Engineering Mathematics for Mechanical Engineers II

Video Lectures

Displaying all 30 video lectures.
Lecture 1
Complex numbers and functions
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Complex numbers and functions
ME565 Lecture 1
Engineering Mathematics at the University of Washington

Complex numbers and functions

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L01.pdf


http://faculty.washington.edu/sbrunton/
Lecture 2
Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions
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Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions
ME565 Lecture 2
Engineering Mathematics at the University of Washington

Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L02.pdf


http://faculty.washington.edu/sbrunton/
Lecture 3
Integration in the complex plane (Cauchy-Goursat Integral Theorem)
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Integration in the complex plane (Cauchy-Goursat Integral Theorem)
ME565 Lecture 3
Engineering Mathematics at the University of Washington

Integration in the complex plane (Cauchy-Goursat Integral Theorem)

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L03.pdf


http://faculty.washington.edu/sbrunton/
Lecture 4
Cauchy Integral Formula
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Cauchy Integral Formula
ME565 Lecture 4
Engineering Mathematics at the University of Washington

Cauchy Integral Formula

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L04.pdf


http://faculty.washington.edu/sbrunton/
Lecture 5
ML Bounds and examples of complex integration
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ML Bounds and examples of complex integration
ME565 Lecture 1
Engineering Mathematics at the University of Washington

ML Bounds and examples of complex integration

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L05.pdf


http://faculty.washington.edu/sbrunton/
Lecture 6
Inverse Laplace Transform and the Bromwich Integral
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Inverse Laplace Transform and the Bromwich Integral
ME565 Lecture 1
Engineering Mathematics at the University of Washington

Inverse Laplace Transform and the Bromwich Integral

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L06.pdf


http://faculty.washington.edu/sbrunton/
Lecture 7
Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation
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Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation
ME565 Lecture 7
Engineering Mathematics at the University of Washington

Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L07.pdf


http://faculty.washington.edu/sbrunton/
Lecture 8
Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation)
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Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation)
ME565 Lecture 8
Engineering Mathematics at the University of Washington

Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation)

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L08.pdf


http://faculty.washington.edu/sbrunton/
Lecture 9
Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle)
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Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle)
ME565 Lecture 9
Engineering Mathematics at the University of Washington

Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle)

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L09.pdf


http://faculty.washington.edu/sbrunton/
Lecture 10
Analytic Solution to Laplace's Equation in 2D (on rectangle)
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Analytic Solution to Laplace's Equation in 2D (on rectangle)
ME565 Lecture 10
Engineering Mathematics at the University of Washington

Analytic Solution to Laplace's Equation in 2D (on rectangle)

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L10.pdf


http://faculty.washington.edu/sbrunton/
Lecture 11
Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series
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Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series
ME565 Lecture 11
Engineering Mathematics at the University of Washington

Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L11.pdf
Matlab code:
* http://faculty.washington.edu/sbrunton/me565/matlab/L11_Lapl...
* http://faculty.washington.edu/sbrunton/me565/matlab/L11_Anal...
* http://faculty.washington.edu/sbrunton/me565/matlab/L11_Hard...


http://faculty.washington.edu/sbrunton/
Lecture 12
Fourier Series
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Fourier Series
ME565 Lecture 12
Engineering Mathematics at the University of Washington

Fourier Series

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L12.pdf
Matlab code: http://faculty.washington.edu/sbrunton/me565/matlab/L12_Four...


http://faculty.washington.edu/sbrunton/
Lecture 13
Infinite Dimensional Function Spaces and Fourier Series
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Infinite Dimensional Function Spaces and Fourier Series
ME565 Lecture 13
Engineering Mathematics at the University of Washington

Infinite Dimensional Function Spaces and Fourier Series

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L13.pdf


http://faculty.washington.edu/sbrunton/
Lecture 14
Fourier Transforms
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Fourier Transforms
ME565 Lecture 14
Engineering Mathematics at the University of Washington

Fourier Transforms

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L14.pdf


http://faculty.washington.edu/sbrunton/
Lecture 15
Properties of Fourier Transforms and Examples
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Properties of Fourier Transforms and Examples
ME565 Lecture 15
Engineering Mathematics at the University of Washington

Properties of Fourier Transforms and Examples

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L15.pdf


http://faculty.washington.edu/sbrunton/
Lecture 16
Discrete Fourier Transforms (DFT)
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Discrete Fourier Transforms (DFT)
ME565 Lecture 16
Engineering Mathematics at the University of Washington

Discrete Fourier Transforms (DFT)

