--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/plotting_using_sage/script.rst Fri Oct 08 11:40:21 2010 +0530
@@ -0,0 +1,257 @@
+.. Objectives
+.. ----------
+
+.. A - Students and teachers from Science and engineering backgrounds
+ B -
+ C -
+ D -
+
+.. Prerequisites
+.. -------------
+
+.. 1. Getting started with lists
+
+.. Author : Nishanth Amuluru
+ Internal Reviewer :
+ External Reviewer :
+ Checklist OK? : <put date stamp here, if OK> [2010-10-05]
+
+Script
+------
+
+Hello friends, welcome to the tutorial on "Plotting using SAGE".
+
+{{{ Show the outline slide }}}
+
+In this tutorial we shall look at
+
+ * 2D plotting in SAGE
+ * 3D plotting in SAGE
+
+We shall first create a symbolic variable ``x``
+::
+
+ x = var('x')
+
+We shall plot the function ``sin(x) - cos(x) ^ 2`` in the range (-5, 5).
+::
+
+ plot(sin(x) - cos(x) ^ 2, (x, -5, 5))
+
+As we can see, the plot is shown.
+
+``plot`` command takes the symbolic function as the first argument and the
+range as the second argument.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 1 %% Define a variable ``y`` and plot the function ``y^2 + 5y - 7`` in the
+ range (-3, 3)
+
+{{{ continue from paused state }}}
+
+::
+
+ y = var('y')
+ plot(y^2 + 5*y -7, (y, -3, 3))
+
+We have seen that plot command plots the given function on a linear range.
+
+What if the x and y values are functions of another variable.
+For instance, lets plot the trajectory of a projectile.
+
+A projectile was thrown at 50 m/s^2 and at an angle of 45 degrees from the
+ground. We shall plot the trajectory of the particle for 5 seconds.
+
+These types of plots can be drawn using the parametric_plot function.
+We first define the time variable.
+::
+
+ t = var('t')
+
+Then we define the x and y as functions of t.
+::
+
+ f_x = 50 * cos(pi/4)
+ f_y = 50 * sin(pi/4) * t - 1/2 * 9.81 * t^2 )
+
+We then call the ``parametric_plot`` function as
+::
+
+ parametric_plot((f_x, f_y), (t, 0, 5))
+
+And we can see the trajectory of the projectile.
+
+The ``parametric_plot`` funciton takes a tuple of two functions as the first
+argument and the range over which the independent variable varies as the second
+argument.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 2 %% A particle is thrown into the air at 10 m/s^2 and at angle of 60 degrees
+ from the top of a 100 m tower. Plot the trajectory of the particle.
+
+{{{ continue from paused state }}}
+
+::
+
+ t = var('t')
+ f_x = 10 * cos(pi/3) * t
+ f_y = 100 + 10 * sin(pi/3) * t - 1/2 * 9.81 * t^2
+ parametric_plot((f_x, f_y), (t,0,5))
+
+Now we shall look at how to plot a set of points.
+
+We have the ``line`` function to acheive this.
+
+We shall plot sin(x) at few points and join them.
+
+First we need the set of points.
+::
+
+ points = [ (x, sin(x)) for x in srange(-2*float(pi), 2*float(pi), 0.75) ]
+
+``srange`` takes a start, a stop and a step argument and returns a list of
+point. We generate list of tuples in which the first value is ``x`` and second
+is ``sin(x)``.
+
+::
+
+ line(points)
+
+plots the points and joins them with a line.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 3 %% Plot the cosine function using line function.
+
+{{{ continue from paused state }}}
+
+::
+
+ points = [ (x, cos(x)) for x in srange(-2*float(pi), 2*float(pi), 0.75) ]
+ line(points)
+
+The ``line`` function behaves like the plot command in matplotlib. The
+difference is that ``plot`` command takes two sequences while line command
+expects a sequence of co-ordinates.
+
+As we can see, the axes limits are set by SAGE. Often we would want to set them
+ourselves. Moreover, the plot is shown here since the last command that is
+executed produces a plot.
+
+Let us try this example
+::
+
+ plot(cos(x), (x,0,2*pi))
+ # Does the plot show up??
+
+As we can see here, the plot is not shown since the last command does not
+produce a plot.
+
+The actual way of showing a plot is to use the ``show`` command.
+
+::
+
+ p1 = plot(cos(x), (x,0,2*pi))
+ show(p1)
+ # What happens now??
+
+As we can see the plot is shown since we used it with ``show`` command.
+
+``show`` command is also used set the axes limits.
+
+::
+
+ p1 = plot(cos(x), (x,0,2*pi))
+ show(p1, xmin=0, xmax=2*pi, ymin=-1.2, ymax=1.2)
+
+As we can see, we just have to pass the right keyword arguments to the ``show``
+command to set the axes limits.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 4 %% Plot the cosine function in the range (-2pi, 2pi) and set the x-axis
+ limits to (-5, 5) and y-axis limits to (-2, 2) respectively.
+
+{{{ continue from paused state }}}
+
+::
+
+ p1 = plot(cos(x), (x, 0, 2*pi))
+ show(p1, xmin=-5, xmax=5, ymin=-2, ymax=2)
+
+The ``show`` command can also be used to show multiple plots.
+::
+
+ p1 = plot(cos(x), (x, 0, 2*pi))
+ p2 = plot(sin(x), (x, 0, 2*pi))
+ show(p1+p2)
+
+As we can see, we can add the plots and use them in the ``show`` command.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 5 %% Plot sin(x) and sin(2*x) in the range (0, 2pi)
+
+{{{ continue from paused state }}}
+
+::
+
+ p1 = plot(sin(x), (x, 0, 2*pi))
+ p2 = plot(sin(2*x), (x, 0, 2*pi))
+ show(p1+p2)
+
+Now we shall look at 3D plotting in SAGE.
+
+We have the ``plot3d`` function that takes a function in terms of two
+independent variables and the range over which they vary.
+
+::
+
+ x, y = var('x y')
+ plot3d(x^2 + y^2, (x, 0, 2), (y, 0, 2))
+
+We get a 3D plot which can be rotated and zoomed using the mouse.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 6 %% Plot the function sin(x)^2 + cos(y)^2 for x in range (0,2) and y in
+ range (-2, 2)
+
+{{{ continue from paused state }}}
+
+::
+
+ x, y = var("x y")
+ plot3d( sin(x)^2 + cos(y)^2, (x, 0, 2), (y, -2, 2))
+
+``parametric_plot3d`` function plots the surface in which x, y and z are
+functions of another variable.
+
+::
+
+ u, v = var("u v")
+ f_x = u
+ f_y = v
+ f_z = u^2 + v^2
+ parametric_plot3d((f_x, f_y, f_z), (u, 0, 2), (v, 0, 2))
+
+{{{ Show summary slide }}}
+
+This brings us to the end of the tutorial.
+we have learnt
+
+ * How to draw 2D plots using plot comand
+ * How to use the parametric_plot and line functions
+ * How to use show command for multiple plots and setting axes limits
+ * How to draw 3D plots
+
+{{{ Show the "sponsored by FOSSEE" slide }}}
+
+#[Nishanth]: Will add this line after all of us fix on one.
+This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India
+
+Hope you have enjoyed and found it useful.
+Thankyou
+