Differential equations and dynamical systems courses - Revision history

Murray at 18:03, 14 November 2010

2010-11-14T18:03:50Z

← Older revision		Revision as of 18:03, 14 November 2010
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	This page collects some information about (ordinary) differential equations and dynamical systems courses offered at Caltech. This page was prepared in preparation for a faculty discussion on integrated ACM ~~106b~~, AM 125b and CDS 140a.		This page collects some information about (ordinary) differential equations and dynamical systems courses offered at Caltech. This page was prepared in preparation for a faculty discussion on integrated ACM 101b, AM 125b and CDS 140a.

Murray: /* CDS 140a: */

2010-11-14T18:03:30Z

CDS 140a:

← Older revision		Revision as of 18:03, 14 November 2010
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	\|		\|

	=== CDS 140a: ===		=== CDS 140a: Introduction to Dynamics ===
	{\|		{\|
	\|- valign=top		\|- valign=top

Murray: /* Possible topics */

2010-11-14T18:02:28Z

Possible topics

← Older revision		Revision as of 18:02, 14 November 2010
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	\| Perko		\| Perko
	\| Verhulst		\| Verhulst
	{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x}}		{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}		{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x\|am=x\|perko=x}}
	{{cds140 section\|title=Jordan form\|cds=x\|perko=x\|verhulst=-}}		{{cds140 section\|title=Matrix exponential, Jordan form\|acm=x\|am=x\|cds=x\|perko=x\|verhulst=-}}
	{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}		{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}
	~~{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}~~		{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x}}		{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x\|bender=x\|am=?}}
	{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x\|bender=x}}		{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x\|bender=s\|verhulst=x\|am=x}}
	{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x\|bender=s\|verhulst=x}}
	{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x\|verhulst=-}}		{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x\|verhulst=-}}
	{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Attractors and structural stability\|cds=?\|perko=x}}		{{cds140 section\|title=Attractors and structural stability\|cds=?\|perko=x\|am=?}}
	{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x\|perko=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=?\|acm=x\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Floquet theory, parametric resonance\|perko=x\|jordan=x\|verhulst~~=x}}~~		{{cds140 section\|title=Floquet theory, parametric resonance\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	~~{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds~~=x\|~~perko=x\|verhulst~~=x}}		{{cds140 section\|title=Lagrange's equations (variational principles), energy-based stability methods\|cds=x}}
	{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}		{{cds140 section\|title=Hamiltonian dynamics\|cds=x}}
	{{cds140 section\|title=Hamiltonian dynamics~~, variational principles~~\|cds=x}}
	{{cds140 section\|title=Ergodicity}}		{{cds140 section\|title=Ergodicity}}
	{{cds140 section\|title=Boundary value problems\|acm=x}}		{{cds140 section\|title=Boundary value problems, Green functions\|acm=x\|am=x}}
	{{cds140 section\|title=Perturbation methods\|acm=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Perturbation methods\|acm=x\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Asymptotic and approximation methods\|acm=x\|verhulst=x}}		{{cds140 section\|title=Asymptotic and approximation methods\|acm=x\|verhulst=x}}
	{{cds140 section\|title=Singular perturbation theory\|jordan=?}}		{{cds140 section\|title=Singular perturbation theory\|jordan=?}}
	{{cds140 section\|title=Method of averaging\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Method of averaging\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Integral equations\|am=x}}		{{cds140 section\|title=Integral equations\|acm=x}}
	{{cds140 section\|title=Partial differential equations\|acm=?}}		{{cds140 section\|title=Partial differential equations\|acm=?}}
			{{cds140 section\|title=Numerical methods\|acm=?}}
	\|}		\|}

Murray: /* Possible topics */

2010-10-28T22:41:41Z

Possible topics

Murray: /* Possible topics */

2010-10-25T17:00:22Z

Possible topics

Murray: /* CDS 140a: */

2010-10-25T16:55:07Z

CDS 140a:

