MATH 234: Calculus--Functions of Several Variables (Lecture 1)

Spring 2011

Meetings: TR 1-2:15PM, VAN VLECK B130
Instructor: Benedek Valkó
Office: 409 Van Vleck
Email: valko at math dot wisc dot edu
Office hours: TR: 9:30-10:30 or by appointment


I will use the class email list to send out corrections, announcements, please check your wisc.edu email regularly.

Do you have a scheduling conflict with the final exam? There will be one (and only one) make-up exam scheduled for this course. According to the official rules we cannot have more than 10% of the students writing the make-up exam.
The alternate time for the final exam is May 11, 2PM. (Van Vleck B139). Please let me know by noon Wednesday (May 4) if you want to take this instead of the regularly scheduled exam. You will need to include your final exam schedule in your email to show that you actually have a scheduling conflict (e.g. a copy from myUW).
If there are more than 24 students signed up for the alternate exam then preference will be given to those with actual scheduling conflict or at least three final exams in 24 hours.
I will send out an email Wednesday afternoon/evening to those who will be allowed to write the exam in the alternate time slot. If you haven't received an email from me about this by Thursday morning then you have to write the final exam in the regular time.

Extra office hours before the final: Monday, May 9, 10AM-12PM, B139 (Van Vleck)

Course description:
This course is the last course in the standard Calculus series at the UW, Math 221-222-234. The series is designed for students with majors in the Physical Sciences or Engineering. Honors students interested in a theoretical approach should consider our sequence 275-276-375-376 instead of 221-222-234. Full credit is not allowed for both 234 and 223. Some majors in the school of business require Math 211-213 instead of Math 221-222-234. Math 213 has some content overlap with Math 234 and full credit cannot be received for both Math 234 and Math 213. Besides the regular lectures, students are required to attend the smaller discussion sections (once a week) where TAs will help with the practical aspects of the subject and will answer any question about the lecture and the assignment. Discussion sections will be hands-on classes.

This course requires a certain level of maturity from the students. Instead of memorizing certain types of problems you will have to understand and apply the techniques and concepts covered in class. This means that you might encounter problems on the exams or assignments that we haven't discussed explicitly. (However every problem will be treatable with the tools learned in class.)
Solutions to homework and practice problems will not be posted, you will be expected to have the ability to decide if your solution is correct or not. Of course your TA or the lecturer will be able to help if you have trouble with a particular problem.

Textbook: M.D. Weir, J. Hass, F.R. Giordano, Thomas' Calculus including Second-order Differential Equations, 11th Edition, Addison Wesley, 2006.

It is very important that you have the correct edition of the textbook!

Prerequisites: Math 221 and 222, or equivalent.

Course Content: we plan to cover the following topics:

Evaluation: Course grade will be based on work in the discussion section (20%), two in-class midterm exams (20%) and a final exam (40%). The final grade will be computed according to the following scale
A: [100,88), AB: [88,86), B: [86,74), BC: [74,72), C: [72,60), D: [60,50), F: [50,0]
There will be no curving in the class, but the instructor reserves the right to modify the final grade lines.

Discussion section grades consist of homework and quizzes. They will be adjusted at the end of the semester so that, even if your TA is a tough grader or gives hard quizzes, your course grade will not suffer. You will not be allowed to use calculators during the quizzes and exams.

Exams:
1st midterm: February 17, in class. Information on the first midterm
2nd midterm: March 31, in class. Information on the second midterm
Final exam: May 9, 5:05PM-7:05PM, INGRAHAM B10. Information on the final exam
Sample final exam (Disclaimer: the actual final exam might contain totally different type of problems...)

You must bring a valid UW Photo ID to all exams.

