ME564 Lecture 1： Overview of engineering mathematics
ME564 Lecture 2： Review of calculus and first order linear ODEs
ME564 Lecture 3： Taylor series and solutions to first and second order linear O
ME564 Lecture 4： Second order harmonic oscillator, characteristic equation, ode
ME564 Lecture 5： Higher-order ODEs, characteristic equation, matrix systems of f
ME564 Lecture 6： Matrix systems of first order equations using eigenvectors and
ME564 Lecture 7： Eigenvalues, eigenvectors, and dynamical systems
ME564 Lecture 8： 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase
ME564 Lecture 9： Linearization of nonlinear ODEs, 2x2 systems, phase portraits
ME564 Lecture 10： Examples of nonlinear systems： particle in a potential well
ME564 Lecture 11： Degenerate systems of equations and non-normal energy growth
ME564 Lecture 12： ODEs with external forcing (inhomogeneous ODEs)
ME564 Lecture 13： ODEs with external forcing (inhomogeneous ODEs) and the convol
ME564 Lecture 14： Numerical differentiation using finite difference
ME564 Lecture 15： Numerical differentiation and numerical integration
ME564 Lecture 16： Numerical integration and numerical solutions to ODEs
ME564 Lecture 17： Numerical solutions to ODEs (Forward and Backward Euler)
ME564 Lecture 18： Runge-Kutta integration of ODEs and the Lorenz equation
ME564 Lecture 19： Vectorized integration and the Lorenz equation
ME564 Lecture 20： Chaos in ODEs (Lorenz and the double pendulum)
ME564 Lecture 21： Linear algebra in 2D and 3D： inner product, norm of a vector,
ME564 Lecture 22： Div, Grad, and Curl
ME564 Lecture 23： Gauss's Divergence Theorem
ME564 Lecture 24： Directional derivative, continuity equation, and examples of
ME564 Lecture 25： Stokes' theorem and conservative vector fields
ME564 Lecture 26： Potential flow and Laplace's equation
ME564 Lecture 27： Potential flow, stream functions, and examples
ME564 Lecture 28： ODE for particle trajectories in a time-varying vector field
ME565 Lecture 1： Complex numbers and functions
ME565 Lecture 2： Roots of unity, branch cuts, analytic functions, and the Cauchy
ME565 Lecture 3： Integration in the complex plane (Cauchy-Goursat Integral Theo
ME565 Lecture 4： Cauchy Integral Formula
ME565 Lecture 5： ML Bounds and examples of complex integration
ME565 Lecture 6： Inverse Laplace Transform and the Bromwich Integral
ME565 Lecture 7： Canonical Linear PDEs： Wave equation, Heat equation, and Lapla
ME565 Lecture 8： Heat Equation： derivation and equilibrium solution in 1D (i.e.,
ME565 Lecture 9： Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle)
ME565 Lecture 10： Analytic Solution to Laplace's Equation in 2D (on rectangle)
ME565 Lecture 11： Numerical Solution to Laplace's Equation in Matlab. Intro to F
ME565 Lecture 12： Fourier Series
ME565 Lecture 13： Infinite Dimensional Function Spaces and Fourier Series
ME565 Lecture 14： Fourier Transforms
ME565 Lecture 15： Properties of Fourier Transforms and Examples
ME565 Lecture 16 Bonus： DFT in Matlab
ME565 Lecture 16： Discrete Fourier Transforms (DFT)
ME565 Lecture 17： Fast Fourier Transforms (FFT) and Audio
ME565 Lecture 18： FFT and Image Compression
ME565 Lecture 19： Fourier Transform to Solve PDEs： 1D Heat Equation on Infinite
ME565 Lecture 20： Numerical Solutions to PDEs Using FFT
ME565 Lecture 21： The Laplace Transform
ME565 Lecture 22： Laplace Transform and ODEs
ME565 Lecture 23： Laplace Transform and ODEs with Forcing and Transfer Functions
ME565 Lecture 24： Convolution integrals, impulse and step responses
ME565 Lecture 25： Laplace transform solutions to PDEs
ME565 Lecture 26： Solving PDEs in Matlab using FFT
ME565 Lecture 27： SVD Part 1
ME565 Lecture 28： SVD Part 2
ME565 Lecture 29： SVD Part 3
