# Learn Differential Equations: Tutorials with Gilbert Strang and Cleve Moler

### Course Description

Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler 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.

Cleve Moler, founder and chief mathematician at MathWorks, and Gilbert Strang, professor and mathematician at Massachusetts Institute of Technology, provide an overview to their in-depth video series about differential equations and the MATLAB® ODE suite.

Differential equations and linear algebra are two crucial subjects in science and engineering. Gilbert Strang's video series develops those subjects both separately and together and supplements Gil Strang's textbook on this subject. Cleve Moler introduces computation for differential equations and explains the MATLAB ODE suite and its mathematical background. Cleve Moler's video series starts with Euler method and builds up to Runge Kutta and includes hands-on MATLAB exercises.

Gilbert Strang, and Cleve Moler. RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler. Fall 2015. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
Prof. Gilbert Strang and Cleve Moler
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### Video Lectures & Study Materials

Visit the official course website for more study materials: https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/

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