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Differential Equations and Dynamical Systems

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2025-07-15 11:05:19
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https://www.youtube.com/watch?v=H0Zbg_CqMCs&list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA&index=7&ab_channel=SteveBrunton
数学
第九師團盧泰愚 发消息
Truth is ever to be found in simplicity.
视频选集
（40/49）
1. Overview
29:31
2. Calculus Review: The Derivative
26:30
3. Gentle Introduction to Modeling with Matrices and Vectors
40:56
4. The Simplest Ordinary Differential Equation (ODE) & Its Exponential Solution
39:17
5. Solving Differential Equations with Power Series
17:04
6. Taylor Series & Power Series Made Easy
28:55
7. Taylor Series of the Exponential Function & Euler's Formula
10:14
8. Second-Order Ordinary Differential Equations
37:03
9. Example of Second-Order ODE: Spring-Mass-Damper
33:00
10. More Examples of Second Order Differential Equations
31:31
11. High-Order Ordinary Differential Equations with More Derivatives
20:23
12. Solving General High-Order, Linear Ordinary Differential Equations (ODEs)
24:56
13. Matrix Systems of Differential Equations
24:58
14. Motivating Eigenvalues & Eigenvectors with Differential Equations
23:58
15. Eigenvalues & Eigenvectors
33:57
16. Solving Systems of Differential Equations with Eigenvalues & Eigenvectors
21:51
17. 2x2 Systems of ODEs: Sources & Sinks
25:11
18. 2x2 Systems of ODEs Saddle Points & Instability
27:43
19. 2x2 Systems of ODEs: Imaginary Eigenvalues & Center Fixed Points
37:49
20. Stability & Eigenvalues: What does it mean to be a stable eigenvalue
14:53
21. What is a Linear Differential Equation
19:15
22. Linearizing Nonlinear Differential Equations Near a Fixed Point
23:28
23. A Particle in a Potential Well Nonlinear Dynamics
13:23
24. Drawing Phase Portraits for Nonlinear Systems
26:01
25. Phase Portrait for Double Well Potential
16:04
26. The Hartman-Grobman Theorem & Structural Stability of Linearization
17:37
27. Non-Normal Linear Systems & Transient Energy Growth
30:23
28. Repeated Eigenvalues and Secular Terms
12:39
29. Systems of Differential Equations Diagonalization & Jordan Canonical Form
34:25
30. Differential Equations with Forcing: Method of Undetermined Coefficients
20:09
31. Differential Equations with Forcing Method of Variation of Parameters
23:25
32. Systems of Differential Equations with Forcing: Example in Control Theory
16:04
33. Linear Systems of Differential Equations with Forcing
41:25
34. Forced Systems of Differential Equations in Matlab and Python
19:26
35. Numerical Differentiation with Finite Difference Derivatives
36:57
36. Numerical Differentiation: Second Derivatives & Differentiating Data
42:16
37. Why we can't take "dt" to 0 in a computer
19:00
38. Numerical Integration: Discrete Riemann Integrals & Trapezoid Rule
29:43
39. Numerical Simulation of Ordinary Differential Equations: Integrating ODEs
23:49
40. Deriving Forward Euler & Backward/Implicit Euler Integration Schemes
23:28
41. Numerical Integration of ODEs with Forward Euler & Backward Euler in Python
31:15
42. Error Analysis of Euler Integration Scheme for DEs Using Taylor Series
12:06
43. Stability of Forward Euler & Backward Euler Integration Schemes for DEs
33:26
44. Runge-Kutta Integrator Overview: All Purpose Numerical Integration of DEs
30:22
45. Coding a Fourth-Order Runge-Kutta Integrator in Python & Matlab
36:52
46. Numerical Integration of Chaotic Dynamics
20:01
47. Chaotic Dynamical Systems
44:01
48. Engineering Math Pre-Req: Quick & Dirty Introduction to Python
41:53
49. Engineering Math Pre-Req: Quick & Dirty Introduction to Matlab
34:51

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