I'll begin the semester by talking about two- and three-dimensional space, and describing gravitational and electrostatic force fields in vector notation.

Read Chapter 12, Sections 1 and 2. To make sure you understand what you need to, on your own, do the odd-numbered problems 1-11 in Section 12.1, and the odd-numbered problems 1-17 in Section 12.2.

Read Section 12.3. Do problems 1, 3, 7, 9, 13, 15, 17, 25, 39, 41, 53, 55, 61, 63.
 

On Monday you can sign up for problems to turn in on Monday, February 3rd. To look at the problems that will be available, look at this copy of the sign-up sheet.

The Special Test, scheduled for Monday, February 10, will cover mainly Sections 7.1 through 7.4, plus 7.8. I'll devote this week to the material it will cover. To prepare for the test, read the sections carefully and do these problems to do on your own:
7.1: odds 1-25.
7.2: 1, 3, 7, 9, 19, 21, 23, 41.
7.3: 1, 3, 5, 7, 9, 31.
7.4: 1, 3, 5, 7, 9, 13, 15, 17, and 55 (without using formula (6)).
7.8: odds 1-39.
Ask in class about any problems or any passages of the text that give you difficulty.

Practice Tests 1 and 2 may be useful.

Your success in this course will depend in part on your background--either on how good it is, or on how well you repair the deficiencies. It's entirely normal to need review. You should feel free to ask questions in class and to ask me for help outside of class with the earlier material. In fact, you're responsible for doing so, and for systematically going back to re-read and re-learn things you need to know. Here are some suggestions of sections in Stewart's book that are particularly important. What I suggest you do is to read these sections carefully, and be sure that you understand the Examples in the sections and how to do problems like them. It may well be that there is some of this material that you have not studied before, and some that you've studied but still need help on.
3.1: Polynomials, exponential functions.
3.4: Trigonometric functions.
3.5: The Chain Rule.
3.7: Hyperbolic functions.
3.8 and 5.6: Logarithms.
5.3 and 5.4: The Fundamental Theorem of Calculus.
5.5: The substitution method.
 

Problem Set 1 is due on Monday. You may turn in up to 30 points' worth of problems that you have signed up for. Feel free to work together with others in the class. Feel free to ask me for help, in my office or by email.

In grading a problem on homework or a test, I use a numerical scale from 0 to 10, thus: 8.5 to 10, A; 6.5 to 8.4, B; 4.5 to 6.4, C; 2.5 to 4.4, D. Interpret all scores according to that conversion table, not as percentages. Here's a link to a statement of criteria for the grades, but the number/letter conversion table at the bottom of that statement is incorrect.

If you receive a rating of less than 7.0 on a problem, that problem will not count. You can work an additional problem later to make up for it. Thus for example, if you do three problems and get scores of 10, 9, and 6, then I'll record "19 out of 20," and you'll have 20 "basis points" toward your semester's requirement.

Throughout this week, I'll continue to devote class time to integration technique. The test is on Monday, February 10. It will be closed-book, closed-notes, no-calculators, no-computers; bare hands.
 

Test on Monday. Beginning on Tuesday, the subject will be parametrized curves. Read Section 10.1 and do these problems on your own: every 4th one: 1, 5, 7, ..., 21. Also do 22 and 29. Later in the week, do these: 23, 27, 31, 39.

Problem Set 2 will be due Tuesday, February 18. To look at the problems that will be available, look at this copy of the sign-up sheet.

If you need a rematch on Test 1, you can sign up in class on Thursday for any time within the hours of the department's make-up lab during the next two weeks. The lab is run by Nam Kwon in Lockett 284, 3:30 to 5:00 p.m. on Mondays and Wednesdays, 7:30 to 9:00 a.m. on Tuesdays and Thursdays.
 

In Section 10.2, pay special attention to the area problems and to Example 3. On your own, do 33, 35, and 37. In Section 10.3, study arclength problems carefully, like Examples 1, 2. On your own, do the odds 1-15. Study Section 10.4 thoroughly; on your own, do the odds 1-29; and 56.

