Nonlinear ordinary differential equations: problems and solutions ; a sourcebook for scientists and engineers
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 587 S. Ill., graph. Darst. |
| ISBN: | 9780199212033 |
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| 245 | 1 | 0 | |a Nonlinear ordinary differential equations |b problems and solutions ; a sourcebook for scientists and engineers |c D. W. Jordan and P. Smith |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2007 | |
| 300 | |a VI, 587 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Differential equations, Nonlinear |v Problems, exercises, etc | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-015740712 | ||
Record in the Search Index
| _version_ | 1804136644995973120 |
|---|---|
| adam_text | Contents
The chapter headings are those of Nonlinear Ordinary Differential Equations but the page
numbers refer to this book. The section headings listed below for each chapter are taken from
Nonlinear Ordinary Differential Equations, and are given for reference and information.
1
Second-order differential equations in the phase plane
1
Phase diagram for the pendulum equation
·
Autonomous equations in the phase plane
·
Mechanical analogy
for the conservative system
χ
= ƒ
(χ)
·
The damped linear oscillator
·
Nonlinear damping: limit cycles
·
Some
applications
·
Parameter-dependent conservative systems
·
Graphical representation of solutions
2
Plane autonomous systems and linearization
63
The general phase plane
·
Some population models
·
Linear approximation at equilibrium points
·
The general
solution of linear autonomous plane systems
·
The phase paths of linear autonomous plane systems
·
Scaling
in the phase diagram for a linear autonomous system
·
Constructing a phase diagram
·
Hamiltonian systems
3
Geometrical aspects of plane autonomous systems
133
The index of a point
·
The index at infinity
·
The phase diagram at infinity
·
Limit cycles and other closed
paths
·
Computation of the phase diagram
·
Homoclinic and heteroclinic paths
4
Periodic solutions; averaging methods
213
An energy-balance method for limit cycles
·
Amplitude and frequency estimates: polar coordinates
·
An
averaging method for spiral phase paths
·
Periodic solutions: harmonic balance
·
The equivalent linear equation
by harmonic balance
5
Perturbation methods
251
Nonautonomos systems: forced oscillations
·
The direct perturbation method for the undamped Duffing equa¬
tion
·
Forced oscillations far from resonance
·
Forced oscillations near resonance with weak excitation
·
The
amplitude equation for the undamped pendulum
·
The amplitude equation for a damped pendulum
·
Soft and
hard springs
·
Amplitude-phase perturbation for the pendulum equation
·
Periodic solutions of autonomous
equations (Lindstedt s method)
·
Forced oscillation of a self-excited equation
·
The perturbation method and
Fourier series
·
Homoclinic bifurcation: an example
6
Singular perturbation methods
289
Non-uniform approximation to functions on an interval
·
Coordinate perturbation
·
Lighthill s method
·
Time-
scaling for series solutions of autonomous equations
·
The multiple-scale technique applied to saddle points
and nodes
·
Matching approximation on an interval
·
A matching technique for differential equations
Contents
7
Forced oscillations: harmonic and subharmonic response, stability, and entrainment
339
General forced periodic solutions
·
Harmonic solutions, transients, and stability for Duffmg s equation
•
The jump phenomenon
·
Harmonic oscillations, stability, and transients for the forced van
der Pol
equation
•
Frequency entrainment for the van
der Pol
equation
·
Subharmonics of Duffmg s equation by perturbation
•
Stability and transients for subharmonics of Duffing s equation
8
Stability
385
Poincaré
stability (stability of paths)
·
Paths and solution curves for general systems
·
Stability of time solu¬
tions: Liapunov stability
·
Liapunov stability of plane autonomous linear systems
·
Structure of the solutions
of n-dimensional linear systems
·
Structure of
n-dimensional
inhomogeneous linear systems
·
Stability and
boundedness for linear systems
·
Stability of linear systems with constant coefficients
·
Linear approximation
at equilibrium points for first-order systems in
и
variables
·
Stability of a class of nonautonomous linear systems
in
η
dimensions
·
Stability of the zero solution of nearly linear systems
9
Stabilty by solution perturbation: Mathieu s equation
417
The stability of forced oscillations by a solution perturbation
·
Equations with periodic coefficients (Floquet
theory)
·
Mathieu s equation arising from a Duffing equation
·
Transition curves for Mathieu s equation by
perturbation
·
Mathieu s damped equation arising from a Duffing equation
10
Liapunov methods for determining stability of the zero solution
449
