1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
|
\documentclass[17pt]{beamer}
\usetheme{Madrid}
\useoutertheme{noslidenum}
\setbeamertemplate{navigation symbols}{}
\usepackage{beamerthemesplit}
\usepackage{ae,aecompl}
\usepackage[scaled=.95]{helvet}
\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathpazo,courier,euler}
\usepackage{listings}
\lstset{language=sh,
basicstyle=\ttfamily\bfseries,
showstringspaces=false,
keywordstyle=\color{black}\bfseries}
\definecolor{NavyBlue}{RGB}{0, 76, 153}
\setbeamercolor{structure}{fg=NavyBlue}
\author[FOSSEE]{}
\institute[IIT Bombay]{}
\date[]{}
% theme split
\usepackage{verbatim}
\newenvironment{colorverbatim}[1][]%
{%
\color{blue}
\verbatim
}%
{%
\endverbatim
}%
% logo
\logo{\includegraphics[height=1.30 cm]{../images/3t-logo.pdf}}
\logo{\includegraphics[height=1.30 cm]{../images/fossee-logo.png}
\hspace{7.5cm}
\includegraphics[scale=0.3]{../images/fossee-logo.png}\\
\hspace{281pt}
\includegraphics[scale=0.80]{../images/3t-logo.pdf}}
\begin{document}
\sffamily \bfseries
\title
[Using Sage for Calculus]
{Using Sage for Calculus}
\author
[FOSSEE]
{\small Talk to a Teacher\\{\color{blue}\url{http://spoken-tutorial.org}}\\National Mission on Education
through ICT\\{\color{blue}\url{http://sakshat.ac.in}} \\ [0.8cm]Script by: Hardik Ghaghada \\Narration by: \\ [0.7cm]
{\small 15 May 2013}}
% slide 1
\begin{frame}
\titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Objectives}
At the end of this tutorial, you will be able to,
\begin{itemize}
\item Learn the range of things for which Sage can be used.
\item Perform integrations \& other Calculus in Sage.
\item Perform matrix algebra in sage.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Differential Expression}
$exp(sin(x^2))/x$\\
w.r.t $x$
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Partial Differential Expression}
$exp(sin(y - x^2))/x$\\
w.r.t $x, y$
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Integration}
\begin{itemize}
\item $diff(f, y)$\\
\item $cos(-x^2 + y)*e^(sin(-x^2 + y))/x$\\
\item $integrate$
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{More on Calculus}
\url{www.sagemath.org/help.html}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Equation}
$Ax = v$\\
where A is the matrix,\\
$matrix([[1,2],[3,4]])$\\
v is the vector,\\
$vector([1,2])$
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Summary}
In this tutorial, we have learnt to,
\begin{itemize}
\item Use functions like lim(), integrate(), integral(), solve()
\item Use sage for performing matrix algebra, integrations \& other calculus
operations using the above mentioned functions.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Evaluation}
\begin{enumerate}
\item How do you find the limit of the function ``x/sin(x)'' as ``x'' tends
to ``0'' from the negative side.
\vspace{3pt}
\vspace{3pt}
\item Solve the system of linear equations
x-2y+3z = 7\\
2x+3y-z = 5\\
x+2y+4z = 9
\end{enumerate}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Solutions}
\begin{enumerate}
\item lim(x/sin(x), x=0, dir=`left')
\vspace{4pt}
\item A = Matrix([[1, -2, 3], \\
\hspace{1.78cm}
[2, 3, -1], \\
\hspace{1.78cm}
[1, 2, 4]]) \\
\vspace{2pt}
b = vector([7, 5, 9])\\
\vspace{2pt}
x = A.solve$\_{\mathrm{right}}$(b)\\
\vspace{2pt}
x
\end{enumerate}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{FOSSEE}
{\color{blue}Free and Open-source Software for \\Science and Engineering Education} \\
\begin{itemize}
\item Goal - enabling all to use open source software tools
\item For more details, please visit {\color{blue}\url{http://fossee.in/}}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{About the Spoken Tutorial Project}
\begin{itemize}
\item Watch the video available at {\color{blue}\url{http://spoken-tutorial.org /What\_is\_a\_Spoken\_Tutorial}}
\item It summarises the Spoken Tutorial project
\item If you do not have good bandwidth, you can download and watch it
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Spoken Tutorial Workshops}The Spoken Tutorial Project Team
\begin{itemize}
\item Conducts workshops using spoken tutorials
\item Gives certificates to those who pass an online test
\item For more details, please write to \\ \hspace {0.5cm}{\color{blue}contact@spoken-tutorial.org}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Acknowledgements}
\begin{itemize}
\item Spoken Tutorial Project is a part of the Talk to a Teacher project
\item It is supported by the National Mission on Education through ICT, MHRD, Government of India
\item More information on this Mission is available at: \\{\color{blue}\url{http://spoken-tutorial.org/NMEICT-Intro}}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\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{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
|
