Ordinary Differential Equations

[Astronuc]

http://www.math.ohio-state.edu/~gerlach/math/BVtypset/BVtypset.html
LINEAR MATHEMATICS IN INFINITE DIMENSIONS
Signals, Boundary Value Problems
and Special Functions
U. H. Gerlach

Date: March 2004

---------------------------------

Differential Equations (Math 3401/3301)
http://tutorial.math.lamar.edu/AllBrowsers/3401/3401.asp

----------------------------------

Computational Science Education Project - ODE's
http://csep1.phy.ornl.gov/CSEP/ODE/ODE.html

 

[Astronuc]

The second link above is old and one will get redirected. Here is the complete document on Differential Equations.

http://tutorial.math.lamar.edu/pdf/DE/DE_Complete.pdf

or on-line: http://tutorial.math.lamar.edu/classes/de/de.aspx

 

[plutoisacomet]

Great link and thanks for the time you put into find them.

 

[sapiental]

very interesting. thank you

 

[Sarliz]

Frobenius series

First off, this is a great link! Thanks for posting!

Second, I'm working on Power Series Methods, Frobenius series, etc., and I'm looking for any help/links on that. I didn't see any on Paul's site. Might be hidden or is there another site that would cover these topics?

Thanks!

 

[jostpuur]

Ordinary Differential Equations and Dynamical Systems

I noticed this link in the bottom of one Wikipedia page about Floquet's theorem:

http://www.mat.univie.ac.at/~gerald/ftp/book-ode/

 

[verbasel]

http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/CourseHome/index.htm

It's the MIT course website for ODE.

The link for the Honours ODE course is this one:
http://ocw.mit.edu/OcwWeb/Mathematics/18-034Spring-2007/CourseHome/index.htm

The MIT http://ocw.mit.edu/OcwWeb/web/courses/courses/index.htm" is a great resource for free online course materials for ALL the undergrad courses they offer.

 

[CFDFEAGURU]

Ordinay Differential Equations

EDIT: this post merged from separate thread by Redbelly98

Here is a link to Paul Dawkins online notes.

http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

Thanks
Matt

 

[Sankaku]

Just want to post these here:

Very slick videos on DE's (thanks to Keesjan)
http://www.math.armstrong.edu/faculty/hollis/

 

[Astronuc]

http://ocw.mit.edu/18-03S06
Differential Equations
As taught in: Spring 2010
http://ocw.mit.edu/courses/mathemat...ations-spring-2010/download-course-materials/

Differential Equations (2006)
http://dspace.mit.edu/bitstream/handle/1721.1/70961/18-03-spring-2006/contents/index.htm?sequence=4
Professor Arthur Mattuck

Lec 1 | MIT 18.03 Differential Equations, Spring 2006
The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves.


Lec 2 | MIT 18.03 Differential Equations, Spring 2006
Euler's Numerical Method for y'=f(x,y) and its Generalizations


Lec 3 | MIT 18.03 Differential Equations, Spring 2006
Solving First-order Linear ODE's; Steady-state and Transient Solutions


Lec 4 | MIT 18.03 Differential Equations, Spring 2006
First-order Substitution Methods: Bernouilli and Homogeneous ODE's


Lec 5 | MIT 18.03 Differential Equations, Spring 2006
First-order Autonomous ODE's: Qualitative Methods, Applications


Lec 6 | MIT 18.03 Differential Equations, Spring 2006
Complex Numbers and Complex Exponentials


Lec 7 | MIT 18.03 Differential Equations, Spring 2006
First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods.


Lec 8 | MIT 18.03 Differential Equations, Spring 2006
Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models.


Lec 9 | MIT 18.03 Differential Equations, Spring 2006
Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases


Lec 10 | MIT 18.03 Differential Equations, Spring 2006
Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations.


Lec 11 | MIT 18.03 Differential Equations, Spring 2006
Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians.


Lec 12 | MIT 18.03 Differential Equations, Spring 2006
Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's.


Lec 13 | MIT 18.03 Differential Equations, Spring 2006
Finding Particular Solution to Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials.


Lec 14 | MIT 18.03 Differential Equations, Spring 2006
Interpretation of the Exceptional Case: Resonance


Lec 15 | MIT 18.03 Differential Equations, Spring 2006
Introduction to Fourier Series; Basic Formulas for Period 2(pi).


Lec 16 | MIT 18.03 Differential Equations, Spring 2006
Continuation: More General Periods; Even and Odd Functions; Periodic Extension.


Lec 17 | MIT 18.03 Differential Equations, Spring 2006
Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds.



Lec 19 | MIT 18.03 Differential Equations, Spring 2006
Introduction to the Laplace Transform; Basic Formulas.


Lec 20 | MIT 18.03 Differential Equations, Spring 2006
Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's


Lec 21 | MIT 18.03 Differential Equations, Spring 2006
Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems.


Lec 22 | MIT 18.03 Differential Equations, Spring 2006
Using Laplace Transform to Solve ODE's with Discontinuous Inputs


Lec 23 | MIT 18.03 Differential Equations, Spring 2006
Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.


Lec 24 | MIT 18.03 Differential Equations, Spring 2006
Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System.


Lec 25 | MIT 18.03 Differential Equations, Spring 2006
Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case).


Lec 26 | MIT 18.03 Differential Equations, Spring 2006
Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.


Lec 27 | MIT 18.03 Differential Equations, Spring 2006
Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients (some review of linear algebra, characteristic equation and eigenvalues, and discussion of stability)

http://www.math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/index.html

Lec 28 | MIT 18.03 Differential Equations, Spring 2006
Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters.


Lec 29 | MIT 18.03 Differential Equations, Spring 2006
Matrix Exponentials; Application to Solving Systems


Lec 30 | MIT 18.03 Differential Equations, Spring 2006
Decoupling Linear Systems with Constant Coefficients


Lec 31 | MIT 18.03 Differential Equations, Spring 2006
Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum.


Lec 32 | MIT 18.03 Differential Equations, Spring 2006
Limit Cycles: Existence and Non-existence Criteria.


Lec 33 | MIT 18.03 Differential Equations, Spring 2006
Relation Between Non-linear Systems and First-order ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle.