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-
-#+TITLE:   Getting started with symbolics
-#+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
-
-* 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
-  - Define the following expression as symbolic
-    expression in sage.
-
-    - x^2+y^2
-    - y^2-4ax
-  
-* Solution 1
-#+begin_src python
-  var('x,y')
-  x^2+y^2
-
-  var('a,x,y')
-  y^2-4*a*x
-#+end_src python
-* Question 2
-  - Find the values of the following constants upto 6 digits  precision 
-   
-    - pi^2
-    - euler_gamma^2
-   
-      
-  - Find the value of the following.
-
-   - sin(pi/4)
-   - ln(23)  
-
-* Solution 2
-#+begin_src python
-  n(pi^2,digits=6)
-  n(sin(pi/4))
-  n(log(23,e))
-#+end_src python
-* Question 3
-  - Define the piecewise function. 
-   f(x)=3x+2 
-   when x is in the closed interval 0 to 4.
-   f(x)=4x^2
-   between 4 to 6. 
-   
-  - Sum  of 1/(n^2-1) where n ranges from 1 to infinity. 
-
-* Solution 3
-#+begin_src python
-  var('x') 
-  h(x)=3*x+2 
-  g(x)= 4*x^2
-  f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x)
-  f
-#+end_src python
-
-#+begin_src python  
-  var('n')
-  f=1/(n^2-1) 
-  sum(f(n), n, 1, oo)
-#+end_src python  
-
-* Question 4
-  - Differentiate the following. 
-      
-    - sin(x^3)+log(3x), to the second order
-    - x^5*log(x^7), to the fourth order
-
-  - Integrate the given expression 
-      
-    - x*sin(x^2) 
-
-  - Find x
-    - cos(x^2)-log(x)=0
-    - Does the equation have a root between 1,2. 
-
-* Solution 4
-#+begin_src python
-  var('x')
-  f(x)= x^5*log(x^7) 
-  diff(f(x),x,5)
-
-  var('x')
-  integral(x*sin(x^2),x) 
-
-  var('x')
-  f=cos(x^2)-log(x)
-  find_root(f(x)==0,1,2)
-#+end_src
-
-* Question 5
-  - Find the determinant and inverse of :
-
-      A=[[x,0,1][y,1,0][z,0,y]]
-
-* Solution 5
-#+begin_src python  
-  var('x,y,z')
-  A=matrix([[x,0,1],[y,1,0],[z,0,y]])
-  A.det()
-  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!
-#+begin_latex
-  \begin{block}{}
-  \begin{center}
-  This spoken tutorial has been produced by the
-  \textcolor{blue}{FOSSEE} team, which is funded by the 
-  \end{center}
-  \begin{center}
-    \textcolor{blue}{National Mission on Education through \\
-      Information \& Communication Technology \\ 
-      MHRD, Govt. of India}.
-  \end{center}  
-  \end{block}
-#+end_latex
-
-
-