--- a/odes.org	Wed Apr 28 16:33:18 2010 +0530
+++ b/odes.org	Thu Apr 29 17:59:25 2010 +0530
@@ -11,40 +11,36 @@
     
     In this tutorial we shall look at solving Ordinary Differential Equations,
     ODE henceforth using odeint in Python. In this tutorial we shall be using
-    the concepts of arrays, functions and lists which we have covered in various
+    the concepts of arrays, functions and lists which we have covered in 
     previous tutorials.
 
     Let's consider the classic problem of the spread of an epidemic in a
     population.
     This is given by the ordinary differential equation dy/dt = ky(L-y) 
     where L is the total population and k is an arbitrary constant. For our
-    problem Let us use L=25000, k=0.00003.
+    problem Let us use L=250000, k=0.00003.
     Let the boundary condition be y(0)=250.
 
     Let's now fire up IPython by typing ipython -pylab interpreter.    
     
-    As we saw in one of earlier session, sometimes pylab wont 'import' all
-    packages. For solving 'ordinary differential equations' also we shall
-    have to import 'odeint' function which is a part of the SciPy package.
+    As we saw in one of the earlier sessions, sometimes we will need more than 
+    pylab to get our job done. For solving 'ordinary differential equations'
+    we shall have to import 'odeint' function, which is a part of the SciPy package.
     So we run the magic command:
 
     In []: from scipy.integrate import odeint
 
-    For now just remember this as a command that does some magic to obtain
-    the function odeint in to our program.
     The details regarding `import' shall be covered in a subsequent tutorial.
 
     We can represent the given ODE as a Python function.
     This function takes the dependent variable y and the independent variable t
     as arguments and returns the ODE.
-    Our function looks like this:
-    (Showing the slide should be sufficient)
 
     Let us now define our function.
 
     In []: def epid(y, t):
       ....     k = 0.00003
-      ....     L = 25000
+      ....     L = 250000
       ....     return k*y*(L-y)
 
     Independent variable t can be assigned the values in the interval of
@@ -118,13 +114,10 @@
 
     In []: pend_sol = odeint(pend_int, initial,t)
 
-    In []: plot(pend_sol[0], t) plot theta against t
-    In []: plot(pend_sol[1], t) will plot omega against t
-    Plotting theta against t and omega against t we obtain the plots as shown
-    in the slide.
+    In []: plot(pend_sol)
+    This gives us 2 plots. The green plot is omega vs t and the blue is theta vs t.
 
-    Thus we come to the end of this tutorial on solving ordinary differential
-    equations in Python. In this tutorial we have learnt how to solve ordinary
+    Thus we come to the end of this tutorial. In this tutorial we have learnt how to solve ordinary
     differential equations of first and second order.
 
 *** Notes