1 % Created 2010-11-11 Thu 02:03 |
|
2 \documentclass[presentation]{beamer} |
|
3 \usepackage[latin1]{inputenc} |
|
4 \usepackage[T1]{fontenc} |
|
5 \usepackage{fixltx2e} |
|
6 \usepackage{graphicx} |
|
7 \usepackage{longtable} |
|
8 \usepackage{float} |
|
9 \usepackage{wrapfig} |
|
10 \usepackage{soul} |
|
11 \usepackage{textcomp} |
|
12 \usepackage{marvosym} |
|
13 \usepackage{wasysym} |
|
14 \usepackage{latexsym} |
|
15 \usepackage{amssymb} |
|
16 \usepackage{hyperref} |
|
17 \tolerance=1000 |
|
18 \usepackage[english]{babel} \usepackage{ae,aecompl} |
|
19 \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} |
|
20 \usepackage{listings} |
|
21 \lstset{language=Python, basicstyle=\ttfamily\bfseries, |
|
22 commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, |
|
23 showstringspaces=false, keywordstyle=\color{blue}\bfseries} |
|
24 \providecommand{\alert}[1]{\textbf{#1}} |
|
25 |
|
26 \title{Getting started with symbolics} |
|
27 \author{FOSSEE} |
|
28 \date{} |
|
29 |
|
30 \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} |
|
31 \begin{document} |
|
32 |
|
33 \maketitle |
|
34 |
|
35 |
|
36 |
|
37 |
|
38 |
|
39 |
|
40 |
|
41 |
|
42 |
|
43 \begin{frame} |
|
44 \frametitle{Outline} |
|
45 \label{sec-1} |
|
46 |
|
47 \begin{itemize} |
|
48 \item Defining symbolic expressions in sage. |
|
49 \item Using built-in constants and functions. |
|
50 \item Performing Integration, differentiation using sage. |
|
51 \item Defining matrices. |
|
52 \item Defining Symbolic functions. |
|
53 \item Simplifying and solving symbolic expressions and functions. |
|
54 \end{itemize} |
|
55 \end{frame} |
|
56 \begin{frame} |
|
57 \frametitle{Question 1} |
|
58 \label{sec-2} |
|
59 |
|
60 \begin{itemize} |
|
61 \item Define the following expression as symbolic |
|
62 expression in sage. |
|
63 |
|
64 \begin{itemize} |
|
65 \item x$^2$+y$^2$ |
|
66 \item y$^2$-4ax |
|
67 \end{itemize} |
|
68 |
|
69 \end{itemize} |
|
70 |
|
71 |
|
72 \end{frame} |
|
73 \begin{frame}[fragile] |
|
74 \frametitle{Solution 1} |
|
75 \label{sec-3} |
|
76 |
|
77 \lstset{language=Python} |
|
78 \begin{lstlisting} |
|
79 var('x,y') |
|
80 x^2+y^2 |
|
81 |
|
82 var('a,x,y') |
|
83 y^2-4*a*x |
|
84 \end{lstlisting} |
|
85 \end{frame} |
|
86 \begin{frame} |
|
87 \frametitle{Question 2} |
|
88 \label{sec-4} |
|
89 |
|
90 |
|
91 \begin{itemize} |
|
92 \item Find the values of the following constants upto 6 digits precision |
|
93 |
|
94 \begin{itemize} |
|
95 \item pi$^2$ |
|
96 \item euler$_{\mathrm{gamma}}$$^2$ |
|
97 \end{itemize} |
|
98 |
|
99 \end{itemize} |
|
100 |
|
101 \begin{itemize} |
|
102 \item Find the value of the following. |
|
103 |
|
104 \begin{itemize} |
|
105 \item sin(pi/4) |
|
106 \item ln(23) |
|
107 \end{itemize} |
|
108 |
|
109 \end{itemize} |
|
110 \end{frame} |
|
111 \begin{frame}[fragile] |
|
112 \frametitle{Solution 2} |
|
113 \label{sec-5} |
|
114 |
|
115 \lstset{language=Python} |
|
116 \begin{lstlisting} |
|
117 n(pi^2,digits=6) |
|
118 n(sin(pi/4)) |
|
119 n(log(23,e)) |
|
120 \end{lstlisting} |
|
121 \end{frame} |
|
122 \begin{frame} |
|
123 \frametitle{Question 3} |
|
124 \label{sec-6} |
|
125 |
|
126 \begin{itemize} |
|
127 \item Define the piecewise function. |
|
128 f(x)=3x+2 |
|
129 when x is in the closed interval 0 to 4. |
|
130 f(x)=4x$^2$ |
|
