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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.
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