# 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 ODEs lecture13.txt

Lecture 19: Introduction to the Laplace Transform; Basic Formulas.

lecture20.txt

Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's.

mit-laplace-trans-lecture25.txt (convolution)

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.