\documentclass[main.tex]{subfiles}

\begin{document}


\slide{First of all ...}{
\blok{Companion website}{http://buon.fjfi.cvut.cz/wp}
\twocolumns{0.5}{
\includegraphics[width=\tw]{figs/qrcode.png}}
{0.5}{
\begin{itemize}
\item This presentation (in latex) .. to be reused/adapted for education.
\item All used examples (ready to be used for education).
\item Other relevant info.
\item Resources.
\end{itemize}
}}

\subsection{Motivation}
\slide{Motivation}{
\blok{Scientific problem}{Theory, {\bf Numerical simulation}, Experiment}
\twocolumns{0.5}{
\fig{0.6}{SoberaniaPend.png}{Soberenia Pendulum}{SobPend}}
{0.5}{
\fig{1}{u10l0c8}{Pendulum analysis @ \cite{PhysClassroomPend}}{PhysClassPend}}
}


\SlideWithFullFigureWithLink{Pendulum basic @ spreadsheet}{examples/Spreadsheets/1D_Pendulum_Basic/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Basic/}
\SlideWithFullFigureWithLink{Pendulum basic @ processing}{examples/Processing/PendulumBasic/Screenshot.png}{https://editor.p5js.org/vojtech.svob/sketches/vTEaAkgs}

\slide{Objectives}{
\blok{(World) Pendulum ... as a gate to physics}{\centering Numerical simulations point of view}
\begin{itemize}
 \item A comprehensive, as simple as possible numerical approach to the Pendulum problem using Euler scheme for solving ordinary differential equations (ODE) developed under various Computer Algebraic Systems:
 \begin{itemize}
 \item spreadsheet (Excel, LibreOffice Calc, Google, gnumeric),
 \item p5* processing,
 \item jupyter notebook (python),
 \item octave (matlab).
\end{itemize}
\item Wide range of simple examples (ready to be used for education)
\item Way to avoid the complex math problems (ODE) in the (early) physics education.
\end{itemize}   
}

\slide{Outline of the talk}{
%\begin{frame}
  \tableofcontents
%\end{frame}
}

\subsection{Vojtech Svoboda @ CTU}
{
\setbeamercolor{background canvas}{bg=}
\includepdf[pages=-]{figs/VS.pdf}
}
%\includepdf[pages=-]{figs/CTU.pdf}

 







%\SlideWithFullFigureWithLink{Let's dive into a problem}{examples/Spreadsheets/1stO_ODE/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1stO_ODE/}




\subsection{Euler method}




\slide{Initial value problem}{
Let's have a general force field $F(t,x,v)$ applying on an object of a mass $m$, having some initial conditions $t_0, v_0, x_0$:
\begin{itemize}
 \item Differential solution: having $dt$ time progress: $a=F/m$, then $v(t)=\int_{t_0}^{t}{adt}$, and $x(t)=\int_{t_0}^{t}{vdt}$ 
 \item Discrete solution: having $\Delta t$ time progress, in principal, we are looking for a time series of object position $(t_0,x_0),(t_1,x_1),..(t_n,x_n)$: $a_i=F_i/m$, then $v_{i+1}=v_{i}+a\cdot\Delta t$, and $x_{i+1}=x_{i}+v_i\cdot\Delta t$ 
\end{itemize}
}

\slide{Discrete solution - towards algorithmization}{
\blok{Recurring principle/algorithm}{\centering ideal for computer algebraic systems}
Having $\Delta t$ time progress, in principal, we are looking for a time series of object position $(t_0,x_0),(t_1,x_1),..(t_n,x_n)$: $a_i=F_i/m$, then $v_{i+1}=v_{i}+a\cdot\Delta t$, and $x_{i+1}=x_{i}+v_i\cdot\Delta t$
\Prescription
}

\slide{Euler method solving ODE - the principle}{
\blok{Let an initial value problem be specified:}
{\centering $\dot {y}=f(t,y),\quad y(t_{0})=y_{0}$}
\twocolumns{0.5}{
\fig{1}{10000000000003E00000025403FFE934.png}{\credit{SzaboMechMod}}{label}
}{0.5}{
\begin{align*}
y_{n+1} &= y_n + h\ f(t_n, y_n),\\
t_{n+1} &= t_n + h
\end{align*}
}
}



\slide{Euler method solving ODE - repetition (loop)}{
\centering
\fig{0.5}{Euler_method.png}{\credit{wiki:EulerMeth}}{label}
}


\SlideWithHeadFullFigureWithLink{Let's dive into a problem}{
\blok{0$^{th}$ order ODE: Constant force}{$F_{ext}=k$}
}{examples/Spreadsheets/0stO_ConstForce/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/0stO_ConstForce/}


\SlideWithHeadFullFigureWithLink{Let's dive into a problem}{
\blok{1$^{st}$ order ODE: Friction force}{$F_{ext}=-b\cdot v$}
}{examples/Spreadsheets/1stO_Friction/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1stO_Friction/}


\end{document}
