70 \end{itemize} |
69 \end{itemize} |
71 |
70 |
72 |
71 |
73 \end{frame} |
72 \end{frame} |
74 \begin{frame}[fragile] |
73 \begin{frame}[fragile] |
75 \frametitle{Solutions 1} |
74 \frametitle{Solution 1} |
76 \label{sec-3} |
75 \label{sec-3} |
77 |
76 |
78 \begin{verbatim} |
77 \lstset{language=Python} |
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78 \begin{lstlisting} |
79 var('x,y') |
79 var('x,y') |
80 x^2+y^2 |
80 x^2+y^2 |
81 |
81 |
82 var('a,x,y') |
82 var('a,x,y') |
83 y^2-4*a*x |
83 y^2-4*a*x |
84 \end{verbatim} |
84 \end{lstlisting} |
85 \end{frame} |
85 \end{frame} |
86 \begin{frame} |
86 \begin{frame} |
87 \frametitle{Questions 2} |
87 \frametitle{Question 2} |
88 \label{sec-4} |
88 \label{sec-4} |
89 |
89 |
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90 |
90 \begin{itemize} |
91 \begin{itemize} |
91 \item Find the values of the following constants upto 6 digits precision |
92 \item Find the values of the following constants upto 6 digits precision |
92 |
93 |
93 \begin{itemize} |
94 \begin{itemize} |
94 \item pi$^2$ |
95 \item pi$^2$ |
95 \end{itemize} |
96 \item euler$_{\mathrm{gamma}}$$^2$ |
96 |
97 \end{itemize} |
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98 |
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99 \end{itemize} |
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100 |
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101 \begin{itemize} |
97 \item Find the value of the following. |
102 \item Find the value of the following. |
98 |
103 |
99 \begin{itemize} |
104 \begin{itemize} |
100 \item sin(pi/4) |
105 \item sin(pi/4) |
101 \item ln(23) |
106 \item ln(23) |
102 \end{itemize} |
107 \end{itemize} |
103 |
108 |
104 \end{itemize} |
109 \end{itemize} |
105 \end{frame} |
110 \end{frame} |
106 \begin{frame}[fragile] |
111 \begin{frame}[fragile] |
107 \frametitle{Solutions 2} |
112 \frametitle{Solution 2} |
108 \label{sec-5} |
113 \label{sec-5} |
109 |
114 |
110 \begin{verbatim} |
115 \lstset{language=Python} |
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116 \begin{lstlisting} |
111 n(pi^2,digits=6) |
117 n(pi^2,digits=6) |
112 n(sin(pi/4)) |
118 n(sin(pi/4)) |
113 n(log(23,e)) |
119 n(log(23,e)) |
114 \end{verbatim} |
120 \end{lstlisting} |
115 \end{frame} |
121 \end{frame} |
116 \begin{frame} |
122 \begin{frame} |
117 \frametitle{Question 2} |
123 \frametitle{Question 3} |
118 \label{sec-6} |
124 \label{sec-6} |
119 |
125 |
120 \begin{itemize} |
126 \begin{itemize} |
121 \item Define the piecewise function. |
127 \item Define the piecewise function. |
122 f(x)=3x+2 |
128 f(x)=3x+2 |
125 between 4 to 6. |
131 between 4 to 6. |
126 \item Sum of 1/(n$^2$-1) where n ranges from 1 to infinity. |
132 \item Sum of 1/(n$^2$-1) where n ranges from 1 to infinity. |
127 \end{itemize} |
133 \end{itemize} |
128 \end{frame} |
134 \end{frame} |
129 \begin{frame}[fragile] |
135 \begin{frame}[fragile] |
130 \frametitle{Solution Q1} |
136 \frametitle{Solution 3} |
131 \label{sec-7} |
137 \label{sec-7} |
132 |
138 |
133 \begin{verbatim} |
139 \lstset{language=Python} |
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140 \begin{lstlisting} |
134 var('x') |
141 var('x') |
135 h(x)=3*x+2 |
142 h(x)=3*x+2 |
136 g(x)= 4*x^2 |
143 g(x)= 4*x^2 |
137 f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x) |
144 f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x) |
138 f |
145 f |
139 \end{verbatim} |
146 \end{lstlisting} |
140 \end{frame} |
147 |
141 \begin{frame}[fragile] |
148 \lstset{language=Python} |
142 \frametitle{Solution Q2} |
149 \begin{lstlisting} |
143 \label{sec-8} |
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144 |
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145 \begin{verbatim} |
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146 var('n') |
150 var('n') |
147 f=1/(n^2-1) |
151 f=1/(n^2-1) |
148 sum(f(n), n, 1, oo) |
152 sum(f(n), n, 1, oo) |
149 \end{verbatim} |
153 \end{lstlisting} |
150 |
154 \end{frame} |
151 \end{frame} |
155 \begin{frame} |
152 \begin{frame} |
156 \frametitle{Question 4} |
153 \frametitle{Questions 3} |
157 \label{sec-8} |
154 \label{sec-9} |
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155 |
158 |
156 \begin{itemize} |
159 \begin{itemize} |
157 \item Differentiate the following. |
160 \item Differentiate the following. |
158 |
161 |
159 \begin{itemize} |
162 \begin{itemize} |
160 \item x$^5$*log(x$^7$) , degree=4 |
163 \item sin(x$^3$)+log(3x), to the second order |
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164 \item x$^5$*log(x$^7$), to the fourth order |
161 \end{itemize} |
165 \end{itemize} |
162 |
166 |
163 \item Integrate the given expression |
167 \item Integrate the given expression |
164 |
168 |
165 \begin{itemize} |
169 \begin{itemize} |
174 \end{itemize} |
178 \end{itemize} |
175 |
179 |
176 \end{itemize} |
180 \end{itemize} |
177 \end{frame} |
181 \end{frame} |
178 \begin{frame}[fragile] |
182 \begin{frame}[fragile] |
179 \frametitle{Solutions 3} |
183 \frametitle{Solution 4} |
180 \label{sec-10} |
184 \label{sec-9} |
181 |
185 |
182 \begin{verbatim} |
186 \lstset{language=Python} |
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187 \begin{lstlisting} |
183 var('x') |
188 var('x') |
184 f(x)= x^5*log(x^7) |
189 f(x)= x^5*log(x^7) |
185 diff(f(x),x,5) |
190 diff(f(x),x,5) |
186 |
191 |
187 var('x') |
192 var('x') |
188 integral(x*sin(x^2),x) |
193 integral(x*sin(x^2),x) |
189 |
194 |
190 var('x') |
195 var('x') |
191 f=cos(x^2)-log(x) |
196 f=cos(x^2)-log(x) |
192 find_root(f(x)==0,1,2) |
197 find_root(f(x)==0,1,2) |
193 \end{verbatim} |
198 \end{lstlisting} |
194 \end{frame} |
199 \end{frame} |
195 \begin{frame} |
