Lecture 1-The Geometrical View of : Direction Fields, Integral Curves.

Lecture 2-Euler’s Numerical Method for and its Generalizations.

Lecture 3-Solving First-order Linear ODE’s; Steady-state and Transient Solutions.

Lecture 4-First-order Substitution Methods: Bernouilli and Homogeneous ODE’s.

Lecture 5-First-order Autonomous ODE’s: Qualitative Methods, Applications.

Lecture 6-Complex Numbers and Complex Exponentials.

Lecture 7-First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Metho

Lecture 8-Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models.

Lecture 9-Solving Second-order Linear ODE’s with Constant Coefficients: The Three Cases

Lecture 10-Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations.

Lecture 11-Theory of General Second-order Linear Homogeneous ODE’s: Superposition, Uniqueness, Wronskians.

Lecture 12-Continuation: General Theory for Inhomogeneous ODE’s. Stability Criteria for the Constant-coefficient ODE’s.

Lecture 13-Finding Particular Sto Inhomogeneous ODE’s: Operator and Solution Formulas Involving Exponentials.

Lecture 14-Interpretation of the Exceptional Case: Resonance.

Lecture 15-Introduction to Fourier Series; Basic Formulas for Period .

Lecture 16-Continuation: More General Periods; Even and Odd Functions; Periodic Extension.

Lecture 17-Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds.

Lecture 18-missing !!!

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

Lecture 24-Introduction to First-order Systems of ODE’s; Solution by Elimination, Geometric Interpretation of a System.

Lecture 25-Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case).

Lecture 26-Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.

Lecture 27-Sketching Solutions of 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.

Lecture 30-Decoupling Linear Systems with Constant Coefficients.

Lecture 31-Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum.

Lecture 32-Limit Cycles: Existence and Non-existence Criteria.

Lecture 33-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.

Home » Uncategorized » Lectures on Differential Equations, MIT-Spring 2006, Prof. Arthur Mattuck

# Lectures on Differential Equations, MIT-Spring 2006, Prof. Arthur Mattuck

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