Rmarkdown Presentation Template

Hung P. Do, PhD, MSEE


  • Equations
    • Maxwell Equations
    • Schrödinger Equation
  • Interactive Plots
  • Tables
  • Interactive Maps
  • R Shiny Apps #1: Simple Nonlinear Exponential Fitting
  • R Shiny Apps #2: Predict next Word using a simple n-gram Language Model
  • Embedded Websites

Maxwell Equations

The coupled partial differential equations that form the foundation of classical electromagnetism. The integral (left) and differential (right) form.

\[ \def\oiint{\int\hspace{-2ex}\int\hspace{-3ex}\bigcirc~} \def\Q#1#2{\frac{\partial #1}{\partial #2}} \begin{array}{ll} \displaystyle\oiint(\vec{D}\cdot\vec{n}\,)d^2A=Q_{\rm free,included}~~~~~~~~~~~~~ &\displaystyle\nabla\cdot\vec{D}=\rho_{\rm free}\\ \displaystyle\oiint(\vec{B}\cdot\vec{n}\,)d^2A=0 &\displaystyle\nabla\cdot\vec{B}=0\\ \displaystyle\oint\vec{E}\cdot d\vec{s}=-\frac{d\Phi}{dt} &\displaystyle\nabla\times\vec{E}=-\Q{\vec{B}}{t}\\ \displaystyle\oint\vec{H}\cdot d\vec{s}=I_{\rm free,included}+\frac{d\Psi}{dt} &\displaystyle\nabla\times\vec{H}=\vec{J}_{\rm free}+\Q{\vec{D}}{t} \end{array} \]

Schrödinger Equation

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system.

\[ \displaystyle -\frac{\hbar^2}{2m}\nabla^2\psi+U\psi=E\psi=i\hbar\Q{\psi}{t} \]

Interactive Plots


Let’s use a linear model to fit miles per gallon (mpg) as a function of weight (wt) and the number of cylinders (cyl).
fit <- lm(mpg~wt+cyl, data=mtcars)
pander(fit, type = 'html', title = 'Linear Model Outputs')
Fitting linear model: mpg ~ wt + cyl
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 39.69 1.715 23.14 3.043e-20
wt -3.191 0.7569 -4.216 0.000222
cyl -1.508 0.4147 -3.636 0.001064

Interactive Maps

R Shiny Apps #1: Simple Nonlinear Exponential Fitting

  • Here is the weblink to a very simple R shiny app that performs the nonlinear exponential fitting.
  • Here is the weblink to the slide deck that describes the app.