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+========
+ Script
+========
+
+{{{ show the welcome slide }}}
+
+Welcome to this tutorial on using Sage.
+
+{{{ show the slide with outline }}} 
+
+In this tutorial we shall quickly look at a few examples of the areas
+(name the areas, here) in which Sage can be used and how it can be
+used.
+
+{{{ show the slide with Calculus outline }}} 
+
+Let us begin with Calculus. We shall be looking at limits,
+differentiation, integration, and Taylor polynomial.
+
+{{{ show sage notebook }}}
+
+We have our Sage notebook running. In case, you don't have it running,
+start is using the command, ``sage --notebook``.
+
+To find the limit of the function x*sin(1/x), at x=0, we say::
+
+   lim(x*sin(1/x), x=0)
+
+We get the limit to be 0, as expected. 
+
+It is also possible to the limit at a point from one direction. For
+example, let us find the limit of 1/x at x=0, when approaching from
+the positive side.::
+
+    lim(1/x, x=0, dir='above')
+
+To find the limit from the negative side, we say,::
+
+    lim(1/x, x=0, dir='above')   
+
+Let us now see how to differentiate, using Sage. We shall find the
+differential of the expression ``exp(sin(x^2))/x`` w.r.t ``x``. We
+shall first define the expression, and then use the ``diff`` function
+to obtain the differential of the expression.::
+
+    var('x')
+    f = exp(sin(x^2))/x
+
+    diff(f, x)
+
+We can also obtain the partial differentiation of an expression w.r.t
+one of the variables. Let us differentiate the expression
+``exp(sin(y - x^2))/x`` w.r.t x and y.::
+
+    var('x y')
+    f = exp(sin(y - x^2))/x
+
+    diff(f, x)
+
+    diff(f, y)
+
+Now, let us look at integration. We shall use the expression obtained
+from the differentiation that we did before, ``diff(f, y)`` ---
+``e^(sin(-x^2 + y))*cos(-x^2 + y)/x``. The ``integrate`` command is
+used to obtain the integral of an expression or function.::
+
+    integrate(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y)
+
+We get back the correct expression. The minus sign being inside or
+outside the ``sin`` function doesn't change much. 
+
+Now, let us find the value of the integral between the limits 0 and
+pi/2. ::
+
+    integral(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y, 0, pi/2)
+
+Let us now see how to obtain the Taylor expansion of an expression
+using sage. Let us obtain the Taylor expansion of ``(x + 1)^n`` up to
+degree 4 about 0.::
+
+    var('x n')
+    taylor((x+1)^n, x, 0, 4)
+
+This brings us to the end of the features of Sage for Calculus, that
+we will be looking at. For more, look at the Calculus quick-ref from
+the Sage Wiki. 
+
+Next let us move on to Matrix Algebra. 
+
+{{{ show the equation on the slides }}}
+
+Let us begin with solving the equation ``Ax = v``, where A is the
+matrix ``matrix([[1,2],[3,4]])`` and v is the vector
+``vector([1,2])``. 
+
+To solve the equation, ``Ax = v`` we simply say::
+
+    x = solve_right(A, v)
+
+To solve the equation, ``xA = v`` we simply say::
+
+    x = solve_left(A, v)
+
+The left and right here, denote the position of ``A``, relative to x. 
+
+
+
+Now, let us look at Graph Theory in Sage. 
+
+Graph: G = Graph({0:[1,2,3], 2:[4]})
+Directed Graph: DiGraph(dictionary)
+Graph families: graphs. tab
+Invariants: G.chromatic polynomial(), G.is planar()
+Paths: G.shortest path()
+Visualize: G.plot(), G.plot3d()
+Automorphisms: G.automorphism group(), G1.is isomorphic(G2), G1.is subgraph(G2)
+
+Now let us look at bits and pieces of Number theory, combinatorics, 
+