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

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