Mechanical Engineering Analysis (Winter 2015) by Steve Brunton | University of Washington

source: Steve Brunton      2016年4月27日
ME565 - Mechanical Engineering Analysis (Winter 2015) by Steve Brunton | University of Washington
Notes: http://faculty.washington.edu/sbrunto...
Course Website: http://faculty.washington.edu/sbrunto...
http://faculty.washington.edu/sbrunton/

Lecture 1: Complex numbers and functions 49:02
2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions 50:19
3: Integration in the complex plane (Cauchy-Goursat Integral Theorem) 50:13
4: Cauchy Integral Formula 47:59
5: ML Bounds and examples of complex integration 50:15
6: Inverse Laplace Transform and the Bromwich Integral 48:49
7: Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation 50:18
8: Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation) 49:28
9: Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle) 47:16
10: Analytic Solution to Laplace's Equation in 2D (on rectangle) 48:05
11: Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series 48:58
12: Fourier Series 50:23
13: Infinite Dimensional Function Spaces and Fourier Series 49:03
14: Fourier Transforms 49:09
15: Properties of Fourier Transforms and Examples 48:22
16: Discrete Fourier Transforms (DFT) 48:39
16 Bonus: DFT in Matlab 7:45
17: Fast Fourier Transforms (FFT) and Audio 48:03
18: FFT and Image Compression 43:40
19: Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain 42:33
20: Numerical Solutions to PDEs Using FFT 50:20
21: The Laplace Transform 49:51
22: Laplace Transform and ODEs 49:48
23: Laplace Transform and ODEs with Forcing and Transfer Functions 49:24
24: Convolution integrals, impulse and step responses 50:25
25: Laplace transform solutions to PDEs 50:23
26: Solving PDEs in Matlab using FFT 50:16
27: SVD Part 1 50:12
28: SVD Part 2 48:46
29: SVD Part 3 47:19