200 \begin{frame} |
196 \frametitle{Question 4} |
201 \frametitle{Question 5} |
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202 \label{sec-10} |
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203 |
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204 \begin{itemize} |
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205 \item Find the determinant and inverse of : |
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206 |
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207 A=[[x,0,1][y,1,0][z,0,y]] |
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208 \end{itemize} |
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209 \end{frame} |
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210 \begin{frame}[fragile] |
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211 \frametitle{Solution 5} |
197 \label{sec-11} |
212 \label{sec-11} |
198 |
213 |
199 \begin{itemize} |
214 \lstset{language=Python} |
200 \item Find the determinant and inverse of : |
215 \begin{lstlisting} |
201 |
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202 A=[[x,0,1][y,1,0][z,0,y]] |
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203 \end{itemize} |
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204 \end{frame} |
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205 \begin{frame}[fragile] |
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206 \frametitle{Solution 4} |
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207 \label{sec-12} |
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208 |
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209 \begin{verbatim} |
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210 var('x,y,z') |
216 var('x,y,z') |
211 A=matrix([[x,0,1],[y,1,0],[z,0,y]]) |
217 A=matrix([[x,0,1],[y,1,0],[z,0,y]]) |
212 A.det() |
218 A.det() |
213 A.inverse() |
219 A.inverse() |
214 \end{verbatim} |
220 \end{lstlisting} |
215 \end{frame} |
221 \end{frame} |
216 \begin{frame} |
222 \begin{frame} |
217 \frametitle{Summary} |
223 \frametitle{Summary} |
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224 \label{sec-12} |
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225 |
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226 \begin{itemize} |
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227 \item We learnt about defining symbolic expression and functions. |
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228 \item Using built-in constants and functions. |
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229 \item Using <Tab> to see the documentation of a function. |
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230 \item Simple calculus operations . |
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231 \item Substituting values in expression using substitute function. |
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232 \item Creating symbolic matrices and performing operation on them . |
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233 \end{itemize} |
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234 \end{frame} |
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235 \begin{frame} |
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236 \frametitle{Thank you!} |
218 \label{sec-13} |
237 \label{sec-13} |
219 |
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220 \begin{itemize} |
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221 \item We learnt about defining symbolic |
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222 expression and functions. |
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223 \item Using built-in constants and functions. |
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224 \item Using <Tab> to see the documentation of a |
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225 function. |
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226 \end{itemize} |
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227 |
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228 |
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229 \end{frame} |
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230 \begin{frame} |
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231 \frametitle{Summary} |
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232 \label{sec-14} |
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233 |
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234 \begin{itemize} |
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235 \item Simple calculus operations . |
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236 \item Substituting values in expression |
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237 using substitute function. |
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238 \item Creating symbolic matrices and |
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239 performing operation on them . |
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240 \end{itemize} |
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241 \end{frame} |
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242 \begin{frame} |
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243 \frametitle{Thank you!} |
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244 \label{sec-15} |
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245 |
238 |
246 \begin{block}{} |
239 \begin{block}{} |
247 \begin{center} |
240 \begin{center} |
248 This spoken tutorial has been produced by the |
241 This spoken tutorial has been produced by the |
249 \textcolor{blue}{FOSSEE} team, which is funded by the |
242 \textcolor{blue}{FOSSEE} team, which is funded by the |