131 between 4 to 6. |
|
132 \item Sum of 1/(n$^2$-1) where n ranges from 1 to infinity. |
|
133 \end{itemize} |
|
134 \end{frame} |
|
135 \begin{frame}[fragile] |
|
136 \frametitle{Solution 3} |
|
137 \label{sec-7} |
|
138 |
|
139 \lstset{language=Python} |
|
140 \begin{lstlisting} |
|
141 var('x') |
|
142 h(x)=3*x+2 |
|
143 g(x)= 4*x^2 |
|
144 f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x) |
|
145 f |
|
146 \end{lstlisting} |
|
147 |
|
148 \lstset{language=Python} |
|
149 \begin{lstlisting} |
|
150 var('n') |
|
151 f=1/(n^2-1) |
|
152 sum(f(n), n, 1, oo) |
|
153 \end{lstlisting} |
|
154 \end{frame} |
|
155 \begin{frame} |
|
156 \frametitle{Question 4} |
|
157 \label{sec-8} |
|
158 |
|
159 \begin{itemize} |
|
160 \item Differentiate the following. |
|
161 |
|
162 \begin{itemize} |
|
163 \item sin(x$^3$)+log(3x), to the second order |
|
164 \item x$^5$*log(x$^7$), to the fourth order |
|
165 \end{itemize} |
|
166 |
|
167 \item Integrate the given expression |
|
168 |
|
169 \begin{itemize} |
|
170 \item x*sin(x$^2$) |
|
171 \end{itemize} |
|
172 |
|
173 \item Find x |
|
174 |
|
175 \begin{itemize} |
|
176 \item cos(x$^2$)-log(x)=0 |
|
177 \item Does the equation have a root between 1,2. |
|
178 \end{itemize} |
|
179 |
|
180 \end{itemize} |
|
181 \end{frame} |
|
182 \begin{frame}[fragile] |
|
183 \frametitle{Solution 4} |
|
184 \label{sec-9} |
|
185 |
|
186 \lstset{language=Python} |
|
187 \begin{lstlisting} |
|
188 var('x') |
|
189 f(x)= x^5*log(x^7) |
|
190 diff(f(x),x,5) |
|
191 |
|
192 var('x') |
|
193 integral(x*sin(x^2),x) |
|
194 |
|
195 var('x') |
|
196 f=cos(x^2)-log(x) |
|
197 find_root(f(x)==0,1,2) |
|
198 \end{lstlisting} |
|
199 \end{frame} |
|
200 \begin{frame} |
|
201 \frametitle{Question 5} |
|
202 \label{sec-10} |
|
203 |
|
204 \begin{itemize} |
|
205 \item Find the determinant and inverse of : |
|
206 |
|
207 A=[[x,0,1][y,1,0][z,0,y]] |
|
208 \end{itemize} |
|
209 \end{frame} |
|
210 \begin{frame}[fragile] |
|
211 \frametitle{Solution 5} |
|
212 \label{sec-11} |
|
213 |
|
214 \lstset{language=Python} |
|
215 \begin{lstlisting} |
|
216 var('x,y,z') |
|
217 A=matrix([[x,0,1],[y,1,0],[z,0,y]]) |
|
218 A.det() |
|
219 A.inverse() |
|
220 \end{lstlisting} |
|
221 \end{frame} |
|
222 \begin{frame} |
|
223 \frametitle{Summary} |
|
224 \label{sec-12} |
|
225 |
|
226 \begin{itemize} |
|
227 \item We learnt about defining symbolic expression and functions. |
|
228 \item Using built-in constants and functions. |
|
229 \item Using <Tab> to see the documentation of a function. |
|
230 \item Simple calculus operations . |
|
231 \item Substituting values in expression using substitute function. |
|
232 \item Creating symbolic matrices and performing operation on them . |
|
233 \end{itemize} |
|
234 \end{frame} |
|
235 \begin{frame} |
|
236 \frametitle{Thank you!} |
|
237 \label{sec-13} |
|
238 |
|
239 \begin{block}{} |
|
240 \begin{center} |
|
241 This spoken tutorial has been produced by the |
|
242 \textcolor{blue}{FOSSEE} team, which is funded by the |
|
243 \end{center} |
|
244 \begin{center} |
|
245 \textcolor{blue}{National Mission on Education through \\ |
|
246 Information \& Communication Technology \\ |
|
247 MHRD, Govt. of India}. |
|
248 \end{center} |
|
249 \end{block} |
|
250 \end{frame} |
|
251 |
|
252 \end{document} |
|