# Math 241 (Vector Calculus) Section 004 Spring, 2015

### Lectures in LeConte 405, 1:10 pm - 2:00 pm MWF

Professor: Peter J. Nyikos

Prof. Nyikos's Office: LeConte 406.     Phone: 7-5134

Email: nyikos @ math.sc.edu

Special office hours for exam week:
Monday, April 27: 10:40 - 12:40 and 2:00 - 3:45
Tuesday, April 28 (reading day): 9:30 - 12:00 and 1:30-3:30
Wednesday, April 29: 1:00 - 4:00
Thursday, April 30: 9:30 - 12:00 and 1:30-4:00
Friday, May 1: 9:30 -12:00

The final exam is on Friday, May 1, at 12:30 p.m.. Information on all final exam times can be found outside of "Self Service Carolina" at this good old fashioned Registrar's website.

Further information on policies and grading can be found by clicking here.
Amendment to the above webpage: Because the ninth quiz was more difficult than intended, the two lowest quiz grades will be dropped, not just the lowest.

The final exam will cover the following sections:
12.2 through 12.5
a 13.2 through 13.4
14.3, the formula for the tangent plane to the graph of a function in 14.4 (optional, could do such problems by 14.6 methods); 14.6, and 14.7
15.2, 15.3, 15.4, and 15.6, 15,7, 15.8
16.2, 16.3, and 16.4.

Answer keys to some quizzes, homework, and tests are in an envelope outside the door of my office along with the 4-page handout on spherical coordinates that was handed out in class. These will be useful for studying for the final along with the practice problems not crossed out below. You may also ignore the setup for the flat topped cone in the 4-page handout on spherical coordinates.

Practice problems :

12.1 numbers 1, 9(b), 13, 15
12.2 numbers 7, 17, 19, 21
12.3 numbers 3, 7, 17, 23, 29 [it is enough to find cosines in 17 and 29]
12.4 numbers 1, 5, 13, 18, 27, 33
12.5 numbers 7, 11, 23, 29, 33

13.1 numbers 5, 7, 17, 19-24
13.2 numbers 3, 5, 9, 19, 21

13.3 numbers 1, 3, 17, 25, 43

13.4 numbers 3,9, 11, 15

14,1 level curves for 1 and -1 on 43, those for 0 and 1 on 45; match equations 56-60 with pictures.
14.2 numbers 5, 7, 13 and Examples 1 and 2
14.3 numbers 15, 17, 29, 31, 33, 35 and 57.
14.4 numbers 1, 3
14.5 numbers 3, 7, 13, 27, 33.
14.6 numbers 7, 11, 21, 41, 43.
14.7 numbers 1, 3, 5

10.3 (a review and warm-up for Section 15.4): numbers 1 (plot only), 3, 5(a)(i), 7, 9, 15, 17, 21, 23
15.3: numbers 3, 5, 9, 13, 39, 45
15.4: numbers 1, 3, 5, 7, 11, 19
15.5: numbers 3, 5
15.6: numbers 3, 5, 11
15.7: numbers 1, 3, 9, 17, 27
15.8: numbers 1, 3, 9, 21, 23

16.2: numbers 1, 9, 13, 19, 21.
16.3: numbers 3, 7, 15, 19
16.4: numbers 1, 3, 19

Only simple calculators (available for \$20 or less) are needed for this course, and they will be needed only a small fraction of the time, outside of class. Neither the quizzes, nor the hour tests, nor the final exam will require their use, although they may save some time on a few problems. Programmable calculators are not permitted for quizzes, hour tests, or the final exam.

Homework handed in on Wednesday, April 22:

1. Integrate f(x, y, z) = x + y + z over the curve C which is the straight line segment from (1, 2, 3) to (0, -1, 1). [To parametrize C, look back on Section 12.5 for parametric equations of lines, confining t to an interval to get a line segment.

2. Let F(x, y, z) = 3yi + 2xj + 4zk. Evaluate the integral of F . dr over C given by r(t) = ti + t^2j + t^4k

The first hour test for this course was on Wednesday, February 11, on Chapter 12 and Sections 13.2 and 13.4 [nothing from 13.1 nor 13.3 was tested]. See practice problems for the kinds of questions that were helpful. The grading scale for this test had the following cutoffs:
A, 86; B+, 79; B, 72; C+, 65; C, 58; D+, 51; D, 44.

The second hour test was on Wednesday, March 18. It covered sections 13.2, 14.1, 14.2, 14.3, 14.5 and 14.6. Practice problems were good preparation; also the quizzes. The grading scale for this test had the following cutoffs:
A, 87; B+, 80; B, 74; C+, 67; C, 61; D+, 54; D, 48.

The third hour test was on Monday, April 20, on Section 14.7 and Sections 15.2 through 15.8.
The grading scale for this test had the following cutoffs:
A, 85; B+, 77; B, 70; C+, 62; C, 55; D+, 47; D, 40.

The textbook for this course is Calculus: Early Transcendentals by James Stewart, 6th edition. This is the same textbook you have been using for the earier semesters. You do not need a special edition for vector calculus nor any expensive website access package.

The course covers the following sections of the textbook:

• 12.1 through 12.5
• 13.1 through 13.4
• 14.1 through 14.7, except 14.5
• 15.1 through 15.8, except 15.5
• 16.1 through 16.4

Learning Outcomes: Students will master concepts and solve problems based upon the topics covered in the course, including the following: vectors and basic operations on them, including dot and cross products; vector-valued functions and their integration and differentiation; functions of several variables and their maximization, differentiation and integration; vector fields; line and path integrals; Green's theorem.

The most emphasis will be on Chapters 14 and 15. Incidentally, the material in 13.3 is covered more thoroughly in Math 550 and/or Math 551, while the Chapter 16 material is covered very thoroughly in Math 550.

The first quiz was on Friday, Jan. 23, on sections 12.1 through 12.3 as far as we got in class on Friday, Jan. 16. The second quiz was on Friday, Jan 28, on cross products and equations of lines. The third quiz was on Friday, Feb. 6, on velocity, acceleration, and speed. The fourth quiz was on Friday, Feb. 13, on arc length. The fifth quiz was on Monday, Feb. 23, on partial derivatives. The sixth quiz was on Friday, Feb. 27, on gradients and directional derivatives. The seventh quiz was on the tangent plane to the graph of a function of two variables. The eighth was on Friday, March 27, on evaluation of a double integral. The ninth was on Friday, April 3, on integration in polar coordinates. The tenth was on Monday, April 13, on converting coordinates of points from one 3D coordinate system to another (rectangular, cylindrical, spherical).

#### Extra Credit Problems

Extra credit problems 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.

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

To get full credit, it is not enough to get the correct answer. You need to get it in such a way that someone who has not seen the problem before can tell that you did, indeed, get the right answer.

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. Also, extra credit will no longer be given after the beginning of the final exam. This is true of any problem crossed out below

The following are worth 10 quiz points apiece.

1. Use Green's theorem to evaluate the integral of (2x + y^2)dx + (x^2 +2y)dy on the counterclockwise-oriented curve C given by y = x^3/4, y=0, x=2.

2. Use Green's theorem to find the area of the region bounded by the curve parametrized by r(t) = 2cos^3 t i + 2 sin^3 t j , t in [0,2pi]. See formula 5 on page 1058 for the application of Green's theorem.