## 2016-06-23

### Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 at MIT

# Click the up-left corner for the playlist of the 68 videos

source: MIT OpenCourseWare     2016年5月6日/上次更新：2016年5月23日
MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: http://ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang, Cleve Moler
Gilbert Strang and Cleve Moler provide an overview to their in-depth video series about differential equations and the MATLAB® ODE suite.
More courses at http://ocw.mit.edu

Introduction to Differential Equations and the MATLAB® ODE Suite 2:53
Overview of Differential Equations 14:04
The Calculus You Need 14:47
Response to Exponential Input 13:20
Response to Oscillating Input 15:55
Solution for Any Input  13:59
Step Function and Delta Function 15:41
Response to Complex Exponential 12:51
Integrating Factor for Constant Rate 13:47
Integrating Factor for a Varying Rate 11:23
The Logistic Equation 13:27
The Stability and Instability of Steady States 21:15
Separable Equations 13:07
Second Order Equations 19:20
Forced Harmonic Motion 15:32
Unforced Damped Motion 14:04
Impulse Response and Step Response 16:02
Exponential Response — Possible Resonance 12:20
Second Order Equations with Damping 13:14
Electrical Networks: Voltages and Currents 16:33
Method of Undetermined Coefficients 16:32
An Example of Undetermined Coefficients 15:49
Variation of Parameters 19:22
Laplace Transform: First Order Equation 22:38
Laplace Transform: Second Order Equation 16:31
Laplace Transforms and Convolution 10:29
Pictures of Solutions 21:01
Phase Plane Pictures: Source, Sink, Saddle 18:26
Phase Plane Pictures: Spirals and Centers 13:46
Two First Order Equations: Stability 10:32
Linearization at Critical Points 15:08
Linearization of Two Nonlinear Equations 21:41
Eigenvalues and Stability: 2 by 2 Matrix, A 19:30
The Tumbling Box in 3-D 22:54
The Column Space of a Matrix 12:44
Independence, Basis, and Dimension 13:20
The Big Picture of Linear Algebra 15:57
Graphs 15:27
Incidence Matrices of Graphs 19:51
Eigenvalues and Eigenvectors 19:01
Diagonalizing a Matrix 11:37
Powers of Matrices and Markov Matrices 17:54
Solving Linear Systems 15:48
The Matrix Exponential 15:32
Similar Matrices 14:51
Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors 15:55
Second Order Systems 16:50
Positive Definite Matrices 21:41
Singular Value Decomposition (the SVD) 14:11
Boundary Conditions Replace Initial Conditions 17:03
Laplace Equation 13:17
Fourier Series 16:36
Examples of Fourier Series 13:56
Fourier Series Solution of Laplace's Equation 14:04
Heat Equation 10:48
Wave Equation 15:14
Euler, ODE1 15:22
Midpoint Method, ODE2 6:46
Classical Runge-Kutta, ODE4 9:38
Order, Naming Conventions 5:26
Estimating Error, ODE23 10:37
ODE45 6:47
Stiffness, ODE23s, ODE15s 7:15
Systems of Equations 14:17
The MATLAB ODE Suite 5:35
Tumbling Box 9:52
Predator-Prey Equations 14:17
Lorenz Attractor and Chaos 10:25