Ordinary Differential Equations

Astronuc

http://www.math.ohio-state.edu/~gerl.../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/AllBr.../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 in to find them.

sapiental

very interesting. thank you

Sarliz

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

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/Mathematic...Home/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/Mathematic...Home/index.htm

The MIT OpenCourseWare webpage is a great resource for free online course materials for ALL the undergrad courses they offer.

CFDFEAGURU

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/mathemati...rse-materials/

Differential Equations (2006)
http://dspace.mit.edu/bitstream/hand...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.
http://www.youtube.com/watch?v=XDhJ8lVGbl8

Lec 2 | MIT 18.03 Differential Equations, Spring 2006
Euler's Numerical Method for y'=f(x,y) and its Generalizations
http://www.youtube.com/watch?v=LbKKzMag5Rc

Lec 3 | MIT 18.03 Differential Equations, Spring 2006
Solving First-order Linear ODE's; Steady-state and Transient Solutions
http://www.youtube.com/watch?v=tVzaX9u6YAE

Lec 4 | MIT 18.03 Differential Equations, Spring 2006
First-order Substitution Methods: Bernouilli and Homogeneous ODE's
http://www.youtube.com/watch?v=WBJ_iXudb-s

Lec 5 | MIT 18.03 Differential Equations, Spring 2006
First-order Autonomous ODE's: Qualitative Methods, Applications
http://www.youtube.com/watch?v=te6Mplq3DCU

Lec 6 | MIT 18.03 Differential Equations, Spring 2006
Complex Numbers and Complex Exponentials
http://www.youtube.com/watch?v=EQJBp6Ym-6A

Lec 7 | MIT 18.03 Differential Equations, Spring 2006
First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods.
http://www.youtube.com/watch?v=SioXozu-Loo

Lec 8 | MIT 18.03 Differential Equations, Spring 2006
Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models.
http://www.youtube.com/watch?v=MdzfsfBNJIw

Lec 9 | MIT 18.03 Differential Equations, Spring 2006
Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases
http://www.youtube.com/watch?v=vP-oRQqmeg4

Lec 10 | MIT 18.03 Differential Equations, Spring 2006
Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations.
http://www.youtube.com/watch?v=YQ7HEE8-OfA

Lec 11 | MIT 18.03 Differential Equations, Spring 2006
Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians.
http://www.youtube.com/watch?v=rZ3-nFV6l8w

Lec 12 | MIT 18.03 Differential Equations, Spring 2006
Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's.
http://www.youtube.com/watch?v=eyNm7XGJr4s

Lec 13 | MIT 18.03 Differential Equations, Spring 2006
Finding Particular Solution to Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials.
http://www.youtube.com/watch?v=9KbpbBMThTE

Lec 14 | MIT 18.03 Differential Equations, Spring 2006
Interpretation of the Exceptional Case: Resonance
http://www.youtube.com/watch?v=Y9_zrupnz0Q

Lec 15 | MIT 18.03 Differential Equations, Spring 2006
Introduction to Fourier Series; Basic Formulas for Period 2(pi).
http://www.youtube.com/watch?v=EWWw0jryj1A

Lec 16 | MIT 18.03 Differential Equations, Spring 2006
Continuation: More General Periods; Even and Odd Functions; Periodic Extension.
http://www.youtube.com/watch?v=xWa5_OXI6VM

Lec 17 | MIT 18.03 Differential Equations, Spring 2006
Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds.
http://www.youtube.com/watch?v=yD0_EQLxHcw


Lec 19 | MIT 18.03 Differential Equations, Spring 2006
Introduction to the Laplace Transform; Basic Formulas.
http://www.youtube.com/watch?v=sZ2qulI6GEk

Lec 20 | MIT 18.03 Differential Equations, Spring 2006
Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's
http://www.youtube.com/watch?v=qZHseRxAWZ8

Lec 21 | MIT 18.03 Differential Equations, Spring 2006
Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems.
http://www.youtube.com/watch?v=3ejfkMHr_DE

Lec 22 | MIT 18.03 Differential Equations, Spring 2006
Using Laplace Transform to Solve ODE's with Discontinuous Inputs
http://www.youtube.com/watch?v=_YVcjNmjHik

Lec 23 | MIT 18.03 Differential Equations, Spring 2006
Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.
http://www.youtube.com/watch?v=peYvLk_HZdw

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.
http://www.youtube.com/watch?v=MCrDzhpu3-s

Lec 25 | MIT 18.03 Differential Equations, Spring 2006
Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case).
http://www.youtube.com/watch?v=heBvViSi9xQ

Lec 26 | MIT 18.03 Differential Equations, Spring 2006
Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
http://www.youtube.com/watch?v=hEtWqTPPXuc

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.youtube.com/watch?v=e3FfmXtkppM
http://www.math.harvard.edu/archive/...ces/index.html

Lec 28 | MIT 18.03 Differential Equations, Spring 2006
Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters.
http://www.youtube.com/watch?v=2SuTN8rpe4I

Lec 29 | MIT 18.03 Differential Equations, Spring 2006
Matrix Exponentials; Application to Solving Systems
http://www.youtube.com/watch?v=zreI4HllD80

Lec 30 | MIT 18.03 Differential Equations, Spring 2006
Decoupling Linear Systems with Constant Coefficients
http://www.youtube.com/watch?v=uNOyxQwIV8o

Lec 31 | MIT 18.03 Differential Equations, Spring 2006
Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum.
http://www.youtube.com/watch?v=UJG0f0BSX14

Lec 32 | MIT 18.03 Differential Equations, Spring 2006
Limit Cycles: Existence and Non-existence Criteria.
http://www.youtube.com/watch?v=z-meBrqcy_I

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.
http://www.youtube.com/watch?v=kRR9EVzr4lc