175, 275 -Homework 10 and suggestions for next week

Homework 10 is due Tuesday, November 18, at the beginning of lecture. The usual considerations apply.

In 175 we will try to cover this week until section 8.7 at least; it is possible this won’t happen until next week. Sections 8.3, 8.4, and 8.5 all introduce important tests for convergence of series; make sure you understand the arguments being presented (rather than just trying to memorize the tests). The material in section 8.6 is particularly important (conditional and absolute convergence). We will also cover some additional material on the p-series displaystyle sum_{n=1}^inftyfrac1{n^p}

Next week we will continue from section 8.7 (or at whatever point in the chapter we find ourselves at that point) on. We will also cover a few additional topics that the book doesn’t mention or doesn’t treat in sufficient detail, once we are done with 8.10. If you want to read ahead, the topics we will cover are uniform vs. pointwise convergence (including Wierstrass test) and infinite products. I will distribute notes of the topics not covered in the book.

In 275 we will cover from section 13.6 on, but the emphasis will be on section 13.8, and the notion of Jacobian. We will also present a few notions from linear algebra to make sense of the general version of the chain rule. Afterwards, we will continue with Chapter 14, which contains the main results from this course you are likely to use in the future. Chapter 14 will take some time to cover. 

Homework 10:

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

  • Turn in the problems listed for Homework 9  that you still have pending.
  • Section 8.4. Exercises 3, 12, 23, 26, 35, 38, 40.
  • Section 8.5. Exercises 4, 8, 10, 25, 31, 34, 44, 47.

Besides the exercises you have pending from last week, there are 15 new problems. Turn in the exercises you have pending, and at least 7 of the new problems. The others (at most 8) will be due December 2, together with the additional exercises for that week. 
275:  

  • Section 13.5. Exercises 4, 8, 19, 22, 30, 45.
  • Section 13.6. Exercises 6, 11, 24, 30.
  • Section 13.7. Exercises 13, 21, 37, 60, 78, 79.
  • Section 13.8. Exercise 1, 6, 16, 21.

There are 20 exercises this week. Turn in at least 10. The remaining problems (at most 10) will be due together with a few additional exercises on December 2.

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