Professor: Peter J. Nyikos

Office: LeConte 406.

Phone: 7-5134

Email: nyikos @ math.sc.edu

**Office hours Monday April 29: 2:00 - 4:00 [revised from earlier].
Tuesday April 30: 2:00-3:00 and 4:30 - 5:30
Wednesday May 1: 2:00-4:00
Thursday, May 2: 1:15-2:30
Friday, May 3: 9:00-12:30
Homework, extra credit papers and test papers that have not yet been picked up are ready to
be picked up.
Answer keys to the three tests are available in envelopes outside the door of my office.
**

**
The final exam is on Tuesday, May 7, from 9:00 to 11:30 am. It is cumulative, but special emphasis is given to
11.8, which was not on the last test, and 10.3 is also covered with problems similar
to the homework and practice problems.
**

The formula sheet that will be handed out with the final exam can be found here: here in pdf format.

TA: Greg Ferrin

Your SI for this course is Matt Csonka, csonka @ email.sc.edu

His sessions start Tuesday, January 22, at the following times
and locations:

Sundays: 8pm, HU207

Tuesdays: 7pm, HU204

Thursdays: 6pm, HU207

The first test in this course was on Thursday, February 28, on Chapter 7 up through 7.5, on techniques of integration.

The second test in this course was on Tuesday, April 2, on sections 6.1, 6.2, 6.3, 6.5; the part of 7.8 used for the integral test; and sections 11.1, 11.2 and 11.3 except the part about error estimates.

The third test in this course was on Thursday, April 18, on Chapter 11 up through Section 11.7 (with 11.7 principally for review), including tests of monotonicity in 11.1, the use of the divergence test in 11.2, and the other tests in 11.3 through 11.6 for convergence.

The textbook for this course is *Calculus: Early Transcendentals *
by James Stewart, 6th edition.

Sections 5.3, 5.4 and 5.5 were reviewed in the first lecture. The rest of the course covers the following sections, in the following order:

- 7.2, 7.1, 7.4, 7.3, 7.5, 7.8
- 6.1, 6.2, 6.3, and 6.5 (and 6.4 if time permits)
- 11.1 through 11.8 (and 11.9 and/or 11.10 if time permits)
- 10.3 (and 10.4 if time permits)

Objectives for this course:

(1) Proficiency in applications of the integral, including the finding of areas, volumes, and average values of functions on intervals;

(2) Mastery of techniques of integration including ordinary and trigonometric substitution, integration by parts, partial fraction techniques, and the evaluation of improper integrals;

(3) Ability to evaluate limits of infinite sequences and series, including power series and Taylor and MacLaurin series, where possible, and otherwise to determine whether they converge or diverge, and to find intervals of convergence for power series;

(4) Achieving a good understanding of polar coordinates, including graphing in polar coordinates and the integration of functions with respect to polar coordinates.

The first quiz was on Wednesday, January 23; it consisted of problems
very similar to the practice problems for Sections 5.3 and 5.5 (see below).

There was a quiz on Wednesday, February 6, on Section 7.4.
There was a quiz on Wednesday, February 20, on Section 6.1.

There was a quiz Wednesday, April 3 on error estimates in Section 11.3.

Practice problems, not to be handed in [in the order in which they came up in
class]:

5.3: 13, 19, 23, 29

5.5: 3, 5, 13, 15, 19, 53, 55, 59

7.2: 3, 7, 9, 29, 37, 43, 45, 57

7.1: 1, 5, 7, 13, 15, 17, 19, 23

7.4: 1, 3b, 5b, 7, 9, 11, 15, 19, 27, 29, 47

6.1: 1, 5, 11, 13, 17, 21, 27

6.2: 3, 5, 7, 19, 21, 23, 59

6.3: 1, 3, 7, 9, 37 both ways

6.5: 3, 7, 9, 13

11.1: 5, 9, 19, 21, 61, 63.

11.2: 11, 13, 17, 25, 35, 37

7.8: 5, 9, 15, 21, 25

11.3: 3, 5, 7, 11, 23, 33

11.4 1, 3, 7, 11, 15, 17, 27, 33

11.5 3, 5, 7, 11, 23, 27

11.6 1, 3, 5, 7, 13, 17

11.7 1, 3, 5, 7, 11, 25, 27

10.3 1, 3, 5

11.8 5, 15 (intervals only)

11.9 3, 5, 7 (compare examples 1 and 5)

Homework to be handed in on Thursday, January 24:

Section 5.3: 28, 38

Section 5.5: 26, 36, 54, 68

Section 7.2: 8, 26, 40

Homework to be handed in on Thursday, February 14:

Section 7.1: 6, 18, 20, 42 (omit
graphs)

Section 7.4: 4b, 16, 24, 42, 48

Homework to be handed in on Tuesday, February 19

Section 7.3: 16, 24

Homework to be handed in on Tuesday, March 26: [2 points off if handed in late, but
by 5pm, otherwise half credit, but only if turned in before the papers are returned]:

Section 6.3: 8 (diagrams optional)

Section 6.5: 6 ** There was a typographical error. Those who did
6 on 6.4 should return their papers to Prof. Nyikos to get credit for it.
**
Section 11.1: 8, 42

Section 11.2: 16

Homework to be handed in on Tuesday, April 23:

Section 11.6: 14

Section 11.8: 6, 12

Section 10.3: 4

Extra credit problems were assigned from time to time. They are to be done ** strictly on your own,**
except that
I am willing to give you advice. You are not to discuss them with
anyone else.

There is no due date for extra credit, but once a fully correct solution
is handed back, the problem is no longer eligible for extra credit. ** This is true of
all problems with lines through them below. **

If you can't quite get the solution to an extra credit problem
but have some ideas, hand it
in for partial credit. I will keep adding to your score as you
improve your work on it.

~~1. number 16, page 441 [worth 10 points quiz if setup is well justified, otherwise 8 quiz points]~~

~~2. Section 6.2, number 30~~

~~3. Section 6.3, number 46b [you may use 46a]~~ [ineligible as of 9:10 am Monday April 29]

~~4. Section 7.1 , number 66, parts a and d~~.

~~5. Section 11.3, number 32, part c. Find the least value of n that works.~~

6. Section 11.4, number 44

~~7. Section 11.4, number 46, proving your answer.~~

8. Section 11.10, number 44, using the interval [0, pi/2] and a=0.

~~9. Section 11.10, number 54, with a=0.~~ [ineligible as of 9:10 am Monday April 29]