Introducing the Liapunov method
·
Topograhic systems and the
Poincaré-Bendixson
theorem
·
Liapunov
stability of the zero solution
·
Asymptotic stability of the zero solution
·
Extending weak Liapunov functions
to asymptotic stability
·
A more general theory for autonomous systems
·
A test for instability of the zero
solution:
η
dimensions
·
Stability and the linear approximation in two dimensions
·
Exponential function of
a matrix
·
Stability and the linear approximation for nth order autonomous systems
·
Special systems
11
The existence of periodic solutions
485
The
Poincaré-Bendixson
theorem and periodic solutions
·
A theorem on the existence of a centre
·
A theorem
on the existence of a limit cycle
·
Van
der
Pol s equation with large parameter
12
Bifurcations and manifolds
497
Examples of simple bifurcations
·
The fold and the cusp
·
Further types of bifurcation
· Hopf
bifurcations
•
Higher-order systems: manifolds
·
Linear approximation: centre manifolds
13
Poincaré
sequences, homoclinic bifurcation, and chaos
533
Poincaré
sequences
·
Poincaré
sections for non-autonomous systems
·
Subharmonics and period doubling
•
Homoclinic paths, strange attractors and chaos
·
The Duffing oscillator
·
A discrete system: the logistic
difference equation
·
Liapunov exponents and difference equations
·
Homoclinic bifurcation for forced systems
•
The horseshoe map
·
Melnikov s method for detecting homoclinic bifurcation
·
Liapunov s exponents and
differential equations
·
Power spectra
·
Some characteristic features of chaotic oscillations
References
585
|
| adam_txt |
Contents
The chapter headings are those of Nonlinear Ordinary Differential Equations but the page
numbers refer to this book. The section headings listed below for each chapter are taken from
Nonlinear Ordinary Differential Equations, and are given for reference and information.
1
Second-order differential equations in the phase plane
1
Phase diagram for the pendulum equation
·
Autonomous equations in the phase plane
·
Mechanical analogy
for the conservative system
χ
= ƒ
(χ)
·
The damped linear oscillator
·
Nonlinear damping: limit cycles
·
Some
applications
·
Parameter-dependent conservative systems
·
Graphical representation of solutions
2
Plane autonomous systems and linearization
63
The general phase plane
·
Some population models
·
Linear approximation at equilibrium points
·
The general
solution of linear autonomous plane systems
·
The phase paths of linear autonomous plane systems
·
Scaling
in the phase diagram for a linear autonomous system
·
Constructing a phase diagram
·
Hamiltonian systems
3
Geometrical aspects of plane autonomous systems
133
The index of a point
·
The index at infinity
·
The phase diagram at infinity
·
Limit cycles and other closed
paths
·
Computation of the phase diagram
·
Homoclinic and heteroclinic paths
4
Periodic solutions; averaging methods
213
An energy-balance method for limit cycles
·
Amplitude and frequency estimates: polar coordinates
·
An
averaging method for spiral phase paths
·
Periodic solutions: harmonic balance
·
The equivalent linear equation
by harmonic balance
5
Perturbation methods
251
Nonautonomos systems: forced oscillations
·
The direct perturbation method for the undamped Duffing equa¬
tion
·
Forced oscillations far from resonance
·
Forced oscillations near resonance with weak excitation
·
The
amplitude equation for the undamped pendulum
·
The amplitude equation for a damped pendulum
·
Soft and
hard springs
·
Amplitude-phase perturbation for the pendulum equation
·
Periodic solutions of autonomous
equations (Lindstedt's method)
·
Forced oscillation of a self-excited equation
·
The perturbation method and
Fourier series
·
Homoclinic bifurcation: an example
6
Singular perturbation methods
289
Non-uniform approximation to functions on an interval
·
Coordinate perturbation
·
Lighthill's method
·
Time-
scaling for series solutions of autonomous equations
·
The multiple-scale technique applied to saddle points
and nodes
·
Matching approximation on an interval
·
A matching technique for differential equations
Contents
7
Forced oscillations: harmonic and subharmonic response, stability, and entrainment
339
General forced periodic solutions
·
Harmonic solutions, transients, and stability for Duffmg's equation
•
The jump phenomenon
·
Harmonic oscillations, stability, and transients for the forced van
der Pol
equation
•
Frequency entrainment for the van
der Pol
equation
·
Subharmonics of Duffmg's equation by perturbation
•
Stability and transients for subharmonics of Duffing's equation
8
Stability
385
Poincaré
stability (stability of paths)
·
Paths and solution curves for general systems
·
Stability of time solu¬
tions: Liapunov stability
·
Liapunov stability of plane autonomous linear systems
·
Structure of the solutions
of n-dimensional linear systems
·
Structure of
n-dimensional
