Homework 2

Submit via the Canvas page by 11:00pm on October 22, 2015. Homework can be submitted up to 24 hours late with a 10% reduction in points possible. If special circumstances warrant turning in assignments late, please make arrangements in advance.

• 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 2.4, 2.5, 3.1, 3.2, 3.7, 3.9, 4.1

• 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. (See the errata online if you want to check.)

  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.