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Ordinary Differential Equations

  1. Feb 11, 2006 #1

    Astronuc

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    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

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

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

    Astronuc

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    Staff: Mentor

    Last edited: Jul 4, 2009
  4. Oct 25, 2007 #3
    Great link and thanks for the time you put in to find them.
     
  5. Oct 25, 2007 #4
    very interesting. thank you
     
  6. Oct 30, 2007 #5
    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!
     
  7. Jan 26, 2009 #6
  8. Jun 28, 2009 #7
  9. Aug 21, 2009 #8
    Last edited by a moderator: Oct 16, 2010
  10. Sep 8, 2009 #9
  11. Nov 24, 2012 #10

    Astronuc

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    Staff: Mentor

    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.
     
    Last edited by a moderator: Sep 25, 2014
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