175, 275 -Homework 9 and suggestions for next week

Homework 9 is due Tuesday, November 11, at the beginning of lecture. The usual considerations apply.

In 175 we will try to cover this week until section 8.4 at least, but probably we won’t get there until next week. The key section here is 8.2; make sure you understand the notions discussed in 8.2 before going further. If you want to read ahead from 8.4, continue with sections 8.5 and 8.6; the difference between conditional and absolute convergence is very important here.

In 275 we will cover from section 13.4 on, and the goal is to reach 13.8, which probably won’t happen until next week or even the one after if things do not go well. Besides these topics, I will discuss the `mean value property’ of harmonic functions.

Homework 9:

175: Do not use the solutions manual for any of these problems. 

  • Section 8.1. Exercises 86, 88, 127. Also, the following exercise:

Starting with a given x_0, define the subsequent terms of a sequence by setting x_{n+1}=x_n+sin(x_n). Determine whether the sequence {x_n} converges, and if it does, find its limit. More precisely: You must indicate for which values of x_0 the sequence diverges, and for which it converges, and for those that converges, you must identify the limit, which may again depend on x_0. You may want to try studying the sequence with different initial values of x_0 (choose a large range of possible values) to get a feeling for what is going on. 

  • Section 8.2. Exercises 14, 22, 38, 40 (do not use a calculator for this one; you can use that 2<e<3<pi if necessary), 64-68, 71.
  • Section 8.3. Exercises 26, 35, 41, 43, 44.

There are 19 problems in total. Turn in at least 10. The others (at most 9) will be due November 18 together with a few additional exercises for that week. I suggest you start working on these problems early, as some may be a bit longer than usual.


  • Section 13.2. Exercises 5, 17, 39, 47, 54.
  • Section 13.3. Exercises 13, 16, 21.
  • Section 13.4. Exercise 27, 36.

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