Note the typed lecture notes on the MIT web site do not always correspond numerically with the corresponding lecture. The videos below are all relavant to the meterial in the current syllabus of sm212.
Lecture 1: The Geometrical View of y'=f(x,y): Direction Fields
lecture1.txt ,
mpeg4 video (~100M)
Lecture 2:
Euler's Numerical Method for y'=f(x,y) and its Generalizations.
lecture2.txt ,
mpeg4 video (~100M)
Lecture 3:
Solving First-order Linear ODE's; Steady-state and Transient Solutions.
lecture3.txt ,
mpeg4 video (~100M)
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 ,
mpeg4 video (~100M)
Lecture 6: Complex Numbers and Complex Exponentials.
lecture6.txt ,
mpeg4 video (~100M - optional)
Lecture 7: First-order Linear with Constant Coefficients:
Behavior of Solutions, Use of Complex Methods.
lecture7.txt ,
mpeg4 video (~100M)
Lecture 8: Applications to Temperature, Mixing, RC-circuit, Decay,
and Growth Models.
lecture8.txt ,
mpeg4 video (~100M)
Lecture 9: Solving Second-order Linear ODE's with Constant
Coefficients: The Three Cases.
lecture9.txt ,
mpeg4 video (~100M)
Lecture 10: Complex Characteristic Roots; Undamped and Damped Oscillations.
lecture10, mpeg4 video (~100M)
Lecture 11: Theory of General Second-order Linear Homogeneous
ODE's: Superposition, Uniqueness, Wronskians.
lecture11, mpeg4 video (~100M)
Lecture 12: General Theory for Inhomogeneous ODE's. Stability
Criteria for the Constant-coefficient ODE's.
lecture12, mpeg4 video (~100M)
lecture13.txt
lecture16.txt
lecture17.txt
lecture18.txt
Lecture 19:
Introduction to the Laplace Transform; Basic Formulas.
mpeg4 video (~100M)
lecture20.txt
Lecture 20:
Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's.
mpeg4 video (~100M)
mit-laplace-trans-lecture25.txt
(convolution)
Lecture 21:
Convolution Formula: Proof, Connection with Laplace Transform, Application to
Physical Problems.
mpeg4 video (~100M)
Lecture 22:
Using Laplace Transform to Solve ODE's with Discontinuous Inputs.
mpeg4 video (~100M)
Lecture 23:
Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.
mpeg4 video (~100M)
lecture23.txt
Lecture 24:
Introduction to First-order Systems of ODE's; Solution by Elimination,
Geometric Interpretation of a System.
mpeg4 video (~100M) lecture24.txt
Lecture 25:
Homogeneous Linear Systems with Constant Coefficients: Solution via
Matrix Eigenvalues (Real and Distinct Case).
mpeg4 video (~100M)
lecture25.txt
Lecture 26:
Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
mpeg4 video (~100M)
Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear
System with Constant Coefficients.
mpeg4 video (~110M)
Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory,
Fundamental Matrix, Variation of Parameters.
mpeg4 video (~105M)
Lecture 29: Matrix Exponentials; Application to Solving Systems of DEs.
mpeg4 video (~97M)
lecture29.txt
Lecture 30: Decoupling Linear Systems with Constant Coefficients.
mpeg4 video (~112M)
lecture31.txt
lecture-topics.txt
lecture-notes.txt
syllabus.txt
recitation-topics.txt