source: Steve Brunton 2016年4月25日

ME564 - Mechanical Engineering Analysis (Fall 2014) by Steve L. Brunton | University of Washington

Notes: http://faculty.washington.edu/sbrunto...

Matlab code: http://faculty.washington.edu/sbrunto...

Course Website: http://faculty.washington.edu/sbrunto...

http://faculty.washington.edu/sbrunton/

Lecture 1: Overview of engineering mathematics 41:16 Overview of engineering mathematics and example weather model in Matlab.

2: Review of calculus and first order linear ODEs 48:43

3: Taylor series and solutions to first and second order linear ODEs 53:23

4: Second order harmonic oscillator, characteristic equation, ode45 in Matlab 51:38

5: Higher-order ODEs, characteristic equation, matrix systems of first order ODEs 49:19

6: Matrix systems of first order equations using eigenvectors and eigenvalues 48:07

7: Eigenvalues, eigenvectors, and dynamical systems 46:54

8: 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits 48:42

9: Linearization of nonlinear ODEs, 2x2 systems, phase portraits 48:40

10: Examples of nonlinear systems: particle in a potential well 50:20

11: Degenerate systems of equations and non-normal energy growth 50:15

12: ODEs with external forcing (inhomogeneous ODEs) 49:36

13: ODEs with external forcing (inhomogeneous ODEs) and the convolution integral 49:52

14: Numerical differentiation using finite difference 49:30

15: Numerical differentiation and numerical integration 48:37

16: Numerical integration and numerical solutions to ODEs 46:33

17: Numerical solutions to ODEs (Forward and Backward Euler) 50:24

18: Runge-Kutta integration of ODEs and the Lorenz equation 48:57

19: Vectorized integration and the Lorenz equation 48:12

20: Chaos in ODEs (Lorenz and the double pendulum) 49:00

21: Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product 48:40

22: Div, Grad, and Curl 49:18

23: Gauss's Divergence Theorem 49:29

24: Directional derivative, continuity equation, and examples of vector fields 45:44

25: Stokes' theorem and conservative vector fields 49:52

26: Potential flow and Laplace's equation 45:57

27: Potential flow, stream functions, and examples 54:15

28: ODE for particle trajectories in a time-varying vector field 49:24

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