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-Exercises
-=========
-
-#. Consider the iteration :math:`$x_{n+1} = f(x_n)$` where
- :math:`$f(x) = kx(1-x)$`. Plot the successive iterates of this
- process.
-
-#. Plot this using a cobweb plot as follows:
-
- #. Start at :math:`$(x_0, 0)$`
- #. Draw line to :math:`$(x_i, f(x_i))$`;
- #. Set :math:`$x_{i+1} = f(x_i)$`
- #. Draw line to :math:`$(x_i, x_i)$`
- #. Repeat from 2 for as long as you want
-
-#. Plot the Koch snowflake. Write a function to generate the necessary
- points given the two points constituting a line.
-
- #. Split the line into 4 segments.
- #. The first and last segments are trivial.
- #. To rotate the point you can use complex numbers, recall that
- :math:`$z e^{j \theta}$` rotates a point :math:`$z$` in 2D by
- :math:`$\theta$`.
- #. Do this for all line segments till everything is done.
-
-#. Show rate of convergence for a first and second order finite
- difference of sin(x)
-
-#. Given, the position of a projectile in in ``pos.txt``, plot it's
- trajectory.
-
- - Label both the axes.
- - What kind of motion is this?
- - Title the graph accordingly.
- - Annotate the position where vertical velocity is zero.
-
-#. Write a Program that plots a regular n-gon(Let n = 5).
-
-#. Create a sequence of images in which the damped oscillator
- (:math:`$e^{-x/10}sin(x)$`) slowly evolves over time.
-
-#. Given a list of numbers, find all the indices at which 1 is present.
- numbers = [1, 1, 3, 4, 3, 6, 7, 8, 1, 2, 4, 1]
-
-#. Given a list of numbers, find all the indices at which 1 is present.
- numbers = [1, 1, 3, 4, 3, 6, 7, 8, 1, 2, 4, 1]. Solve the problem using a
- functional approach.
-
-..
- Local Variables:
- mode: rst
- indent-tabs-mode: nil
- sentence-end-double-space: nil
- fill-column: 77
- End:
-