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L16.pdf


http://faculty.washington.edu/sbrunton/
Lecture 17
Bonus: DFT in Matlab
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Bonus: DFT in Matlab
ME565 Lecture 16 Bonus
Engineering Mathematics at the University of Washington

Bonus material on the DFT in Matlab


http://faculty.washington.edu/sbrunton/
Lecture 18
Fast Fourier Transforms (FFT) and Audio
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Fast Fourier Transforms (FFT) and Audio
ME565 Lecture 17
Engineering Mathematics at the University of Washington

Fast Fourier Transforms (FFT) and Audio

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L17.pdf
Matlab code:
* http://faculty.washington.edu/sbrunton/me565/matlab/EX1_FFT....
* http://faculty.washington.edu/sbrunton/me565/matlab/EX2_FFT....


http://faculty.washington.edu/sbrunton/
Lecture 19
FFT and Image Compression
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FFT and Image Compression
ME565 Lecture 18
Engineering Mathematics at the University of Washington

FFT and Image Compression

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L18.pdf
Matlab code: http://faculty.washington.edu/sbrunton/me565/matlab/compress...


http://faculty.washington.edu/sbrunton/
Lecture 20
Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain
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Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain
ME565 Lecture 19
Engineering Mathematics at the University of Washington

Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L19.pdf


http://faculty.washington.edu/sbrunton/
Lecture 21
Numerical Solutions to PDEs Using FFT
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Numerical Solutions to PDEs Using FFT
ME565 Lecture 20
Engineering Mathematics at the University of Washington

Numerical Solutions to PDEs Using FFT

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L20.pdf
Matlab code:
* http://faculty.washington.edu/sbrunton/me565/matlab/HeatConv...
* http://faculty.washington.edu/sbrunton/me565/matlab/HeatFFT....
* http://faculty.washington.edu/sbrunton/me565/matlab/HeatBoth...
* http://faculty.washington.edu/sbrunton/me565/matlab/Spectral...
* http://faculty.washington.edu/sbrunton/me565/matlab/benchSpe...
* http://faculty.washington.edu/sbrunton/me565/matlab/smoothFF...


http://faculty.washington.edu/sbrunton/
Lecture 22
The Laplace Transform
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The Laplace Transform
ME565 Lecture 21
Engineering Mathematics at the University of Washington

Laplace Transform

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L21.pdf


http://faculty.washington.edu/sbrunton/
Lecture 23
Laplace Transform and ODEs
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Laplace Transform and ODEs
ME565 Lecture 22
Engineering Mathematics at the University of Washington

Laplace Transform and ODEs

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L22.pdf


http://faculty.washington.edu/sbrunton/
Lecture 24
Laplace Transform and ODEs with Forcing and Transfer Functions
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Laplace Transform and ODEs with Forcing and Transfer Functions
ME565 Lecture 23
Engineering Mathematics at the University of Washington

Laplace Transform and ODEs with Forcing and Transfer Functions

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L23.pdf


http://faculty.washington.edu/sbrunton/
Lecture 25
Convolution integrals, impulse and step responses
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Convolution integrals, impulse and step responses
ME565 Lecture 24
Engineering Mathematics at the University of Washington

Convolution integrals, impulse response and step response

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L24.pdf


http://faculty.washington.edu/sbrunton/
Lecture 26
Laplace transform solutions to PDEs
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Laplace transform solutions to PDEs
ME565 Lecture 25
Engineering Mathematics at the University of Washington

Laplace transform solutions to PDEs

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L25.pdf


http://faculty.washington.edu/sbrunton/
Lecture 27
Solving PDEs in Matlab using FFT
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Solving PDEs in Matlab using FFT
ME565 Lecture 26
Engineering Mathematics at the University of Washington

Solving PDEs in Matlab using FFT

Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L26.pdf


http://faculty.washington.edu/sbrunton/
Lecture 28
SVD Part 1
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SVD Part 1
UW ME 565 Lecture 27 by Steve Brunton.

Singular Value Decomposition (SVD)

http://faculty.washington.edu/sbrunton/me565/
Lecture 29
SVD Part 2
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SVD Part 2
UW ME565 Lecture 28 by Steve Brunton.

Singular Value Decomposition (SVD)

http://faculty.washington.edu/sbrunton/me565/
Lecture 30
SVD Part 3
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SVD Part 3
UW ME565 Lecture 29 by Steve Brunton.

Singular Value Decomposition (SVD)

http://faculty.washington.edu/sbrunton/me565/