Homework 1

Due to the dropbox by 11:00pm on October 3, 2013

See Homework format for a discussion of formatting. Please use latex if possible for the analytical questions and turn in m-files (or Python scripts) for the coding parts, along with any results such as plots and required discussion of these. Using matlab publish or an IPython notebook is a nice way to combine them. Some samples of how you might do this will appear soon at Homework format.

There are some e-books listed in the Complex analysis section of the bibliography that may be useful if you need a review.

• Download the ATAP files and Chebfun and make sure this is working for you. See Software for the course for links and options.
• Do the following exercises from ATAP:

• Exercises 2.2, 2.4, 2.5, 3.1, 3.2, 3.7, 3.9.

• Do part (a) of Exercise 3.6 (Chebyshev series of sign(\(x\))). But note that there is a typo in the solution given in book – the exponent of \((-1)\) is wrong.

  Fix this and test your solution by computing and plotting the polynomial defined by the partial sums of degree 99 and 199. You should see that the agreement is better in the latter case except very close to the discontinuity. This Gibbs phenomenon will be studied further later.

  Note: the truncated Chebyshev series is not the same function as the Chebyshev interpolant and so the results should look similar to what’s shown in Chapter 9 for this function, but not identical for the same degree polynomial.