
(nth-Order)
122
2.5
Mechanical Vibrations I: Formulation and Free Response
124
2.5.1
Formulation of Equations
124
2.5.2
Simple Harmonic Motion (No Damping,
5 = 0) 128
2.5.3
Free Response with Friction (S
> 0) 135
2.6
The Method of Undetermined Coefficients
142
2.7
Mechanical Vibrations II: Forced Response
159
2.7.1
Friction is Absent
(0 = 0) 159
2.7.2
Friction is Present
(á
> 0)
(Damped Forced Oscillations)
168
2.8
Linear Electric Circuits
174
2.9
Euler
Equation
179
2.10
Variation of Parameters (Second-Order)
185
2.11
Variation of Parameters (nth-Order)
193
CHAPTER
3
The Laplace Transform
197
3.1
Definition and Basic Properties
197
3.1.1
The Shifting Theorem (Multiplying by an Exponential)
205
3.1.2
Derivative Theorem (Multiplying by
t
) 210
3.2
Inverse Laplace Transforms (Roots, Quadratics, and Partial
Fractions)
213
3.3
Initial Value Problems for Differential Equations
225
3.4
Discontinuous Forcing Functions
234
3.4.1
Solution of Differential Equations
239
3.5
Periodic Functions
248
3.6
Integrals and the Convolution Theorem
253
3.6.1
Derivation of the Convolution Theorem (optional)
256
3.7
Impulses and Distributions
260
CHAPTER
4
An Introduction to Linear Systems of Differential Equations
and Their Phase Plane
265
4.1
Introduction
265
4.2
Introduction to Linear Systems of Differential Equations
268
CONTENTS
Vii
4.2.1
Solving Linear Systems Using Eigenvalues and Eigenvectors
of the Matrix
269
4.2.2
Solving Linear Systems if the Eigenvalues are Real
and Unequal
272
4.2.3
Finding General Solutions of Linear Systems in the Case
of Complex Eigenvalues
276
4.2.4
Special Systems with Complex Eigenvalues (optional)
279
4.2.5
General Solution of a Linear System if the Two Real Eigenvalues
are Equal (Repeated) Roots
281
4.2.6
Eigenvalues and Trace and Determinant (optional)
283
4.3
The Phase Plane for Linear Systems of Differential Equations
287
4.3.1
Introduction to the Phase Plane for Linear Systems of Differential
Equations
287
4.3.2
Phase Plane for Linear Systems of Differential Equations
295
4.3.3
Real Eigenvalues
296
4.3.4
Complex Eigenvalues
304
4.3.5
General Theorems
310
CHAPTER
5
Mostly
Nonlinear First-Order Differential Equations
315
5.1
First-Order Differential Equations
315
5.2
Equilibria and Stability
316
5.2.1
Equilibrium
316
5.2.2
Stability
317
5.2.3
Review of Linearization
318
5.2.4
Linear Stability Analysis
318
5.3
One-Dimensional Phase Lines
322
5.4
Application to Population Dynamics: The Logistic
Equation
327
CHAPTER
6
Nonlinear Systems of Differential Equations in the Plane
332
6.1
Introduction
332
6.2
Equilibria of Nonlinear Systems, Linear Stability Analysis of
Equilibrium, and the Phase Plane
335
6.2.1
Linear Stability Analysis and the Phase Plane
336
6.2.2
Nonlinear Systems: Summary, Philosophy, Phase Plane, Direction
Field, Nullclines
341
6.3
Population Models
349
6.3.1
Two Competing Species
350
6.3.2
Predator-Prey Population Models
356
6.4
Mechanical Systems
363
6.4.1
Nonlinear Pendulum
363
6.4.2
Linearized Pendulum
364
viii
CONTENTS
6.4.3
Conservative Systems
and the
Energy Integral
364
6.4.4
The Phase
Plane
and the Potential
367
Answers to Odd-Numbered Exercises
379
Index
429
|
| adam_txt |
CONTENTS
I·········!