Important deadlines:http://registrar.wisc.edu/spring_deadlines_at_a_glance.htm

Homework and quizzes: Homework will be assigned every week and it should be handed in at the beginning of every discussion section (starting with the 2nd week). Your TA will decide how much of the assignment will be graded. Each week there will be a short quiz at the beginning of the discussion section (connected to one of the previous homework problems).
It is not hard to find the solutions to (some of) the homework questions. (E.g. the internet, your fellow classmates, solution manual...) However, do NOT consult any of these solutions when working on an assignment or you will learn nothing from it and your chance of passing the course will be greatly diminished.

Discussion sections:

Section TA Time Room
301 Hu, Yueke M 08:50-09:40 AM B219
302 Hu, Yueke W 08:50-09:40 AM B219
303 Hu, Yueke M 09:55-10:45 AM B321
304 Hu, Yueke W 09:55-10:45 AM B321
305 Nezhmetdinov, Timur M 11:05-11:55 AM B321
306 Nezhmetdinov, Timur W 11:00-11:50 AM B325
307 Nezhmetdinov, Timur M 12:05-12:55 PM B219
308 Nezhmetdinov, Timur W 12:05-12:55 PM B219
309 Holcomb, Diane M 01:20-02:10 PM B115 (room change!)
310 Holcomb, Diane W 01:20-02:10 PM B223
311 Holcomb, Diane M 02:25-03:15 PM B235
312 Holcomb, Diane W 02:25-03:15 PM B235

Communication: Email is not an efficient way to communicate with the lecturer in a big class like this one. The best way to reach me is by talking to me after the lecture or coming to my office hours. Please only use email if you cannot reach me in any other way and it is really urgent. Be sure to include 234 in the subject line. I will not answer math related questions via email (as it is too cumbersome) only in person.

How to get help? Your first line of help in this class is your discussion TA, during discussion sections and during their office hours. I will be available at the office hours listed above.

Aditional sources of help (see Getting help in your math class for a more complete list):


What to do before the semester starts? We will start with a review of Chapter 13 (Vector valued functions). This is usually covered in 222 so it should be familiar to you. As a preparation you should read Chapter 12 and 13 and go over some of the problems in 12.

Schedule:

The homework assigned in week N is due in the discussion section in week N+1.