Problem Set 3 will be due Thursday, February 27. To look at the problems that will be available, look at the sign-up sheet, which I'll pass around Wednesday 2/19.
 

Problem Set 4 will be due Thursday, March 6. The sign-up sheet will be available at this link by Tuesday 2/25.

I suggest a second careful study of Section 10.4. Pay special attention to the method for finding tangents to polar curves, and to Example 11. On your own, do 57, 59, 61, 63, 65, and 67; sketch the curves in those problems, and sketch the tangent lines that are mentioned.

With regard to Example 11 and Figure 17: A natural question is, what's the smallest value of p such that the set of all points ((r,t)) satisfying r=sin(8t/5) is obtained if you just consider 0 < t < p? With the help of a little experimentation with the computer, and a little thought, we found that the answer is p=10 pi. Another way to put the question is: Find the smallest p such that x(t+p)=x(t) and y(t+p)=y(t) for all t. (That's where x(t)=sin(8t/5)cos(t), y(t)=sin(8t/5)sin(t) are a Cartesian parametrization of the curve.) If we pick p to fit that criterion, then it's clear that to use t beyond the interval [0,p] is to start re-tracing points on the graph a second time. To problems 73 and 75 to make sure you understand the problem of finding "p." Of course in some cases, like problem 56(c), there is no p, and it's necessary to use all real t to get the whole curve.

Read the part of Section 10.5 dealing with areas. On your own, do problems 1, 5, 7, 9, 13, 21, 27, 29, 31, 33.

Read Section 10.6. Do problems 1, 5, 11, 13, 19, and 21.
 

Prepare for Test 2, which will be March 10. It will cover the material from Weeks 4, 5, and 6. The lecture on March 6 will be a quick review.
 

The next problem set will be due Thursday, March 20. The sign-up sheet, which you can find at this link, will be passed around on Wednesday. Pay attention to the instructions on the sign-up sheet. Please try to do a good job of exposition (readability, neatness, clarity) on your problems, and always provide a sketch when one will be of use. Feel free to come see me or email me for hints. Notice that the double-asterisk problems must be signed-up for by a team of two persons, who will then share the 40 points.

Read Section 10.6 again, this time focussing on hyperbolas.

• Notice that in drawing by hand a hyperbola, it's a big help to draw the asymptotes first.
• Study the geometric definition of the hyperbola at the bottom of p. 678. Do problem 46 on your own.
• Study the reflection property of the hyperbola, stated in problem 54. (No need to do this problem unless you want to.)

Study Section 10.7, on conics and polar coordinates. On your own, do the odds 1-17 in 10.7.
 

Review Sections 12.1, 12.2, and 12.3 and read Section 12.4 on the cross product. In 12.4, on your own, do these problems: 1, 3, 5, 9, 11, 15, 17, 19, 23, 25, 27, 29, 39, 41, 42, 43, 45. The objective is to become thoroughly familiar with the cross product.

Read Section 12.5, on equations of lines and planes. On your own, do these problems: 1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 25, 29, 33, 35, 43, 57, 63, 65. The objective is to learn how to use the tools of this chapter to deal with basic problems concerning points, lines, and planes in 3-space.

Problem Set 6 will be due Thursday, March 27. The sign-up sheet will be passed around on Wednesday
 

Keep on studying Chapter 12, Sections 1-5, and doing the problems there. Be sure to write out the proofs called for in 12.4:42 and 43. Doing these problems thoughtfully is probably essential to learning the material. There's an interplay between the computations and the visualization. It's the geometrical pictures that clarify everything eventually.

Read Section 13.1. On your own, do problems 7-12 and the odds 13-31.

Read Section 13.2. On your own, do problems 1, 3, 11, 15, 17, 19, 29, 45, 47, 49, 51.
 

Read Section 13.3. On your own, do problems 1, 3, 7, 11, 13, 15, 17.

Read Section 13.4. On your own, do problems 3, 5, 7, 9, 15, 19, 21, 25.

