Engineering Mathematics for Mechanical Engineers I

Video Lectures

Displaying all 28 video lectures.
Lecture 1
Overview of engineering mathematics
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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
Review of calculus and first order linear ODEs
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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
Taylor series and solutions to first and second order linear ODEs
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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
Second order harmonic oscillator, characteristic equation, ode45 in Matlab
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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
Higher-order ODEs, characteristic equation, matrix systems of first order ODEs
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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
Matrix systems of first order equations using eigenvectors and eigenvalues
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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
Eigenvalues, eigenvectors, and dynamical systems
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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
2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits
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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
Linearization of nonlinear ODEs, 2x2 systems, phase portraits
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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
Examples of nonlinear systems: particle in a potential well
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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
Degenerate systems of equations and non-normal energy growth
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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
ODEs with external forcing (inhomogeneous ODEs)
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ODEs with external forcing (inhomogeneous ODEs)
ODEs with external forcing (inhomogeneous ODEs)

Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L12.pdf
Lecture 13
ODEs with external forcing (inhomogeneous ODEs) and the convolution integral
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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
Numerical differentiation using finite difference
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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
Numerical differentiation and numerical integration
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Numerical differentiation and numerical integration
Numerical differentiation and numerical integration

Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L15.pdf
Lecture 16
Numerical integration and numerical solutions to ODEs
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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
Numerical solutions to ODEs (Forward and Backward Euler)
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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
Runge-Kutta integration of ODEs and the Lorenz equation
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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
Vectorized integration and the Lorenz equation
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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
Chaos in ODEs (Lorenz and the double pendulum)
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Chaos in ODEs (Lorenz and the double pendulum)
Chaos in ODEs (Lorenz and the double pendulum)
Lecture 21
Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product
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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
Div, Grad, and Curl
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Div, Grad, and Curl
Div, Grad, and Curl

Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L22.pdf
Lecture 23
Gauss's Divergence Theorem
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Gauss's Divergence Theorem
Gauss's Divergence Theorem

Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L23.pdf
Lecture 24
Directional derivative, continuity equation, and examples of vector fields
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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
Stokes' theorem and conservative vector fields
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Stokes' theorem and conservative vector fields
Stokes' theorem and conservative vector fields

Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L25.pdf
Lecture 26
Potential flow and Laplace's equation
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Potential flow and Laplace's equation
Potential flow and Laplace's equation

Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L26.pdf
Lecture 27
Potential flow, stream functions, and examples
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Potential flow, stream functions, and examples
Potential flow and Laplace's equation

Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L27.pdf
Lecture 28
ODE for particle trajectories in a time-varying vector field
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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...