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MIT OpenCourseWare

Learn Differential Equations

This is an in-depth series of videos about differential equations and the MATLAB ODE suite. These videos are suitable for students and life-long learners to enjoy. (from ocw.mit.edu )

Instructor

Prof. Gilbert Strang and Dr. Cleve Moler.

Mathematics

2016

Lecture 01 - Overview of Differential Equations

Lecture 02 - The Calculus You Need

Lecture 03 - Response to Exponential Input

Lecture 04 - Response to Oscillating Input

Lecture 05 - Solution for Any Input

Lecture 06 - Step Function and Delta Function

Lecture 07 - Response to Complex Exponential

Lecture 08 - Integrating Factor for Constant Rate

Lecture 09 - Integrating Factor for a Varying Rate

Lecture 10 - The Logistic Equation

Lecture 11 - The Stability and Instability of Steady States

Lecture 12 - Separable Equations

Lecture 13 - Second Order Equations

Lecture 14 - Forced Harmonic Motion

Lecture 15 - Unforced Damped Motion

Lecture 16 - Impulse Response and Step Response

Lecture 17 - Exponential Response ? Possible Resonance

Lecture 18 - Second Order Equations with Damping

Lecture 19 - Electrical Networks: Voltages and Currents

Lecture 20 - Method of Undetermined Coefficients

Lecture 21 - An Example of Undetermined Coefficients

Lecture 22 - Variation of Parameters

Lecture 23 - Laplace Transform: First Order Equation

Lecture 24 - Laplace Transform: Second Order Equation

Lecture 25 - Laplace Transforms and Convolution

Lecture 26 - Pictures of Solutions

Lecture 27 - Phase Plane Pictures: Source, Sink, Saddle

Lecture 28 - Phase Plane Pictures: Spirals and Centers

Lecture 29 - Two First Order Equations: Stability

Lecture 30 - Linearization at Critical Points

Lecture 31 - Linearization of Two Nonlinear Equations

Lecture 32 - Eigenvalues and Stability: 2 by 2 Matrix, A

Lecture 33 - The Tumbling Box in 3-D

Lecture 34 - The Column Space of a Matrix

Lecture 35 - Independence, Basis, and Dimension

Lecture 36 - The Big Picture of Linear Algebra

Lecture 37 - Graphs

Lecture 38 - Incidence Matrices of Graphs

Lecture 39 - Eigenvalues and Eigenvectors

Lecture 40 - Diagonalizing a Matrix

Lecture 41 - Powers of Matrices and Markov Matrices

Lecture 42 - Solving Linear Systems

Lecture 43 - The Matrix Exponential

Lecture 44 - Similar Matrices

Lecture 45 - Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors

Lecture 46 - Second Order Systems

Lecture 47 - Positive Definite Matrices

Lecture 48 - Singular Value Decomposition (the SVD)

Lecture 49 - Boundary Conditions Replace Initial Conditions

Lecture 50 - Laplace Equation

Lecture 51 - Fourier Series

Lecture 52 - Examples of Fourier Series

Lecture 53 - Fourier Series Solution of Laplace's Equation

Lecture 54 - Heat Equation

Lecture 55 - Wave Equation