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diff --git a/using_sage_for_calculus/slides.org b/using_sage_for_calculus/slides.org new file mode 100644 index 0000000..c5e35c8 --- /dev/null +++ b/using_sage_for_calculus/slides.org @@ -0,0 +1,117 @@ +#+LaTeX_CLASS: beamer +#+LaTeX_CLASS_OPTIONS: [presentation] +#+BEAMER_FRAME_LEVEL: 1 + +#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} +#+COLUMNS: %45ITEM %10BEAMER_env(Env) %10BEAMER_envargs(Env Args) %4BEAMER_col(Col) %8BEAMER_extra(Extra) +#+PROPERTY: BEAMER_col_ALL 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 :ETC + +#+LaTeX_CLASS: beamer +#+LaTeX_CLASS_OPTIONS: [presentation] + +#+LaTeX_HEADER: \usepackage[english]{babel} \usepackage{ae,aecompl} +#+LaTeX_HEADER: \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} + +#+LaTeX_HEADER: \usepackage{listings} + +#+LaTeX_HEADER:\lstset{language=Python, basicstyle=\ttfamily\bfseries, +#+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 + + |