Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler | Mathematics | MIT OpenCourseWare

Lecture Videos

An Example of Undetermined Coefficients

Boundary Conditions Replace Initial Conditions

Diagonalizing a Matrix

Eigenvalues and Eigenvectors

Electrical Networks: Voltages and Currents

Examples of Fourier Series

Exponential Response – Possible Resonance

Forced Harmonic Motion

Fourier Series

Fourier Series Solution of Laplace's Equation

Gilbert and Cleve Introduction

Graphs

Heat Equation

Impulse Response and Step Response

Incidence Matrices of Graphs

Independence, Basis, and Dimension

Integrating Factor for a Varying Rate

Integrating Factor for Constant Rate

Laplace Equation

Laplace Transform: First Order Equation

Laplace Transform: Second Order Equation

Laplace Transforms and Convolution

Linearization at Critical Points

Linearization of two nonlinear equations

Lorenz Attractor and Chaos

Method of Undetermined Coefficients

Order, Naming Conventions

Overview of Differential Equations

Phase Plane Pictures: Source, Sink, Saddle

Phase Plane Pictures: Spirals and Centers

Pictures of Solutions

Positive Definite Matrices

Powers of Matrices and Markov Matrices

Predator-Prey Equations

Response to Complex Exponential

Response to Exponential Input

Response to Oscillating Input

Second Order Equations

Second Order Equations with Damping

Second Order Systems

Separable Equations

Similar Matrices

Singular Value Decomposition (the SVD)

Solution for Any Input

Solving Linear Systems

Step Function and Delta Function

Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors

Systems of Equations

The Big Picture of Linear Algebra

The Calculus You Need

The Column Space of a Matrix

The Logistic Equation

The MATLAB ODE Suite

The Matrix Exponential

The Stability and Instability of Steady States

Tumbling Box

Two First Order Equations: Stability

Unforced Damped Motion

Variation of Parameters

Wave Equation

Euler, ODE1

Eigenvalues and Stability: 2 by 2 Matrix, A

Midpoint Method, ODE2

The Tumbling Box in 3-D

Classical Runge-Kutta, ODE4

Estimating Error, ODE23

Stiffness, ODE23s, ODE15s

ODE45

Course Info

Instructors

Departments

Mathematics

As Taught In

Fall 2015

Level

Undergraduate

Topics

Learning Resource Types

Lecture Videos

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