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Code:	ME 564
Subject:	Mechanical Engineering
Topic:	Applied Mathematics
Views:	43,281

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Name:	University of Washington (Washington)
Type:	University

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Engineering Mathematics for Mechanical Engineers I

Video Lectures

Displaying all 28 video lectures.

Lecture 1 Play Video	Overview of engineering mathematics Overview of engineering mathematics and example weather model in Matlab. Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L01.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L01_weat...
Lecture 2 Play Video	Review of calculus and first order linear ODEs Review of calculus (derivative, power series, chain rule), and first order linear ordinary differential equations (ODEs) with examples. Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L02.pdf
Lecture 3 Play Video	Taylor series and solutions to first and second order linear ODEs Taylor series and solutions to first and second order linear ODEs Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L03.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L03_Tayl...
Lecture 4 Play Video	Second order harmonic oscillator, characteristic equation, ode45 in Matlab Second order harmonic oscillator, characteristic equation, ode45 in Matlab Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L04.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L04_Spri...
Lecture 5 Play Video	Higher-order ODEs, characteristic equation, matrix systems of first order ODEs Higher-order linear ODEs, characteristic equation, matrix systems of first order equations Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L05.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L05_ode4...
Lecture 6 Play Video	Matrix systems of first order equations using eigenvectors and eigenvalues Matrix systems of first order equations, diagonalizing using eigenvectors and eigenvalues Higher-order linear ODEs, characteristic equation, matrix systems of first order equations Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L06.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L05_ode4...
Lecture 7 Play Video	Eigenvalues, eigenvectors, and dynamical systems Eigenvalues, eigenvectors, and dynamical systems Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L06.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L05_ode4...
Lecture 8 Play Video	2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits Examples of 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L08.pdf
Lecture 9 Play Video	Linearization of nonlinear ODEs, 2x2 systems, phase portraits Linearization of nonlinear ODEs, 2x2 systems, phase portraits Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L09.pdf
Lecture 10 Play Video	Examples of nonlinear systems: particle in a potential well Examples of nonlinear systems: particle in a potential well Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L10.pdf
Lecture 11 Play Video	Degenerate systems of equations and non-normal energy growth Degenerate systems of equations and non-normal energy growth Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L11.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L11_nonN...
Lecture 12 Play Video	ODEs with external forcing (inhomogeneous ODEs) ODEs with external forcing (inhomogeneous ODEs) Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L12.pdf
Lecture 13 Play Video	ODEs with external forcing (inhomogeneous ODEs) and the convolution integral ODEs with external forcing (inhomogeneous ODEs) and the convolution integral Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L13.pdf
Lecture 14 Play Video	Numerical differentiation using finite difference Numerical differentiation using finite difference Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L14.pdf Matlab code: * http://faculty.washington.edu/sbrunton/me564/matlab/L14_Fini... * http://faculty.washington.edu/sbrunton/me564/matlab/L14_Fini...
Lecture 15 Play Video	Numerical differentiation and numerical integration Numerical differentiation and numerical integration Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L15.pdf
Lecture 16 Play Video	Numerical integration and numerical solutions to ODEs Numerical integration and numerical solutions to ODEs Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L16.pdf Misc. Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L16_misc.pd... Matlab code: * http://faculty.washington.edu/sbrunton/me564/matlab/L15_Nume... * http://faculty.washington.edu/sbrunton/me564/matlab/L16_Spri...
Lecture 17 Play Video	Numerical solutions to ODEs (Forward and Backward Euler) Numerical solutions to ODEs (Forward and Backward Euler) Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L17.pdf Matlab code: * http://faculty.washington.edu/sbrunton/me564/matlab/L17_pend... * http://faculty.washington.edu/sbrunton/me564/matlab/L17_simp...
Lecture 18 Play Video	Runge-Kutta integration of ODEs and the Lorenz equation Runge-Kutta integration of ODEs and the Lorenz equation Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L18.pdf Matlab code: * http://faculty.washington.edu/sbrunton/me564/matlab/rk4singl... * http://faculty.washington.edu/sbrunton/me564/matlab/lorenz.m * http://faculty.washington.edu/sbrunton/me564/matlab/L18_simu... * http://faculty.washington.edu/sbrunton/me564/matlab/L18_simu...
Lecture 19 Play Video	Vectorized integration and the Lorenz equation Vectorized integration and the Lorenz equation Matlab code: * http://faculty.washington.edu/sbrunton/me564/matlab/lorenz3D... * http://faculty.washington.edu/sbrunton/me564/matlab/L18_simu...
Lecture 20 Play Video	Chaos in ODEs (Lorenz and the double pendulum) Chaos in ODEs (Lorenz and the double pendulum)
Lecture 21 Play Video	Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L21.pdf
Lecture 22 Play Video	Div, Grad, and Curl Div, Grad, and Curl Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L22.pdf
Lecture 23 Play Video	Gauss's Divergence Theorem Gauss's Divergence Theorem Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L23.pdf
Lecture 24 Play Video	Directional derivative, continuity equation, and examples of vector fields Directional derivative, continuity equation, and examples of vector fields Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L24.pdf
Lecture 25 Play Video	Stokes' theorem and conservative vector fields Stokes' theorem and conservative vector fields Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L25.pdf
Lecture 26 Play Video	Potential flow and Laplace's equation Potential flow and Laplace's equation Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L26.pdf
Lecture 27 Play Video	Potential flow, stream functions, and examples Potential flow and Laplace's equation Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L27.pdf
Lecture 28 Play Video	ODE for particle trajectories in a time-varying vector field ODE for particle trajectories in a time-varying vector field Matlab code: * http://faculty.washington.edu/sbrunton/me564/matlab/doublegy... * http://faculty.washington.edu/sbrunton/me564/matlab/integrat... * http://faculty.washington.edu/sbrunton/me564/matlab/rk4singl...