← Older revision		Revision as of 16:55, 25 October 2010
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	''' Partially overlapping courses'''		''' Partially overlapping courses'''
	* ACM ~~106b~~, AM 125b		* ACM 101b, AM 125b
	\|		\|
	'''Topics ([http://www.cds.caltech.edu/~marsden/cds140a-09/home Fall 2009]) '''		'''Topics ([http://www.cds.caltech.edu/~marsden/cds140a-09/home Fall 2009]) '''

Murray: /* ACM 101b: Methods of Applied Mathematics */

2010-10-25T16:54:17Z

ACM 101b: Methods of Applied Mathematics

← Older revision		Revision as of 16:54, 25 October 2010
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	\| width=50% \|		\| width=50% \|
	'''Catalog listing'''		'''Catalog listing'''
	Analytical methods for the formulation and solution of initial and boundary value problems for ordinary and partial differential equations. Techniques include the use of complex variables, generalized eigenfunction expansions, transform methods and applied spectral theory, linear operators, nonlinear methods, asymptotic and approximate methods, Weiner-Hopf, and integral equations. Taught concurrently with CDS 140 and AM 125. Instructors: Marsden, Murray.		<font color=blue>Analytical methods for the formulation and solution of initial and boundary value problems for ordinary and partial differential equations. Techniques include the use of complex variables, generalized eigenfunction expansions, transform methods and applied spectral theory, linear operators, nonlinear methods, asymptotic and approximate methods, Weiner-Hopf, and integral equations. </font> Taught concurrently with CDS 140 and AM 125. Instructors: Marsden, Murray.

	'''Dependent courses''':		'''Dependent courses''':

Murray: /* Possible topics */

2010-10-25T16:12:47Z

Possible topics

Murray at 03:47, 22 October 2010

2010-10-22T03:47:51Z

← Older revision		Revision as of 03:47, 22 October 2010
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	\| width=50% \|		\| width=50% \|
	'''Catalog listing'''		'''Catalog listing'''
	~~nalytical~~ methods for the formulation and solution of initial and boundary value problems for ordinary and partial differential equations. Techniques include the use of complex variables, generalized eigenfunction expansions, transform methods and applied spectral theory, linear operators, nonlinear methods, asymptotic and approximate methods, Weiner-Hopf, and integral equations. Taught concurrently with CDS 140 and AM 125. Instructors: Marsden, Murray.		Analytical methods for the formulation and solution of initial and boundary value problems for ordinary and partial differential equations. Techniques include the use of complex variables, generalized eigenfunction expansions, transform methods and applied spectral theory, linear operators, nonlinear methods, asymptotic and approximate methods, Weiner-Hopf, and integral equations. Taught concurrently with CDS 140 and AM 125. Instructors: Marsden, Murray.

	'''Dependent courses''':		'''Dependent courses''':
Line 89:		Line 89:
	\| Jordan/Smith		\| Jordan/Smith
	\| Perko		\| Perko
	{{cds140 section\|title=Existence and uniqueness of solutions}}		{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x}}
	{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)}}		{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}
	{{cds140 section\|title=~~Analytical~~ methods for ~~solving nonlinear~~ ODEs}}		{{cds140 section\|title=Jordan form\|cds=x}}
	{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc}}		{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}
	{{cds140 section\|title=Stability, Lyapunov stability}}		{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}
	{{cds140 section\|title=Stability of limit cycles, orbital stability}}		{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x}}
	{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc}}		{{cds140 section\|title=Poincare-Bendixon theory\|cds=x}}
			{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x}}
			{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x}}
			{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x}}
			{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x}}
			{{cds140 section\|title=Attractors and structural stability\|cds=?}}
			{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x}}
	{{cds140 section\|title=Floquet theory, parametric resonance}}		{{cds140 section\|title=Floquet theory, parametric resonance}}
	{{cds140 section\|title=Hamiltonian dynamics, ~~from~~ variational principles}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}
	{{cds140 section\|title=~~Invariant manifolds~~, ~~ergodicity~~}}		{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}
	{{cds140 section\|title=Boundary value problems}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}
	{{cds140 section\|title=Perturbation methods}}		{{cds140 section\|title=Ergodicity}}
			{{cds140 section\|title=Boundary value problems\|acm=x}}
			{{cds140 section\|title=Perturbation methods\|acm=x}}
			{{cds140 section\|title=Asymptotic and approximation methods\|acm=x}}
	{{cds140 section\|title=Singular perturbation theory}}		{{cds140 section\|title=Singular perturbation theory}}
			{{cds140 section\|title=Method of averaging}}
			{{cds140 section\|title=Integral equations\|am=x}}
			{{cds140 section\|title=Partial differential equations\|acm=?}}
	\|}		\|}