Problem Sets 7 and 8 will be due Thursday, April 3 and Thursday, April 10 respectively. The sign-up sheets will be passed around Monday, March 31, and both are available to look at at this link.
 

Test 3 on Monday will cover the material of Weeks 9, 10, and 11.

The remainder of the semester will be devoted to infinite sequences and series, including most of Chapter 11. We'll begin with a discussion of complex numbers, so that we can cover the case of complex-valued series. Read Basic Tools, the handout I gave you which is one section of a certain textbook on complex analysis. Do the fifteen problems there, on your own. Next, Read Section 11.1 of the text and do these problems on your own: odds 1-13, 17, 21, 25, 29, 33, 37. Read Section 11.2 and do these problems on your own: odds 1-37.
 

Review Section 11.1, paying special attention to the ten numbered definitions and theorems.

Review Section 11.2, paying special attention to the numbered items 1-8 and the Examples 2, 3, 4, 6, and 9. . Example 6 is called a telescoping sum, the kind of thing that's a little hard to recognize. Example 7 gives you a proof that the harmonic series diverges. I proved that in class using the integral test.

Read Section 11.3 on the integral test and estimates of sums. On your own, do the odd-numbered problems 1-23.

Read Section 11.4 on the comparison tests. On your own, do the odd-numbered problems 1-31.

Problem Set 9 is due Thursday, April 23. There's no sign-up sheet. You may work alone or in a team of 2, 3, or 4. If you work in a team, you'll share the total score. A paper done by n people should deal with precisely 3n problems. Everyone should try to bring his or her number of basis points up to 210. For each problem, follow the instructions carefully, and write a clear explanation of how you arrive at your answer. Give your reasons for your answer. If you apply a theorem, state the theorem. You'll be graded in part on neatness, exposition, clear and correct reasoning. You may choose your problems from the following list, and do a roughly equal number of problems from each of the three sections.

11.2: 12, 14, 16, 18, 20, 22, 24, 26, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48*, 50*, 52*, 54*, 56*, 58*, 60*, 62*, 64*, 66*, 68*.

11.3: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26*, 28*, 30*, 32*, 34*, 36*, 38*.

11.4: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38*, 40*, 42*, 44*, 46*.
 

Read Section 11.5 on alternating series. On your own, do problems 1, 5, 9, 13, 17, 19, 21, 13, 25, 29, 31.

Read Section 11.6 on absolute convergence and the ratio and root tests. On your own, do problems 1, 3, 7, 11, 15, 27, 33.

Read Section 11.7 on strategy for testing series. Do the odd problems 1-15.

Problem Set 10 is due Thursday, April 30. The instructions are the same as for Problem Set 9 above. This time, everyone should try to bring his or her number of basis points up to 250. You may choose your problems from the following list, choosing at least some problems from each of the three sections.

11.5: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32*, 34*, 36*.

11.6: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28*, 30*, 32*, 34*, 36*, 38*.

11.7: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20*, 22*, 24*, 26*, 28*, 30*, 32*, 34*, 36*, 38*.
 

Test 4 on Monday, covering our work so far in Chapter 11.

Read Section 11.8 on power series. Do the odds 1-15 on your own.

Read Section 11.9 on representations of functions as power series. On your own, do problems 1, 3, 5, 11, 13, 19, 21, 25, 27, 29, 31.

Read Section 11.10 on Taylor and Maclaurin series. On your own, do problems 1, 3, 5, 9, 11, 13, 15, 37, 41, 53.

Problem Set 11 is due Thursday, May 8. The instructions are the same as for Problem Set 9 above. This time, everyone should try to bring his or her number of basis points up to 290. You may choose your problem from the following list, choosing at least some problems from each of the three sections.

11.8: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24*, 26*, 28*, 30*, 32*, 34*, 36*, 38*.

11.9: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34*, 36*, 38*, 40*.

11.10: 2, 4, 6, 8, 10, 12, 14, 16; 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50*, 52*, 54*, 56*, 58*, 60*.

Final Exam on Thursday, May 15, 12:30 - 2:30 p.m. The final will cover the material dealt with in weeks 4 through 14.