Course Information

Course

Code:	18.03
Subject:	Mathematics
Topic:	Differential Equations
Views:	126,022

Educator

Name:	Massachusetts Institute of Technology (MIT)
Type:	University

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Instructor

Name

Arthur Mattuck

Differential Equations

Video Lectures

Displaying all 32 video lectures.

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