Engineering Mathematics (UW ME564 and ME565)
4.0
(3)
27 learners
What you'll learn
This course includes
- 46.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 58 lessons • 46.5 hours of video
Engineering Mathematics (UW ME564 and ME565)
58 lessons
• 46.5 hours
Engineering Mathematics (UW ME564 and ME565)
58 lessons
• 46.5 hours
- ME564 Lecture 1: Overview of engineering mathematics 41:16
- ME564 Lecture 2: Review of calculus and first order linear ODEs 48:43
- ME564 Lecture 3: Taylor series and solutions to first and second order linear ODEs 53:24
- ME564 Lecture 4: Second order harmonic oscillator, characteristic equation, ode45 in Matlab 51:38
- ME564 Lecture 5: Higher-order ODEs, characteristic equation, matrix systems of first order ODEs 49:20
- ME564 Lecture 6: Matrix systems of first order equations using eigenvectors and eigenvalues 48:07
- ME564 Lecture 7: Eigenvalues, eigenvectors, and dynamical systems 46:54
- ME564 Lecture 8: 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits 48:42
- ME564 Lecture 9: Linearization of nonlinear ODEs, 2x2 systems, phase portraits 48:40
- ME564 Lecture 10: Examples of nonlinear systems: particle in a potential well 50:20
- ME564 Lecture 11: Degenerate systems of equations and non-normal energy growth 50:15
- ME564 Lecture 12: ODEs with external forcing (inhomogeneous ODEs) 49:36
- ME564 Lecture 13: ODEs with external forcing (inhomogeneous ODEs) and the convolution integral 49:52
- ME564 Lecture 14: Numerical differentiation using finite difference 49:30
- ME564 Lecture 15: Numerical differentiation and numerical integration 48:37
- ME564 Lecture 16: Numerical integration and numerical solutions to ODEs 46:33
- ME564 Lecture 17: Numerical solutions to ODEs (Forward and Backward Euler) 50:24
- ME564 Lecture 18: Runge-Kutta integration of ODEs and the Lorenz equation 48:57
- ME564 Lecture 19: Vectorized integration and the Lorenz equation 48:12
- ME564 Lecture 20: Chaos in ODEs (Lorenz and the double pendulum) 49:00
- ME564 Lecture 21: Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product 48:40
- ME564 Lecture 22: Div, Grad, and Curl 49:18
- ME564 Lecture 23: Gauss's Divergence Theorem 49:29
- ME564 Lecture 24: Directional derivative, continuity equation, and examples of vector fields 45:44
- ME564 Lecture 25: Stokes' theorem and conservative vector fields 49:52
- ME564 Lecture 26: Potential flow and Laplace's equation 45:57
- ME564 Lecture 27: Potential flow, stream functions, and examples 54:15
- ME564 Lecture 28: ODE for particle trajectories in a time-varying vector field 49:24
- ME565 Lecture 1: Complex numbers and functions 49:02
- ME565 Lecture 2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions 50:19
- ME565 Lecture 3: Integration in the complex plane (Cauchy-Goursat Integral Theorem) 50:13
- ME565 Lecture 4: Cauchy Integral Formula 47:59
- ME565 Lecture 5: ML Bounds and examples of complex integration 50:15
- ME565 Lecture 6: Inverse Laplace Transform and the Bromwich Integral 48:49
- ME565 Lecture 7: Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation 50:18
- ME565 Lecture 8: Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation) 49:28
- ME565 Lecture 9: Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle) 47:16
- ME565 Lecture 10: Analytic Solution to Laplace's Equation in 2D (on rectangle) 48:05
- ME565 Lecture 11: Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series 48:58
- ME565 Lecture 12: Fourier Series 50:23
- ME565 Lecture 13: Infinite Dimensional Function Spaces and Fourier Series 49:03
- ME565 Lecture 14: Fourier Transforms 49:09
- ME565 Lecture 15: Properties of Fourier Transforms and Examples 48:22
- ME565 Lecture 16 Bonus: DFT in Matlab 07:45
- ME565 Lecture 17: Fast Fourier Transforms (FFT) and Audio 48:03
- ME565 Lecture 16: Discrete Fourier Transforms (DFT) 48:39
- ME565 Lecture 18: FFT and Image Compression 43:40
- ME565 Lecture 19: Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain 42:33
- ME565 Lecture 20: Numerical Solutions to PDEs Using FFT 50:20
- ME565 Lecture 21: The Laplace Transform 49:51
- ME565 Lecture 22: Laplace Transform and ODEs 49:48
- ME565 Lecture 23: Laplace Transform and ODEs with Forcing and Transfer Functions 49:24
- ME565 Lecture 24: Convolution integrals, impulse and step responses 50:25
- ME565 Lecture 25: Laplace transform solutions to PDEs 50:23
- ME565 Lecture 26: Solving PDEs in Matlab using FFT 50:16
- ME 565 Lecture 27: SVD Part 1 50:12
- ME565 Lecture 28: SVD Part 2 48:46
- ME565 Lecture 29: SVD Part 3 47:19
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