【英字】MIT公开课 微分方程和MATLAB应用
OCW原地址: http://t.cn/RtqkvP6 || 自压720P，Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler，57p开始MATLAB。并不太算是专项的微分方程课程，相应的线性代数和微分方程的课程都可以很方便地找到就不重复劳动了。Prof. Gilbert Strang真的让人肃然起敬，82岁仍坚持在一线，他的线性代数和微分方程是我听过讲得最透彻的。
视频选集
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Introduction to Differential Equations and the MATLAB® ODE Suite
02:52
Overview of Differential Equations
14:03
The Calculus You Need
14:47
Response to Exponential Input
13:19
Response to Oscillating Input
15:54
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
13:06
Second Order Equations
19:20
Forced Harmonic Motion
15:32
Unforced Damped Motion
14:03
Impulse Response and Step Response
16:01
Exponential Response — Possible Resonance
12:19
Second Order Equations with Damping
13:14
Electrical Networks Voltages and Currents
16:33
Method of Undetermined Coefficients
16:31
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
10:28
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
10:31
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
22:53
The Column Space of a Matrix
12:43
Independence, Basis, and Dimension
13:19
The Big Picture of Linear Algebra
15:57
Graphs
15:26
Incidence Matrices of Graphs
19:50
Eigenvalues and Eigenvectors
19:01
Diagonalizing a Matrix
11:36
Powers of Matrices and Markov Matrices
17:53
Solving Linear Systems
15:47
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)
14:10
Boundary Conditions Replace Initial Conditions
17:03
Laplace Equation
13:17
Fourier Series
16:35
Examples of Fourier Series
13:55
Fourier Series Solution of Laplace s Equation
14:03
Heat Equation
10:48
Wave Equation
15:13
Euler, ODE1
15:22
Midpoint Method, ODE2
06:45
Classical Runge-Kutta, ODE4
09:38
Order, Naming Conventions
05:25
Estimating Error, ODE23
10:37
ODE45
06:46
Stiffness, ODE23s, ODE15s
07:14
Systems of Equations
14:16
The MATLAB ODE Suite
05:34
Tumbling Box
09:51
Predator-Prey Equations
14:17
Lorenz Attractor and Chaos
10:24
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