Murray: /* Textbooks */

2010-10-22T03:35:29Z

Textbooks

Show changes

← Older revision		Revision as of 18:02, 14 November 2010
Line 90:		Line 90:
	\| Perko		\| Perko
	\| Verhulst		\| Verhulst
	{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x}}		{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}		{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x\|am=x\|perko=x}}
	{{cds140 section\|title=Jordan form\|cds=x\|perko=x\|verhulst=-}}		{{cds140 section\|title=Matrix exponential, Jordan form\|acm=x\|am=x\|cds=x\|perko=x\|verhulst=-}}
	{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}		{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}
	~~{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}~~		{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x}}		{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x\|bender=x\|am=?}}
	{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x\|bender=x}}		{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x\|bender=s\|verhulst=x\|am=x}}
	{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x\|bender=s\|verhulst=x}}
	{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x\|verhulst=-}}		{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x\|verhulst=-}}
	{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Attractors and structural stability\|cds=?\|perko=x}}		{{cds140 section\|title=Attractors and structural stability\|cds=?\|perko=x\|am=?}}
	{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x\|perko=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=?\|acm=x\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	{{cds140 section\|title=Floquet theory, parametric resonance\|perko=x\|jordan=x\|verhulst~~=x}}~~		{{cds140 section\|title=Floquet theory, parametric resonance\|perko=x\|jordan=x\|verhulst=x\|am=x}}
	~~{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds~~=x\|~~perko=x\|verhulst~~=x}}		{{cds140 section\|title=Lagrange's equations (variational principles), energy-based stability methods\|cds=x}}
	{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}		{{cds140 section\|title=Hamiltonian dynamics\|cds=x}}
	{{cds140 section\|title=Hamiltonian dynamics~~, variational principles~~\|cds=x}}
	{{cds140 section\|title=Ergodicity}}		{{cds140 section\|title=Ergodicity}}
	{{cds140 section\|title=Boundary value problems\|acm=x}}		{{cds140 section\|title=Boundary value problems, Green functions\|acm=x\|am=x}}
	{{cds140 section\|title=Perturbation methods\|acm=x\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Perturbation methods\|acm=x\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Asymptotic and approximation methods\|acm=x\|verhulst=x}}		{{cds140 section\|title=Asymptotic and approximation methods\|acm=x\|verhulst=x}}
	{{cds140 section\|title=Singular perturbation theory\|jordan=?}}		{{cds140 section\|title=Singular perturbation theory\|jordan=?}}
	{{cds140 section\|title=Method of averaging\|jordan=x\|verhulst=x}}		{{cds140 section\|title=Method of averaging\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Integral equations\|am=x}}		{{cds140 section\|title=Integral equations\|acm=x}}
	{{cds140 section\|title=Partial differential equations\|acm=?}}		{{cds140 section\|title=Partial differential equations\|acm=?}}
			{{cds140 section\|title=Numerical methods\|acm=?}}
	\|}		\|}

← Older revision		Revision as of 03:47, 22 October 2010
Line 13:		Line 13:
	\| width=50% \|		\| width=50% \|
	'''Catalog listing'''		'''Catalog listing'''
	~~nalytical~~ methods for the formulation and solution of initial and boundary value problems for ordinary and partial differential equations. Techniques include the use of complex variables, generalized eigenfunction expansions, transform methods and applied spectral theory, linear operators, nonlinear methods, asymptotic and approximate methods, Weiner-Hopf, and integral equations. Taught concurrently with CDS 140 and AM 125. Instructors: Marsden, Murray.		Analytical methods for the formulation and solution of initial and boundary value problems for ordinary and partial differential equations. Techniques include the use of complex variables, generalized eigenfunction expansions, transform methods and applied spectral theory, linear operators, nonlinear methods, asymptotic and approximate methods, Weiner-Hopf, and integral equations. Taught concurrently with CDS 140 and AM 125. Instructors: Marsden, Murray.

