\chead{
      \textbf{
          \begin{Large}
          Universidade Federal de Goi\'as\\
          \end{Large}
      \begin{large}INSTITUTO DE MATEM\'ATICA E ESTATISTICA\end{large}\\
      Campus Samambaia -  74001-970 - Goi\^ania\\
      http://www.ime.ufg.br - (62) 3521 1742 - (62) 3521-1208 - secretaria.ime@ufg.br
      }
}


\begin{center}
  \LARGE{\textbf{Plano de Ensino}}
\end{center}

\PlanSection{01. Dados de Identifica\c{c}\~ao da Disciplina:}
{   
   \begin{center}\begin{small}
      \begin{tabular}{|l|p{5cm}|l|p{5cm}|}
         \hline
         \textbf{Semestre:} & 2023.2 &
         \textbf{Curso:} & Matem\'atica
         \\
         
         \hline
         \textbf{Turma:} & A
         &
         \textbf{C\'odigo Componente:} & IME0495
         \\
         
         \hline
         \textbf{Componente:} & \uppercase{Mathematical Investigations With Free Software Tools: Calculations, Visualizations And Animations.}
         &
         \textbf{UA Respons\'avel:} & IME
         \\
         
         \hline
         \textbf{Carga Hor\'aria:} & 64
         &
         \textbf{UA Solicitante:} & IME
         \\
         
         \hline
         \textbf{Te\'orica/Pr\'atica:}
         &
         64/-
         &
         
         \textbf{EAD/PCC:}
         &
         -/-
         \\
         
         
         \hline
         \textbf{Hor\'arios:}
         &
         24t56
         &
         
         \textbf{Docente:}
         &
         Prof(a) Ole Peter Smith
         \\
         
         \hline
      \end{tabular}
   \end{small}\end{center}
}

\PlanSection{02. Ementa:}
{
  Drawing and visualizing functions depending on parameters using Geogebra. Introduction to derivatives, visualization. Geometrical constructions with Geogebra and TikZ/LaTeX. Introductions to graphical formats, bitmaps versus vectorial grahics. SVG, TikZ. Parameterized planar curves; derivatives and curvature. Other tools for calculus and visualization: Python, Javascript.
}


\PlanSection{03. Programa:}
{
  \begin{enumerate}
\item Drawing and visualizing functions depending on parameters using Geogebra. 
\item Introduction to derivatives, visualization. 
\item Geometrical constructions with Geogebra and TikZ/LaTeX. 
\item Introductions to graphical formats, bitmaps versus vectorial grahics. SVG, TikZ. 
\item Parameterized planar curves; derivatives and curvature. 
\item Other tools for calculus and visualization: Python, Javascript.
\end{enumerate}
}


\PlanSection{04. Cronograma:}
{
  \begin{enumerate}
 \item Functions and derivatives. 16hs.

 \begin{enumerate}
 \item Visualization and animation of functions with parameters (Geogebra).
 \item Introduction and visualizations of derivatives (Geogebra).
 \item Approximating functions with derivatives and Taylors Formula (Python).
 \end{enumerate}

 \item Planar Analytical Geometry. 16hs.

 \begin{enumerate}
 \item Triangles (Geogebra, TikZ).
 \item Convex and biconvex parametrizations (Geogebra and TikZ). 
 \item Geometrical constructions (Geogebra, TikZ).
 \item Parametrization of circles, parabolas, ellipsis and hyperbolas (Geogebra, TikZ). 
 \end{enumerate}

 \item Parametrized Planar Curves. 16hs.

 \begin{enumerate}
 \item Curve investigations. Determinant, curvature and evolutes (Geogebra, SVG/Javascript).
 \item Parabolas, ellipsis and hyperbolas revisited (Geogebra, SVG/Javascript).
 \item Cycloids and Trochoids (Geogebra, SVG/Javascript).
 \end{enumerate}

 \item Assessment activities. 16hs.
\end{enumerate}
}


\PlanSection{05. Objetivos Gerais:}
{
  \begin{enumerate}
 \item Familiarize the students with classes in english.
 \item Introducing the students to mathematical modelling, investigation and concepts.
 \item Introducing the students to visualization of mathematical models.
 \item Introducing the students to free mathematical software tools.
 \item Familiarize with the ideas of free software and available tools. 
\end{enumerate}
}



\PlanSection{06. Objetivos Espec\'{\i}ficos:}
{
  \begin{enumerate}
 \item Introducing the students to parameterized functions, derivatives and Taylors formula.
 \item Introducing the students to Geometrical constructions.
 \item Familiarize the students with parametrization of geometrical objects.
 \item Introduce the students to parameterized planar curves and curvature.
 \item Familiarize the students to the use of the english language in class room situations.
 \item Introduce the students to free software tools, such as Geogebra, Python, $\LaTeX$/TikZ, SVG and Javascript.
\end{enumerate}
}


