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diff --git a/getting_started_with_symbolics/slides.org b/getting_started_with_symbolics/slides.org index 5d9391e..15d793b 100644 --- a/getting_started_with_symbolics/slides.org +++ b/getting_started_with_symbolics/slides.org @@ -18,7 +18,7 @@ #+LaTeX_HEADER: commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, #+LaTeX_HEADER: showstringspaces=false, keywordstyle=\color{blue}\bfseries} -#+TITLE: Getting started with symbolics +#+TITLE: #+AUTHOR: FOSSEE #+EMAIL: #+DATE: @@ -29,15 +29,37 @@ #+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 -* Outline - - Defining symbolic expressions in sage. - - Using built-in constants and functions. - - Performing Integration, differentiation using sage. - - Defining matrices. - - Defining Symbolic functions. - - Simplifying and solving symbolic expressions and functions. - -* Question 1 +* +#+begin_latex +\begin{center} +\vspace{12pt} +\textcolor{blue}{\huge Getting started with Symbolics} +\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, + + - Define symbolic expressions in sage. + - Use built-in constants and functions. + - Perform Integration, differentiation using sage. + - Define matrices. + - Define Symbolic functions. + - Simplify0and solve symbolic expressions and functions. + +* Pre-requisite + Spoken tutorial on - + - Getting started with Sage Notebook. +* Exercise 1 - Define the following expression as symbolic expression in sage. @@ -52,11 +74,11 @@ var('a,x,y') y^2-4*a*x #+end_src python -* Question 2 +* Exercise 2 - Find the values of the following constants upto 6 digits precision - pi^2 - - euler_gamma^2 + - euler\_gamma^2 - Find the value of the following. @@ -70,7 +92,7 @@ n(sin(pi/4)) n(log(23,e)) #+end_src python -* Question 3 +* Exercise 3 - Define the piecewise function. f(x)=3x+2 when x is in the closed interval 0 to 4. @@ -94,7 +116,7 @@ sum(f(n), n, 1, oo) #+end_src python -* Question 4 +* Exercise 4 - Differentiate the following. - sin(x^3)+log(3x), to the second order @@ -122,8 +144,8 @@ find_root(f(x)==0,1,2) #+end_src -* Question 5 - - Find the determinant and inverse of : +* Exercise 5 + - Find the determinant and inverse of A=[[x,0,1][y,1,0][z,0,y]] @@ -135,23 +157,45 @@ A.inverse() #+end_src * Summary - - We learnt about defining symbolic expression and functions. - - Using built-in constants and functions. - - Using <Tab> to see the documentation of a function. - - Simple calculus operations . - - Substituting values in expression using substitute function. - - Creating symbolic matrices and performing operation on them . -* Thank you! +In this tutorial, we have learnt to, + +- Define symbolic expression and functions using the method ``var``. +- Use built-in constants like pi,e,oo and functions like + sum,sin,cos,log,exp and many more. +- Use <Tab> to see the documentation of a function. +- Do simple calculus using functions like -- + - diff()--to find a differential of a function + - integral()--to integrate an expression + - simplify--to simplify complicated expression. +- Substitute values in expressions using ``substitute`` function. +- Create symbolic matrices and perform operations on them like -- + - det()--to find out the determinant of a matrix + - inverse()--to find out the inverse of a matrix. +* Evaluation +1. How do you define a name 'y' as a symbol? + +2. Get the value of pi upto precision 5 digits using sage? + +3. Find third order differential function of + + f(x)=sin(x^2)+exp(x^3) +* Solutions + 1. var('y') + + 2. n(pi,5) + + 3. diff(f(x),x,3) +* #+begin_latex \begin{block}{} \begin{center} - This spoken tutorial has been produced by the - \textcolor{blue}{FOSSEE} team, which is funded by the + \textcolor{blue}{\Large THANK YOU!} \end{center} + \end{block} +\begin{block}{} \begin{center} - \textcolor{blue}{National Mission on Education through \\ - Information \& Communication Technology \\ - MHRD, Govt. of India}. + For more Information, visit our website\\ + \url{http://fossee.in/} \end{center} \end{block} #+end_latex |