	'''Dependent courses''':		'''Dependent courses''':
Line 89:		Line 89:
	\| Jordan/Smith		\| Jordan/Smith
	\| Perko		\| Perko
	{{cds140 section\|title=Existence and uniqueness of solutions}}		{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x}}
	{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)}}		{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}
	{{cds140 section\|title=~~Analytical~~ methods for ~~solving nonlinear~~ ODEs}}		{{cds140 section\|title=Jordan form\|cds=x}}
	{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc}}		{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}
	{{cds140 section\|title=Stability, Lyapunov stability}}		{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}
	{{cds140 section\|title=Stability of limit cycles, orbital stability}}		{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x}}
	{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc}}		{{cds140 section\|title=Poincare-Bendixon theory\|cds=x}}
			{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x}}
			{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x}}
			{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x}}
			{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x}}
			{{cds140 section\|title=Attractors and structural stability\|cds=?}}
			{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x}}
	{{cds140 section\|title=Floquet theory, parametric resonance}}		{{cds140 section\|title=Floquet theory, parametric resonance}}
	{{cds140 section\|title=Hamiltonian dynamics, ~~from~~ variational principles}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}
	{{cds140 section\|title=~~Invariant manifolds~~, ~~ergodicity~~}}		{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}
	{{cds140 section\|title=Boundary value problems}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}
	{{cds140 section\|title=Perturbation methods}}		{{cds140 section\|title=Ergodicity}}
			{{cds140 section\|title=Boundary value problems\|acm=x}}
			{{cds140 section\|title=Perturbation methods\|acm=x}}
			{{cds140 section\|title=Asymptotic and approximation methods\|acm=x}}
	{{cds140 section\|title=Singular perturbation theory}}		{{cds140 section\|title=Singular perturbation theory}}
			{{cds140 section\|title=Method of averaging}}
			{{cds140 section\|title=Integral equations\|am=x}}
			{{cds140 section\|title=Partial differential equations\|acm=?}}
	\|}		\|}

← Older revision		Revision as of 22:41, 28 October 2010
Line 89:		Line 89:
	\| Jordan/Smith		\| Jordan/Smith
	\| Perko		\| Perko
	{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x\|bender=x}}		\| Verhulst
			{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x}}
	{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}		{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}
	{{cds140 section\|title=Jordan form\|cds=x\|perko=x\|}}		{{cds140 section\|title=Jordan form\|cds=x\|perko=x\|verhulst=-}}
	{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}		{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}
	{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}		{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}
	{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x\|bender=x}}		{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x\|bender=x\|verhulst=x}}
	{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x\|bender=x}}		{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x\|bender=x}}
	{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x\|bender=s}}		{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x\|bender=s\|verhulst=x}}
	{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x\|verhulst=-}}
	{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Attractors and structural stability\|cds=?\|perko=x}}		{{cds140 section\|title=Attractors and structural stability\|cds=?\|perko=x}}
	{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x\|perko=x\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Floquet theory, parametric resonance\|perko=x\|jordan=x}}		{{cds140 section\|title=Floquet theory, parametric resonance\|perko=x\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x\|perko=x}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x\|perko=x\|verhulst=x}}
	{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}		{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}
	{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}
	{{cds140 section\|title=Ergodicity}}		{{cds140 section\|title=Ergodicity}}
	{{cds140 section\|title=Boundary value problems\|acm=x}}		{{cds140 section\|title=Boundary value problems\|acm=x}}
	{{cds140 section\|title=Perturbation methods\|acm=x\|jordan=x}}		{{cds140 section\|title=Perturbation methods\|acm=x\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Asymptotic and approximation methods\|acm=x}}		{{cds140 section\|title=Asymptotic and approximation methods\|acm=x\|verhulst=x}}
	{{cds140 section\|title=Singular perturbation theory\|jordan=?}}		{{cds140 section\|title=Singular perturbation theory\|jordan=?}}
	{{cds140 section\|title=Method of averaging\|jordan=x}}		{{cds140 section\|title=Method of averaging\|jordan=x\|verhulst=x}}
	{{cds140 section\|title=Integral equations\|am=x}}		{{cds140 section\|title=Integral equations\|am=x}}
	{{cds140 section\|title=Partial differential equations\|acm=?}}		{{cds140 section\|title=Partial differential equations\|acm=?}}

