Math 199 Past Preparation Assignments

Complete list of past reading assignments, Spring 2009

For Friday, January 23: Please read the course information document completely. Next time we will cover Section 6.2, on integration by parts, so please also read in detail pages 514-516 in your text and at least skim the rest of the section. You'll turn in exercise 3 and your reading question at the beginning of class on Friday.
For Monday, January 26: We will cover the material on pages 521 to 525 of your text (note that this is only half of Section 6.3). Read with attention all the text of the section through Example 3.1. Make sense of Examples 3.4 and 3.6 (and read the paragraphs just before each one). Skim the rest of the material. Write up an answer to problem 1 in the exercises (not Writing Exercise 1). Make sure to show all your steps, and turn that and your reading question in on Monday.
For Wednesday, January 28: Next time we'll finish the material in Section 6.3. Carefully read all of the section beginning with the heading "Trigonometric substitution" on page 525. Make sure you understand the three examples. Prepare the solution to Exercise 17 to turn in; make sure to show all your steps. Also, don't forget to write down a question you have after doing the reading.
For Friday, January 30: Next time we’ll have a quiz on Sections 6.2 and 6.3; come prepared for that. After that we will go over how to integrate integrals with quadratic denominators; you actually already know everything you need to solve these problems, but it will be important to review it before moving on to Section 6.4. So the reading assignment comes from back in Section 6.1. I’d like you to read through Examples 1.4 and 1.5 on pages 511-512, paying attention to the details of the problems (ugly as they may seem at first). If you need a review on completing the square, I’d recommend the following two example videos online:
- http://www.youtube.com/watch?v=A9s1RtFls64
- http://www.youtube.com/watch?v=GV2OVD7bKKY
Then work exercise 23 in Section 6.1, and, as always, write a question about what you’ve read (or watched).
For Wednesday, February 4 (Class cancelled Monday, Feb. 2): We'll move on next time to Section 6.4. Read with attention all the text through Example 4.2, and Remark 4.1 on page 532. Also read the "Brief Summary of Integration Techniques" portion at the end of the section. Skim the rest of the section, and write up Exercise 1 and a reading question to turn in next time.
For Friday, February 6: Friday we will review integration techniques; there will be no new reading for class. Instead, look at problems 1-44 of the Review Exercises beginning on page 561. From this list, write out the solution for (1) a problem using u-substitution or integration by parts, (2) an integral involving powers of trig functions or a trigonometric substitution, and (3) an integral whose solution involves partial fractions. Also, as usual, write down a question---this time it can be about anything we've covered so far.
For Monday, February 9: On Monday we'll cover the first half of Section 6.6 on improper integrals. Read the section from the beginning through the end of Example 6.7 on page 552. Skim the rest of the section through Example 6.10, and prepare Exercise 1 and a written question to turn in.
For Wednesday, February 11: On Wednesday we will finish Section 6.6 on improper integrals. Read all of pages 555 and 556 of your text (including Example 6.13) and the paragraph at the bottom of page 557. Skim the other examples of the comparison test, and reread any parts you'd like from the first half of the section. Prepare Exercise 39 and a reading question to be turned in in class.
For Friday, February 13: On Friday we will review for the first midterm, which will be given during class on Monday and cover all of Chapter 6 (with the exception of Section 6.5). The first hour will involve an INTEGRATION BEE, where you will be competing as tables to see who are our class champs at integration. There will be prizes for the winners, so come ready to compete. For the second hour, we'll just be asking and answering questions, so please come to class having prepared questions to ask. Also, please try to have worked as many problems as possible from the review at the end of Chapter 6 in your text (including those 44 integrals!).
For Friday, February 20: On Friday we will cover Section 8.1. Read pages 612, 613, and 615 in your text, and skim the rest of the section. Prepare Exercises 1 and 5(a) to submit in class, along with a question you had while reading.
For Monday, February 23: On Monday we will begin our study of Section 8.2 in the text. Please read pages 626 through the end of Example 2.3 on page 629, and the two sentences immediately following the example. Then skim the rest of the section. For your preparation assignment, please turn in Exercise 26 (you might need a calculator for that one--send me an email if that's a problem for you) and, as always, a question you had while reading.
For Wednesday, February 25: ReadTheorem 2.2 on page 631 and the paragraph right above it. Then read the kth-Term Test for Divergence, the paragraph right after it, and Remark 2.1 on page 632. To finish off Section 8.2, read Example 2.7. Then turn over to Section 8.3 and read the first paragraph of the section (page 836), followed by Theorem 3.1 (try to understand what the pictures on page 637 are demonstrating), and Example 3.1. Then skim the rest of pages 639 and 640. Write up Writing Exercise #2 at the top of page 634; also, use the Integral Test to do exercise 9 on page 646. Finally, write down a reading question, and turn these things in on Wednesday.
For Friday, February 27: Next time we will learn about the integral test and the comparison tests in Section 8.3. The best way to learn about these tests is to see examples and work problems yourself. For that reason, the reading assignment will be a bit longer. Please skim (again) the argument on pages 636 and 637, and then reread Theorem 3.1 and Example 3.1, followed by the boxed statement on page 639. Read Theorem 3.3 on page 641 and the paragraph directly above and below it. Then read Examples 3.5, 3.6, and 3.7, and the paragraph after Example 3.7. Read Theorem 3.4 and Examples 3.8 and 3.9. For your problem, test the convergence of the sum, from k = 1 to infinity, of 4/(4k-2), and do it in three ways--once using the integral test, once by using the comparison test (comparing it to the harmonic series), and once more by using the limit comparison test (again using the harmonic series). And again, don't forget to write down a reading question!
