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#+LaTeX_CLASS: beamer
#+LaTeX_CLASS_OPTIONS: [presentation]
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#+LaTeX_HEADER: \usepackage{listings}
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#+LaTeX_HEADER: commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen},
#+LaTeX_HEADER: showstringspaces=false, keywordstyle=\color{blue}\bfseries}
#+TITLE:
#+AUTHOR: FOSSEE
#+EMAIL:
#+DATE:
#+DESCRIPTION:
#+KEYWORDS:
#+LANGUAGE: en
#+OPTIONS: H:3 num:nil toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t
#+OPTIONS: TeX:t LaTeX:nil skip:nil d:nil todo:nil pri:nil tags:not-in-toc
*
#+begin_latex
\begin{center}
\vspace{12pt}
\textcolor{blue}{\huge Using Sage}
\end{center}
\vspace{18pt}
\begin{center}
\vspace{10pt}
\includegraphics[scale=0.95]{../images/fossee-logo.png}\\
\vspace{5pt}
\scriptsize Developed by FOSSEE Team, IIT-Bombay. \\
\scriptsize Funded by National Mission on Education through ICT\\
\scriptsize MHRD,Govt. of India\\
\includegraphics[scale=0.30]{../images/iitb-logo.png}\\
\end{center}
#+end_latex
* Objectives
At the end of this tutorial, you will be able to,
- Learn the range of things for which Sage can be used.
- Know some of the functions for Calculus.
- Learn about graph theory and number theory using Sage.
* Pre-requisite
Spoken tuorial on -
- Getting started with Sage
* Equation
Ax = v,
where A is the matrix,'' matrix([[1,2],[3,4]])''
v is the vector, ''vector([1,2])''.
* Summary
In this tutorial, we have learnt to,
- Use functions for calculus like --
- lim()-- to find out the limit of a function
- diff()-- to find out the differentiation of an expression
- integrate()-- to integrate over an expression
- integral()-- to find out the definite integral of an
expression by specifying the limits
- solve()-- to solve a function, relative to it's postion.
- Create Both a simple graph and a directed graph, using the
functions ``graph()`` and ``digraph()`` respectively.
- Use functions for Number theory.For eg:
- primes\_range()-- to find out the prime numbers within the
specified range
- factor()-- to find out the factorized form of the number specified
- Permutations(), Combinations()-- to obtain the required permutation
and combinations for the given set of values.
* Evaluation
1. How do you find the limit of the function ``x/sin(x)`` as ``x`` tends
to ``0`` from the negative side.
2. List all the primes between 2009 and 2900.
3. Solve the system of linear equations
x-2y+3z = 7
2x+3y-z = 5
x+2y+4z = 9
* Solutions
1. lim(x/sin(x), x=0, dir="below")
2. prime\_range(2009, 2901)
3. A = Matrix([[1, -2, 3],
[2, 3, -1],
[1, 2, 4]])
b = vector([7, 5, 9])
solve\_right(A, b)
*
#+begin_latex
\begin{block}{}
\begin{center}
\textcolor{blue}{\Large THANK YOU!}
\end{center}
\end{block}
\begin{block}{}
\begin{center}
For more Information, visit our website\\
\url{http://fossee.in/}
\end{center}
\end{block}
#+end_latex
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