# Ordinary Differential Equations

1. Feb 11, 2006

### Staff: Mentor

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

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

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

Last edited: Feb 12, 2006
2. Oct 21, 2007

### Staff: Mentor

Last edited: Jul 4, 2009
3. Oct 25, 2007

### plutoisacomet

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

4. Oct 25, 2007

### sapiental

very interesting. thank you

5. Oct 30, 2007

### 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!

6. Jan 26, 2009

### jostpuur

7. Jun 28, 2009

### verbasel

8. Aug 21, 2009

### CFDFEAGURU

Last edited by a moderator: Oct 16, 2010
9. Sep 8, 2009

### Sankaku

10. Nov 24, 2012

### Staff: Mentor

http://ocw.mit.edu/18-03S06
Differential Equations
As taught in: Spring 2010

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.

Last edited by a moderator: Sep 25, 2014