  # Engineering Mathematics for Mechanical Engineers I

## Video Lectures

Displaying all 28 video lectures.
 Lecture 1 Play Video Overview of engineering mathematicsOverview 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 ODEsReview 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 ODEsTaylor 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 MatlabSecond 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 ODEsHigher-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 eigenvaluesMatrix 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 systemsEigenvalues, 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 portraitsExamples 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 portraitsLinearization 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 wellExamples 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 growthDegenerate 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 integralODEs 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 differenceNumerical 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 integrationNumerical differentiation and numerical integration Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L15.pdf Lecture 16 Play Video Numerical integration and numerical solutions to ODEsNumerical 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 equationRunge-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 equationVectorized 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 productLinear 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 CurlDiv, Grad, and Curl Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L22.pdf Lecture 23 Play Video Gauss's Divergence TheoremGauss'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 fieldsDirectional 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 fieldsStokes' theorem and conservative vector fields Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L25.pdf Lecture 26 Play Video Potential flow and Laplace's equationPotential flow and Laplace's equation Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L26.pdf Lecture 27 Play Video Potential flow, stream functions, and examplesPotential 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 fieldODE 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...