Differential equations MIT courseware
These videos from http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/VideoLectures/index.htm are for the benefit of my SM212 students.
Note the typed lecture notes on the MIT web site do not always correspond numerically with the corresponding lecture. The videos below are all relevant to the material in the current syllabus of SM212.
Lecture 1: The Geometrical View of y'=f(x,y): Direction Fields lecture1.txt
Lecture 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations. lecture2.txt
Lecture 3: Solving First-order Linear ODE's; Steady-state and Transient Solutions. lecture3.txt
Lecture 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's. lecture4.txt optional
Lecture 5: First-order Autonomous ODE's: Qualitative Methods, Applications. lecture5.txt
Lecture 6: Complex Numbers and Complex Exponentials. lecture6.txt ( optional)
Lecture 7: First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods. lecture7.txt
Lecture 8: Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models. lecture8.txt
Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases. lecture9.txt
Lecture 10: Complex Characteristic Roots; Undamped and Damped Oscillations. lecture10
Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians. lecture11
Lecture 12: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's. lecture12
Lecture 13: Finding Particular Solutions to Inhomogeneous ODEslecture13.txt
Lecture 19: Introduction to the Laplace Transform; Basic Formulas.
Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's.
Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems.
Lecture 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs.
Lecture 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.lecture23.txt
Lecture 24: Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System. lecture24.txt
Lecture 25: Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case) lecture25.txt
Lecture 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients.
Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters.
Lecture 29: Matrix Exponentials; Application to Solving Systems of DEs. lecture29.txt
Lecture 30: Decoupling Linear Systems with Constant Coefficients.