← Older revision		Revision as of 17:00, 25 October 2010
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	\| Perko		\| Perko
	{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x\|bender=x}}
	{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}		{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}
	{{cds140 section\|title=Jordan form\|cds=x\|perko=x}}		{{cds140 section\|title=Jordan form\|cds=x\|perko=x\|}}
	{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}		{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}
	{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}		{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}
	{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x\|bender=x}}
	{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x}}		{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x\|bender=x}}
	{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x\|bender=s}}
	{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x}}		{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x}}

← Older revision		Revision as of 16:12, 25 October 2010
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	\| Jordan/Smith		\| Jordan/Smith
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	{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x}}		{{cds140 section\|title=Existence and uniqueness of solutions\|acm=x\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}		{{cds140 section\|title=Linear ODEs, with inputs (convolution equation)\|acm=x\|cds=x}}
	{{cds140 section\|title=Jordan form\|cds=x}}		{{cds140 section\|title=Jordan form\|cds=x\|perko=x}}
	{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}		{{cds140 section\|title=Transform methods (eg, Laplace, Fourier)\|acm=x}}
	{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}		{{cds140 section\|title=Spectral theory for linear ODEs\|acm=x}}
	{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x}}		{{cds140 section\|title=Phase space diagrams, sinks, sources, saddles, limit cycles, etc\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Poincare-Bendixon theory\|cds=x}}		{{cds140 section\|title=Poincare-Bendixon theory\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x}}		{{cds140 section\|title=Analytical methods for solving nonlinear ODEs\|acm=x\|jordan=x}}
	{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x}}		{{cds140 section\|title=Stability of equilibrium points, Lyapunov stability\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x}}		{{cds140 section\|title=Invariant manifolds (stable, unstable, center)\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x}}		{{cds140 section\|title=Stability of limit cycles, orbital stability, Poincare maps\|cds=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Attractors and structural stability\|cds=?}}		{{cds140 section\|title=Attractors and structural stability\|cds=?\|perko=x}}
	{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x}}		{{cds140 section\|title=Bifurcations, including saddle node, pitchfork, Hopf, etc\|cds=x\|acm=x\|perko=x\|jordan=x}}
	{{cds140 section\|title=Floquet theory, parametric resonance}}		{{cds140 section\|title=Floquet theory, parametric resonance\|perko=x\|jordan=x}}
	{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x\|perko=x}}
	{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}		{{cds140 section\|title=Lagrange's equations, energy-based stability methods\|cds=x}}
	{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}		{{cds140 section\|title=Hamiltonian dynamics, variational principles\|cds=x}}
	{{cds140 section\|title=Ergodicity}}		{{cds140 section\|title=Ergodicity}}
	{{cds140 section\|title=Boundary value problems\|acm=x}}		{{cds140 section\|title=Boundary value problems\|acm=x}}
	{{cds140 section\|title=Perturbation methods\|acm=x}}		{{cds140 section\|title=Perturbation methods\|acm=x\|jordan=x}}
	{{cds140 section\|title=Asymptotic and approximation methods\|acm=x}}		{{cds140 section\|title=Asymptotic and approximation methods\|acm=x}}
	{{cds140 section\|title=Singular perturbation theory}}		{{cds140 section\|title=Singular perturbation theory\|jordan=?}}
	{{cds140 section\|title=Method of averaging}}		{{cds140 section\|title=Method of averaging\|jordan=x}}
	{{cds140 section\|title=Integral equations\|am=x}}		{{cds140 section\|title=Integral equations\|am=x}}
	{{cds140 section\|title=Partial differential equations\|acm=?}}		{{cds140 section\|title=Partial differential equations\|acm=?}}