inhomogeneous linear systems
·
Stability and
boundedness for linear systems
·
Stability of linear systems with constant coefficients
·
Linear approximation
at equilibrium points for first-order systems in
и
variables
·
Stability of a class of nonautonomous linear systems
in
η
dimensions
·
Stability of the zero solution of nearly linear systems
9
Stabilty by solution perturbation: Mathieu's equation
417
The stability of forced oscillations by a solution perturbation
·
Equations with periodic coefficients (Floquet
theory)
·
Mathieu's equation arising from a Duffing equation
·
Transition curves for Mathieu's equation by
perturbation
·
Mathieu's damped equation arising from a Duffing equation
10
Liapunov methods for determining stability of the zero solution
449
Introducing the Liapunov method
·
Topograhic systems and the
Poincaré-Bendixson
theorem
·
Liapunov
stability of the zero solution
·
Asymptotic stability of the zero solution
·
Extending weak Liapunov functions
to asymptotic stability
·
A more general theory for autonomous systems
·
A test for instability of the zero
solution:
η
dimensions
·
Stability and the linear approximation in two dimensions
·
Exponential function of
a matrix
·
Stability and the linear approximation for nth order autonomous systems
·
Special systems
11
The existence of periodic solutions
485
The
Poincaré-Bendixson
theorem and periodic solutions
·
A theorem on the existence of a centre
·
A theorem
on the existence of a limit cycle
·
Van
der
Pol's equation with large parameter
12
Bifurcations and manifolds
497
Examples of simple bifurcations
·
The fold and the cusp
·
Further types of bifurcation
· Hopf
bifurcations
•
Higher-order systems: manifolds
·
Linear approximation: centre manifolds
13
Poincaré
sequences, homoclinic bifurcation, and chaos
533
Poincaré
sequences
·
Poincaré
sections for non-autonomous systems
·
Subharmonics and period doubling
•
Homoclinic paths, strange attractors and chaos
·
The Duffing oscillator
·
A discrete system: the logistic
difference equation
·
Liapunov exponents and difference equations
·
Homoclinic bifurcation for forced systems
•
The horseshoe map
·
Melnikov's method for detecting homoclinic bifurcation
·
Liapunov's exponents and
differential equations
·
Power spectra
·
Some characteristic features of chaotic oscillations
References
585 |
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| discipline | Mathematik |
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| id | DE-604.BV022534180 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:07:44Z |
| indexdate | 2024-07-09T20:59:41Z |
| institution | BVB |
| isbn | 9780199212033 |
| language | English |
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| spelling | Jordan, Dominic W. Verfasser (DE-588)115172602 aut Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers D. W. Jordan and P. Smith 1. publ. Oxford Oxford Univ. Press 2007 VI, 587 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations, Nonlinear Problems, exercises, etc Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 s DE-604 Smith, Peter 1935- Verfasser (DE-588)141762349 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015740712&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jordan, Dominic W. Smith, Peter 1935- Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers Differential equations, Nonlinear Problems, exercises, etc Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd |
| subject_GND | (DE-588)4478411-9 (DE-588)4143389-0 |
| title | Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers |
| title_auth | Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers |
| title_exact_search | Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers |
| title_exact_search_txtP | Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers |
| title_full | Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers D. W. Jordan and P. Smith |
| title_fullStr | Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers D. W. Jordan and P. Smith |
| title_full_unstemmed | Nonlinear ordinary differential equations problems and solutions ; a sourcebook for scientists and engineers D. W. Jordan and P. Smith |
| title_short | Nonlinear ordinary differential equations |
| title_sort | nonlinear ordinary differential equations problems and solutions a sourcebook for scientists and engineers |
| title_sub | problems and solutions ; a sourcebook for scientists and engineers |
| topic | Differential equations, Nonlinear Problems, exercises, etc Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd |
| topic_facet | Differential equations, Nonlinear Problems, exercises, etc Nichtlineare gewöhnliche Differentialgleichung Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015740712&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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