\PlanSection{07. Metodologia:}
{
  The 4 weekly one-hour classes (in english) will be executed as:

\begin{itemize}
 \item 2 hours of proposed activities in computer lab (generally on wednesdays).
 \item 2 hours online (synchronous) via Google Meet (https://meet.google.com/hjg-aaup-ype), the teacher exposing his
 screen, exhibiting the working methods.
\end{enumerate}

Throughout the course, students are encouraged to produce their own graphics and animations, using avaliable software tools.
}


\PlanSection{08. Avalia\c{c}\~oes:}
{
  During the course, 2 tests will be applied. In each of them, the student will receive a proposed exam by email, containing selected draw able situations. The students will then have at the least on week, to elaborate response, to be delivered electronically.

Proposed schedule (may be altered negociating with the students):

- Exam 1: 13-20/12/2023.
- Exam 2: 29/01-05/02/2024.

The final mark will be the geometrical mean of the marks of the two exams.
}


\PlanSection{09. Bibliografia:}
{
  \textbf{[1]:} REIS, G. L. e SILVA, V. V.; Geometria Anal\'{\i}tica, Rio de Janeiro LTC Editora, 2 a Edi\c{c}\~ao, 1997.

\textbf{[2]:} LEITHOLD, L. O C\'alculo com Geometria Anal\'{\i}tica. 3 ed. V. 1. S\~ao Paulo: Harbra, 1994.

\textbf{[3]:} APOSTOL, T. Linear Algebra A First Course with Applications to Differential Equations, Wiley- Interscience, 1997.

\textbf{[4]:} RUGGIERO, M. A. G.; LOPES, V. L. R.; C\'alculo num\'erico Aspectos te\'oricos e computacionais; 2 a ed.; Makron Books, S\~ao Paulo, 1996.

\textbf{[5]:} NETTO, S. L. Constru\c{c}\~oes Geom\'etricas: Exerc\'{\i}cios e Solu\c{c}\~oes. Sociedade Brasileira de Matem\'atica, 1a ed. Rio de Janeira, 2006.


}

\PlanSection{10. Bibliografia Complementar:}
{
  \textbf{[1]:} \'AVILA, G. S. S. C\'alculo: Fun\c{c}\~oes de uma Vari\'avel. 7 ed. V. 1. Rio de Janeiro: LTC, 1994.

\textbf{[2]:} KOLMAN, B.; HILL, D.. Introdu\c{c}\~ao a \'Algebra Linear e Aplica\c{c}\~oes, LTC, 2006.

\textbf{[3]:} BURDEN, R. L.; FAIRES, J. D. An\'alise Num\'erica; Cengage Learning, S\~ao Paulo, 2003.


}

\PlanSection{11.  Livros Texto:}
{
   \textbf{[1]:} REIS, G. L. e SILVA, V. V.; Geometria Anal\'{\i}tica, Rio de Janeiro LTC Editora, 2 a Edi\c{c}\~ao, 1997.

\textbf{[2]:} NETTO, S. L. Constru\c{c}\~oes Geom\'etricas: Exerc\'{\i}cios e Solu\c{c}\~oes. Sociedade Brasileira de Matem\'atica, 1a ed. Rio de Janeira, 2006.

\textbf{[3]:} RUGGIERO, M. A. G.; LOPES, V. L. R.; C\'alculo num\'erico Aspectos te\'oricos e computacionais; 2 a ed.; Makron Books, S\~ao Paulo, 1996.
}


\PlanSection{12. Hor\'arios:}
{
   \begin{center}
\begin{small}
\begin{tabular}{lll}
\hline
   \textbf{Dia} & \textbf{Hor\'ario} & \textbf{Sala Distribuida}\\
\hline

   2$^a$ & A5 & 105, CAC (20)\\
   2$^a$ & A6 & 105, CAC (20)\\
   4$^a$ & A5 & 105, CAC (20)\\
   4$^a$ & A6 & 105, CAC (20)\\
\end{tabular}
\end{small}\end{center}

}


\PlanSection{13. Hor\'ario de Atendimento do(a)s Professor(a):}
{
   \begin{small}
\begin{tabular}{ll}
   \textbf{1. } & 2a 15-16, via google meet: https://meet.google.com/hjg-aaup-ype.\\
   \textbf{2. } & 4a 19-20, via google meet: https://meet.google.com/hjg-aaup-ype.\\
\end{tabular}
\end{small}
}

\PlanSection{14. Professor(a):}
{
   \begin{small}
\begin{tabular}{lll}
   Ole Peter Smith. & Email: ole@ufg.br, & IME\\
\end{tabular}
\end{small}
}




\vspace{0.2cm}

\begin{center}
\underline{\hspace{8cm}}\\\small{Prof(a) Ole Peter Smith}\end{center}


