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Video Lectures



Video Lectures

These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring 2003 and do not correspond precisely to the lectures taught in the Spring of 2006. Professor Mattuck has inspired and informed generations of MIT students with his engaging lectures.

The videotaping was made possible by The d'Arbeloff Fund for Excellence in MIT Education.

Note: Lecture 18, 34, and 35 are not available.


LEC #TOPICS
1The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves.
2Euler's Numerical Method for y'=f(x,y) and its Generalizations.
3Solving First-order Linear ODE's; Steady-state and Transient Solutions.
4First-order Substitution Methods: Bernouilli and Homogeneous ODE's.
5First-order Autonomous ODE's: Qualitative Methods, Applications.
6Complex Numbers and Complex Exponentials.
7First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods.
8Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models.
9Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases.
10Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations.
11Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians.
12Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's.
13Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials.
14Interpretation of the Exceptional Case: Resonance.
15Introduction to Fourier Series; Basic Formulas for Period 2(pi).
16Continuation: More General Periods; Even and Odd Functions; Periodic Extension.
17Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds.
19Introduction to the Laplace Transform; Basic Formulas.
20Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's.
21Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems.
22Using Laplace Transform to Solve ODE's with Discontinuous Inputs.
23Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.
24Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System.
25Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case).
26Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
27Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients.
28Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters.
29Matrix Exponentials; Application to Solving Systems.
30Decoupling Linear Systems with Constant Coefficients.
31Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum.
32Limit Cycles: Existence and Non-existence Criteria.
33Relation Between Non-linear Systems and First-order ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle.

 








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