Preface
ix
CHAPTER
1
First-Order Differential Equations and Their Applications
1
1.1
Introduction to Ordinary Differential Equations
1
1.2
The Definite Integral and the Initial Value Problem
4
1.2.1
The Initial Value Problem and the Indefinite Integral
5
1.2.2
The Initial Value Problem and the Definite Integral
6
1.2.3
Mechanics I: Elementary Motion of a Particle with Gravity Only
8
1.3
First-Order Separable Differential Equations
13
1.3.1
Using Definite Integrals for Separable Differential Equations
16
1.4
Direction Fields
19
1.4.1
Existence and Uniqueness
25
1.5
Euler's Numerical Method (optional)
31
1.6
First-Order Linear Differential Equations
37
1.6.1
Form of the General Solution
37
1.6.2
Solutions of Homogeneous First-Order Linear Differential
Equations
39
1.6.3
Integrating Factors for First-Order Linear Differential Equations
42
1.7
Linear First-Order Differential Equations with Constant
Coefficients and Constant Input
48
1.7.1
Homogeneous Linear Differential Equations with Constant
Coefficients
48
1.7.2
Constant Coefficient Linear Differential Equations with Constant
Input
50
1.7.3
Constant Coefficient Differential Equations with Exponential
Input
52
1.7.4
Constant Coefficient Differential Equations with Discontinuous
Input
52
1.8
Growth and Decay Problems
59
1.8.1
A First Model of Population Growth
59
1.8.2
Radioactive Decay
65
1.8.3
Thermal Cooling
68
1.9
Mixture Problems
74
1.9.1
Mixture Problems with a Fixed Volume
74
1.9.2
Mixture Problems with Variable Volumes
77
1.10
Electronic Circuits
82
1.11
Mechanics II: Including Air Resistance
88
1.12
Orthogonal Trajectories (optional)
92
Vi
CONTENTS
CHAPTER
2
Linear Second- and Higher-Order Differential Equations
96
2.1
General Solution of Second-Order Linear Differential
Equations
96
2.2
Initial Value Problem (for Homogeneous Equations)
100
2.3
Reduction of Order
107
2.4
Homogeneous Linear Constant Coefficient Differential Equations
(Second Order)
112
2.4.1
Homogeneous Linear Constant Coefficient Differential Equations
(nth-Order)
122
2.5
Mechanical Vibrations I: Formulation and Free Response
124
2.5.1
Formulation of Equations
124
2.5.2
Simple Harmonic Motion (No Damping,
5 = 0) 128
2.5.3
Free Response with Friction (S
> 0) 135
2.6
The Method of Undetermined Coefficients
142
2.7
Mechanical Vibrations II: Forced Response
159
2.7.1
Friction is Absent
(0 = 0) 159
2.7.2
Friction is Present
(á
> 0)
(Damped Forced Oscillations)
168
2.8
Linear Electric Circuits
174
2.9
Euler
Equation
179
2.10
Variation of Parameters (Second-Order)
185
2.11
Variation of Parameters (nth-Order)
193
CHAPTER
3
The Laplace Transform
197
3.1
Definition and Basic Properties
197
3.1.1
The Shifting Theorem (Multiplying by an Exponential)
205
3.1.2
Derivative Theorem (Multiplying by
t
) 210
3.2
Inverse Laplace Transforms (Roots, Quadratics, and Partial
Fractions)
213
3.3
Initial Value Problems for Differential Equations
225
3.4
Discontinuous Forcing Functions
234
3.4.1
Solution of Differential Equations
239
3.5
Periodic Functions
248
3.6
Integrals and the Convolution Theorem
253
3.6.1
Derivation of the Convolution Theorem (optional)
256
3.7
Impulses and Distributions
260
CHAPTER
4
An Introduction to Linear Systems of Differential Equations
and Their Phase Plane
265
4.1
Introduction
265
4.2
Introduction to Linear Systems of Differential Equations
268
CONTENTS
Vii
4.2.1
Solving Linear Systems Using Eigenvalues and Eigenvectors
of the Matrix
269
4.2.2
Solving Linear Systems if the Eigenvalues are Real
and Unequal
272
4.2.3
Finding General Solutions of Linear Systems in the Case
of Complex Eigenvalues
276
4.2.4
Special Systems with Complex Eigenvalues (optional)
279
4.2.5
General Solution of a Linear System if the Two Real Eigenvalues
are Equal (Repeated) Roots
281
4.2.6
Eigenvalues and Trace and Determinant (optional)
283
4.3
The Phase Plane for Linear Systems of Differential Equations
287
4.3.1
