Differential Equations & Linear Algebra
MIT 18.03 — Gilbert Strang & Cleve Moler
68 video lectures covering first-order ODEs, second-order equations, Laplace transforms, systems and phase planes, linear algebra essentials (eigenvalues, SVD, matrix exponential), partial differential equations (Fourier series, heat & wave equations), and numerical methods with MATLAB.
68
Video Lectures
7
Sections
MIT
OpenCourseWare
Free
Open Access
Introduction & First Order Equations
0. Gilbert Strang & Cleve Moler Introduction
1. Overview of Differential Equations
2. The Calculus You Need
3. Response to Exponential Input
4. Response to Oscillating Input
5. Solution for Any Input
6. Step Function and Delta Function
7. Response to Complex Exponential
8. Integrating Factor for Constant Rate
9. Integrating Factor for a Varying Rate
10. The Logistic Equation
11. Stability and Instability of Steady States
12. Separable Equations
Second Order Equations
13. Second Order Equations
14. Forced Harmonic Motion
15. Unforced Damped Motion
16. Impulse Response and Step Response
17. Exponential Response – Possible Resonance
18. Second Order Equations with Damping
19. Electrical Networks: Voltages and Currents
20. Method of Undetermined Coefficients
21. An Example of Undetermined Coefficients
22. Variation of Parameters
Laplace Transforms
23. Laplace Transform: First Order Equation
24. Laplace Transform: Second Order Equation
25. Laplace Transforms and Convolution
Systems of Equations & Phase Plane
26. Pictures of Solutions
27. Phase Plane Pictures: Source, Sink, Saddle
28. Phase Plane Pictures: Spirals and Centers
29. Two First Order Equations: Stability
30. Linearization at Critical Points
31. Linearization of Two Nonlinear Equations
32. Eigenvalues and Stability: 2×2 Matrix A
33. The Tumbling Box in 3-D
Linear Algebra Essentials
34. The Column Space of a Matrix
35. Independence, Basis, and Dimension
36. The Big Picture of Linear Algebra
37. Graphs
38. Incidence Matrices of Graphs
39. Eigenvalues and Eigenvectors
40. Diagonalizing a Matrix
41. Powers of Matrices and Markov Matrices
42. Solving Linear Systems
43. The Matrix Exponential
44. Similar Matrices
45. Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors
46. Second Order Systems
47. Positive Definite Matrices
48. Singular Value Decomposition (SVD)
Partial Differential Equations
49. Boundary Conditions Replace Initial Conditions
50. Laplace Equation
51. Fourier Series
52. Examples of Fourier Series
53. Fourier Series Solution of Laplace’s Equation
54. Heat Equation
55. Wave Equation
Numerical Methods (MATLAB)
56. Euler Method (ODE1)
57. Midpoint Method (ODE2)
58. Classical Runge-Kutta (ODE4)
59. Order, Naming Conventions
60. Estimating Error (ODE23)
61. ODE45
62. Stiffness (ODE23s, ODE15s)
63. Systems of Equations
64. The MATLAB ODE Suite
65. Tumbling Box
66. Predator-Prey Equations
67. Lorenz Attractor and Chaos
Laplace Transforms — a second treatment (12 lectures)
Dr. Trefor Bazett works through the Laplace transform in detail: existence and inverses, transforms of derivatives, convolution, discontinuous and periodic forcing, and the Dirac delta. Full playlist.
Intro to the Laplace Transform & Three Examples
3 Properties of Laplace Transforms: Linearity, Existence, and Inverses
The Laplace Transform of Derivatives and Integrals
Using Laplace Transforms to solve Differential Equations ***full example***
Translation and Inverse Laplace Transforms
Inverse Laplace Transform Example using Partial Fractions
How to use Laplace Transform to solve Differential Equations ** Full Example **
The Convolution of Two Functions | Definition & Properties
Laplace Transform and Piecewise or Discontinuous Functions
Periodic Functions and the Laplace Transform
The Dirac Delta 'Function': How to model an impulse or infinite spike
Solving ODEs with Delta functions using Laplace Transforms