MIT Learn Differential Equations
4.0
(2)
20 learners
What you'll learn
This course includes
- 16.3 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 68 lessons • 16.3 hours of video
MIT Learn Differential Equations
68 lessons
• 16.3 hours
MIT Learn Differential Equations
68 lessons
• 16.3 hours
- Gilbert and Cleve Introduction02:53
- Overview of Differential Equations14:04
- The Calculus You Need14:47
- Response to Exponential Input13:20
- Response to Oscillating Input15:55
- Solution for Any Input13:59
- Step Function and Delta Function15:41
- Response to Complex Exponential12:51
- Integrating Factor for Constant Rate13:47
- Integrating Factor for a Varying Rate11:23
- The Logistic Equation13:27
- The Stability and Instability of Steady States21:15
- Separable Equations13:07
- Second Order Equations19:20
- Forced Harmonic Motion15:32
- Unforced Damped Motion14:04
- Impulse Response and Step Response16:01
- Exponential Response – Possible Resonance12:20
- Second Order Equations with Damping13:14
- Electrical Networks: Voltages and Currents16:33
- Method of Undetermined Coefficients16:32
- An Example of Undetermined Coefficients15:49
- Variation of Parameters19:22
- Laplace Transform: First Order Equation22:38
- Laplace Transform: Second Order Equation16:31
- Laplace Transforms and Convolution10:29
- Pictures of Solutions21:01
- Phase Plane Pictures: Source, Sink, Saddle18:26
- Phase Plane Pictures: Spirals and Centers13:46
- Two First Order Equations: Stability10:32
- Linearization at Critical Points15:08
- Linearization of two nonlinear equations21:41
- Eigenvalues and Stability: 2 by 2 Matrix, A19:30
- The Tumbling Box in 3-D22:54
- The Column Space of a Matrix12:44
- Independence, Basis, and Dimension13:20
- The Big Picture of Linear Algebra15:57
- Graphs15:27
- Incidence Matrices of Graphs19:51
- Eigenvalues and Eigenvectors19:01
- Diagonalizing a Matrix11:37
- Powers of Matrices and Markov Matrices17:54
- Solving Linear Systems15:48
- The Matrix Exponential15:32
- Similar Matrices14:51
- Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors15:55
- Second Order Systems16:50
- Positive Definite Matrices21:41
- Singular Value Decomposition (the SVD)14:11
- Boundary Conditions Replace Initial Conditions17:03
- Laplace Equation13:17
- Fourier Series16:36
- Examples of Fourier Series13:56
- Fourier Series Solution of Laplace's Equation14:04
- Heat Equation10:48
- Wave Equation15:14
- Euler, ODE115:22
- Midpoint Method, ODE206:46
- Classical Runge-Kutta, ODE409:38
- Order, Naming Conventions05:26
- Estimating Error, ODE2310:37
- ODE4506:47
- Stiffness, ODE23s, ODE15s07:15
- Systems of Equations14:17
- The MATLAB ODE Suite05:35
- Tumbling Box09:52
- Predator-Prey Equations14:17
- Lorenz Attractor and Chaos10:25
