**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.

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.

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

**Prerequisites:** Math 221 and 222, or equivalent.

- Review of vector-valued functions (13.1, 13.3, 13.4)
- Partial derivatives (14.1-14.8, 14.10)
- Multiple integrals (15.1-15.6)
- Integration of vector fields (16.1-16.8)

**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 |

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

**Math Lab:**a free, drop-in tutorial program in B227 Van Vleck. Tutoring is available Monday through Thursday from 3:30-8:30PM and Sunday 3:30-6:50PM.**Mathematics Tutorial Program:**Free small group tutoring is offered to students who are in danger of getting a D or F, for students who have not had a math course in several years, or for students who are retaking the course. A significant time commitment is required. Any student can apply to the program, but after the first two weeks of the semester, a referral from an instructor is required. Students may apply in room 321 Van Vleck.**Tutoring in University Residence Halls:**free, drop-in math tutoring is available in Bradley Learning Community, Holt Commons, Elizabeth Waters Hall, Chadbourne Residential College, Witte Hall, Multicultural Learning Community Den, Multicultural Student Center Satellite, Sellery Hall, Ogg Hall, Smith Hall and Friedrick Hall. Tutoring is available every evening Sunday-Wednesday at a subset of these locations. This table has more information.**GUTS:**Greater University Tutoring Service offers free small group, individual, and drop-in tutoring at various locations around campus. It is staffed mostly by student volunteers. Stop by their office (333 East Campus Mall, Rm. 4413, Monday-Friday) to sign up for a tutor or try drop-in tutoring.**Private Tutors:**A list of tutors is available at the link or from the receptionist on the second floor of Van Vleck.

**Schedule:**

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. Taylor’s formula in two variables 15.1. Double integrals |

7. | March 1, 3 |
14.10. Taylor’s 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. Stokes’ 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. Stokes’ theorem 16.8. The divergence theorem |

15. | May 3, 5 |
16.7. Stokes’ 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. |