Symmetric matrices have n perpendicular eigenvectors and n real eigenvalues.

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

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.