Week Dates Covered topics Homework Suggested reading for next week
1. Jan. 18, 20 Review:
13.1. Vector functions and space curves, velocity and acceleration;
13.3, 13.4. Arc length, curvature, normal and binormal
13.1: 2, 4, 11, 13, 14, 34, 36, 43, 45, 49 (b)
13.3: 2, 3, 6, 10, 12, 13, 15, 16
13.4: 1, 3, 5, 6, 7, 11, 18, 20
14.1. Functions of several variables
14.2. Limits & continuity
14.3. Partial derivatives
2. Jan. 25, 27 14.1. Functions of several variables
14.2. Limits & continuity
14.1: 2, 6, 9, 13, 14, 15, 16, 17, 18, 19, 23, 29, 31, 32, 38.
14.2: 1, 4, 6, 9, 13, 16, 18, 20, 21, 23, 24
14.3. Partial derivatives
14.4 Chain Rule
3. Feb. 1, 3 14.3 Partial derivatives
14.4 Chain rule
14.2: 29, 30, 31, 35, 38, 40, 44, 48
14.3: 3, 12, 17, 18, 21, 26, 29, 43, 51 (a, b, e, f), 52, 63, 64
14.4: 1, 4, 7, 9, 10
14.4 Chain rule
14.5 Directional derivatives and gradient vectors
14.6 Tangent Planes and Differentials
4. Feb. 8, 10 14.5 Directional derivatives and gradient vectors
14.6 Tangent Planes and Differentials
14.4: 19, 22, 24, 25, 31, 42, 49
14.5: 5, 9, 11, 16, 17, 21, 22, 27, 31,
14.6: 3, 6, 8, 10, 11
Review the sections we have covered up to this point.
5. Feb. 15, 17 Review session
First Midterm Exam
No homework this week. 14.7. Extreme values and saddle points
14.8. Lagrange multipliers
6. Feb. 22, 24 14.6 Tangent planes and differentials
14.7. Extreme values and saddle points
14.8. Lagrange multipliers
14.6: 15, 18, 21, 22, 32, 35, 39, 40
14.7: 1, 3, 9, 10, 16, 21, 22, 35, 36, 40, 44 (a, c, e), 45, 46
14.8. Lagrange multipliers
14.10. Taylorís formula in two variables
15.1. Double integrals
7. March 1, 3 14.10. Taylorís formula in two variables
15.1. Double integrals
14.8: 1, 4, 8, 19, 24, 27, 29, 43
14.10: 1, 4
15.1: 1, 5, 6, 8, 11, 12, 13, 18, 19, 20
Since we did not have time to discuss integrals over non-rectangular regions in detail you do not have to hand in the red problems for next week.
If you want to practice multiple integrals you can try doing these problems from 15.1: 2, 3, 4, 14
15.1. Double integrals
15.2. Areas, moments and centers of mass
8. March 8, 10 15.1. Double integrals
15.2. Areas, moments and centers of mass
15.1: 6, 11, 13, 19, 22, 25, 33, 36, 42, 44, 51, 60
15.2: 6, 11, 13, 21, 26, 28, 37, 43, 45
15.3. Double integrals in Polar Form
15.4. Triple Integrals in Rectangular Coordinates
9. March 22, 24 15.3. Double integrals in Polar Form
15.4. Triple Integrals in Rectangular Coordinates
15.3: 1, 3, 6, 9, 11, 12, 14, 15, 19, 22, 25, 27, 34, 38
15.4: 3, 6, 7, 10, 13, 22 (a, c, e), 23
Review the sections we have covered up to this point.
10. March 29, 31 Review session
Second Midterm
No homework this week. 15.5. Masses and Moments in three dimensions
15.6. Triple integrals in spherical and cylindrical coordinates
11. April 5, 7 15.5. Masses and Moments in three dimensions
15.6. Triple integrals in spherical and cylindrical coordinates
16.1 Line Integrals
15.5: 2, 7, 13
15.6: 1, 7, 11, 12 (a), 14, 17, 18, (in the last two problems you only need to set up the integral, you don't have to evaluate them), 21, 24, 28, 33, 38, 39, 44, 52, 59
16.1: 1-8
16.2. Vector Fields, Work, Flux and Circulation
16.3. Path independence, Potential Functions and Conservative Fields
12. April 12, 14 16.2. Vector Fields, Work, Flux and Circulation
16.3. Path independence, Potential Functions and Conservative Fields
16.1: 9, 12, 15, 22, 24, 26
16.2: 1, 2, 5, 7, 8, 14, 15, 18, 19, 23, 26, 27, 37, 41
16.3. Path independence, Potential Functions and Conservative Fields
16.4. Green's theorem in the plane
13. April 19, 21 16.3. Path independence, Potential Functions and Conservative Fields
16.4. Green's theorem in the plane
16.5. Surface area and surface integrals
16.3: 1, 3, 6, 8, 10, 11, 14, 17, 19, 20, 26, 27, 33
16.4: 1, 6, 7, 9, 11, 14, 15
16.5. Surface area and surface integrals
16.6. Parametrized surfaces
14. April 26, 28 16.5. Surface area and surface integrals
16.6. Parametrized surfaces
16.7. Stokesí theorem
16.5: 2, 5, 11, 14, 17, 19, 23, 24, 28, 33, 36
16.6: 3, 5, 6, 14, 19, 21, 25, 29, 32, 36, 40, 44
16.7. Stokesí theorem
16.8. The divergence theorem
15. May 3, 5 16.7. Stokesí theorem
16.8. The divergence theorem
Last week: no homework.
Practice problems (do not hand these in!):
16.7: 1,3,7,9,13,15,17
16.8: 5, 7, 11, 15
Review the sections we have covered up to this point.