For Monday, March 2: On Monday we will continue our discussion of the comparison tests from today's worksheet. For next time, review Examples 3.5 through 3.9 in Section 8.3, especially Example 3.7. Write up answers to Writing Exercises 1 and 4 at the end of Section 8.3, and write down a question you have on series--this time it can be about anything having to do with what we've covered so far.
For Wednesday, March 4: We will cover Section 8.4 on Wednesday. Please come to class having read from the beginning of the section up through the statement of Theorem 4.1 (the Alternating Series Test), as well as Examples 4.2, 4.3, and 4.4. Then read Theorem 4.2 and Example 4.5. Prepare Writing Exercise 4 and (regular) Exercise 1 to turn in during class, along with a reading question.
For Friday, March 6: For Friday please read Section 8.5 through Theorem 5.1, and read Example 5.3, the paragraph after it, and the box containing the Ratio Test (page 658). Then read Examples 5.4 through 5.7. Prepare Exercise 11 to turn in on Friday, along with a reading question. The Ratio Test may or may not seem pretty straightforward to you, so feel free to get creative with your questions.
For Monday, March 9: Read the section on the Root Test (page 661) and the "Summary of Convergence Tests" that follows it. Then, using the Root Test and the fact that the limit of k^1/k as k approaches infinity is 1, answer Exercise 11 on page 663. Turn that problem and a reading question in on Monday.
For Wednesday, March 11: Next time we'll review all the series convergence tests. There will be nothing to turn in for next time, but in order to be ready, you should work all the problems on Monday's worksheet, all of the extra practice series at the end of Worksheet #13, and some exercises from Section 8.5 in your text.
For Friday, March 13: Again, there will be nothing to turn in next time. Spend your time going over Worksheet #19 and preparing for the test. Be sure to note the times and locations of the mock exam and midterm, listed above.
For Friday, 3/20: On Friday we will talk more about power series and how they relate to functions (and why they're awesome). In preparation for that, please read the paragraphs between Examples 6.4 and 6.5 on pages 667 through 668 of your text, and Example 6.6 through the end of the section. Prepare and turn in a reading question and an answer to the following question: The geometric series formula shows that a/(1-x) is equal to the summation of ax^k as goes from 0 to infinity (assuming that |x|<1). Using that fact, what function does the sum from k = 0 to infinity of kax^k-1 equal when it converges?
For Monday, 3/30: After the break, we will spend a week and a half going over Sections 8.7 and 8.8 on Taylor series. For Monday, March 30, please read Section 8.7 from the beginning through Example 7.2. Work Exercise 1 from the section, showing all your work, and write down a reading question.
For Wednesday, 4/1: Be sure to try to get through all of Monday's worksheet. On Wednesday you'll discuss the remainder term, which will give us an idea of how far off Taylor series approximations can be. In preparation for class, please read Theorem 7.1 and the paragraph that follows it on page 675, and then skip over to Examples 7.6 and 7.7 and read those. Prepare Problem 27 to turn in, along with a reading question.
For Friday, 4/3: Friday we will conclude our discussion of Section 8.7 in the text by seeing some shortcuts for finding Taylor series. In preparation, please read Example 7.8 on pages 681 and 682 of your text. Prepare Exercise 35 and a reading question for turning in. The quiz on Friday will cover Section 8.7.
For Monday, 4/6: Monday we will begin our discussion of Section 8.8. This section contains many applications of Taylor series. We've already talked about one--using Taylor series to approximate functions, like in Problems 2 and 4 above. In preparation for Monday's class, read about some other applications in Examples 8.3, 8.4, and 8.5 on pages 687-689 of your text. Prepare Exercises 7 and 15 and a reading question to turn in.
For Wednesday, 4/8: Because of time concerns, we will not be covering the binomial series, which is found towards the end of Section 8.8; there's not much to it---it's just another power series, though it's very useful in practice, and I'd encourage you to read up on it (pages 691 to 692 of your text) for your own personal enrichment. On Wednesday we’ll begin Chapter 9 by covering (all of) Section 9.1 on parametrically defined curves. Please read the first two examples in detail, and skim the rest of the section. Prepare Exercises 1 and 3 to turn in along with a reading question.
For Friday, 4/10: On Friday we will begin Section 9.2 on Calculus and Parametric Equations. Please read the section up to, but not including, Theorem 2.2 on page 730. Work exercises 1, 9, and 15, and turn these and a readinq question in on Friday.
For Monday, 4/13: On Monday we'll finish Section 9.2 by learning about the area enclosed by a parametric curve. Please read from Theorem 2.2 on page 730 through the end of the section, and then prepare Exercise 21 and a reading question to hand in.
For Wednesday, April 15: On Wednesday we'll cover Section 9.3, discussing how to find the lengths of parametric curves and the surface area of solids of revolution. Please read Theorem 3.1 on page 735 and Examples 3.1, 3.2; then read from halfway down page 738 ("Much as we did in section 5.4...") through the boxed formula at the top of page 739, followed by Example 3.6. Turn in a reading question and the following problems:
- Using the parametric formula for arc length, find the length of the curve x = t², y = t³ between t = 0 and t = 1.}
- Find the surface area when the curve x = r cos t, y = r sin t, with t between 0 and pi, is revolved around the x-axis.