Introduction to the Phase Plane for Linear Systems of Differential
Equations
287
4.3.2
Phase Plane for Linear Systems of Differential Equations
295
4.3.3
Real Eigenvalues
296
4.3.4
Complex Eigenvalues
304
4.3.5
General Theorems
310
CHAPTER
5
Mostly
Nonlinear First-Order Differential Equations
315
5.1
First-Order Differential Equations
315
5.2
Equilibria and Stability
316
5.2.1
Equilibrium
316
5.2.2
Stability
317
5.2.3
Review of Linearization
318
5.2.4
Linear Stability Analysis
318
5.3
One-Dimensional Phase Lines
322
5.4
Application to Population Dynamics: The Logistic
Equation
327
CHAPTER
6
Nonlinear Systems of Differential Equations in the Plane
332
6.1
Introduction
332
6.2
Equilibria of Nonlinear Systems, Linear Stability Analysis of
Equilibrium, and the Phase Plane
335
6.2.1
Linear Stability Analysis and the Phase Plane
336
6.2.2
Nonlinear Systems: Summary, Philosophy, Phase Plane, Direction
Field, Nullclines
341
6.3
Population Models
349
6.3.1
Two Competing Species
350
6.3.2
Predator-Prey Population Models
356
6.4
Mechanical Systems
363
6.4.1
Nonlinear Pendulum
363
6.4.2
Linearized Pendulum
364
viii
CONTENTS
6.4.3
Conservative Systems
and the
Energy Integral
364
6.4.4
The Phase
Plane
and the Potential
367
Answers to Odd-Numbered Exercises
379
Index
429 |
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| id | DE-604.BV023238203 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:22:54Z |
| indexdate | 2024-07-09T21:13:49Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016423788 |
| oclc_num | 227010350 |
| open_access_boolean | |
| owner | DE-29T DE-824 DE-703 DE-11 |
| owner_facet | DE-29T DE-824 DE-703 DE-11 |
| physical | XIII, 430 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Campbell, Stephen L. 1945- Verfasser (DE-588)129968188 aut Introduction to differential equations with dynamical systems Stephen L. Campbell and Richard Haberman Princeton [u.a.] Princeton Univ. Press 2008 XIII, 430 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamique différentiable Équations différentielles Differentiable dynamical systems Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Haberman, Richard Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016423788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Campbell, Stephen L. 1945- Haberman, Richard Introduction to differential equations with dynamical systems Dynamique différentiable Équations différentielles Differentiable dynamical systems Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4013396-5 |
| title | Introduction to differential equations with dynamical systems |
| title_auth | Introduction to differential equations with dynamical systems |
| title_exact_search | Introduction to differential equations with dynamical systems |
| title_exact_search_txtP | Introduction to differential equations with dynamical systems |
| title_full | Introduction to differential equations with dynamical systems Stephen L. Campbell and Richard Haberman |
| title_fullStr | Introduction to differential equations with dynamical systems Stephen L. Campbell and Richard Haberman |
| title_full_unstemmed | Introduction to differential equations with dynamical systems Stephen L. Campbell and Richard Haberman |
| title_short | Introduction to differential equations with dynamical systems |
| title_sort | introduction to differential equations with dynamical systems |
| topic | Dynamique différentiable Équations différentielles Differentiable dynamical systems Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamique différentiable Équations différentielles Differentiable dynamical systems Differential equations Gewöhnliche Differentialgleichung Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016423788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT campbellstephenl introductiontodifferentialequationswithdynamicalsystems AT habermanrichard introductiontodifferentialequationswithdynamicalsystems |