MTH164: Multidimensional Calculus

Solutions to the final exam

Final, May 5, 1600-1900 Strong Auditorium Lower

Practice Final

You may bring one piece of paper -- regular size, front and back -- with formulas on it to each exam.

Course Number
 Time
 Location
 Instructor
 Office Hours
 E-mail
58597 MWF 1000-1050 109 B&L Thomas Tucker M 2-3:30, Tu 1-2:30 803 Hylan ttucker@math.rochester.edu
58588 MWF 0900-0950 208 Gavett Andrew Ledoan MW 1230-1400, 908 Hylan ledoan@math.rochester.edu

Recitation
 Time
 Teaching Assistant
 E-mail
106 Hylan W 1100-1150 Suresh Eswarathasan suresh@mail.rochester.edu
102 Hylan W 1100-1150 William Orr billorr@mail.rochester.edu
1104 Hylan W 1300-1350 Suresh Eswarathasan
1104 Hylan W 1525-1615 William Orr
1104 Hylan Th 1100-1150 Tyle Stelzig tstelzig@mail.rochester.edu
102 Hylan Th 1230-1320 Suresh Eswarathasan
1104 Hylan Th 1230-1320 Alex Halperin ahalperi@mail.rochester.edu
203 Hylan Th 1550-1640 William Orr
201 Hylan F 1300-1350 Johnathan Garneau jgarneau@mail.rochester.edu
WeBWorK Matthew Conomos mconomos@mail.rochester.edu
Prerequisites:
MTH143, MTH162, or MTH172.
Textbook:
James Stewart, Calculus: Early Transcendentals, Fifth Edition, Thomson Brooks/Cole, 2003.
Syllabus:
The course covers Chapters 12 through 16 of the textbook. The main topics are vectors and the geometry of space, vector functions, partial derivatives, multiple integrals, and cector calculus.
Grading Policy:
The course grade will be derived from the following components.
  • WeBWorK 20% of grade
  • Midterm 1 20% of grade (here is the Practice Midterm #1) -- Midterm 1 is in Dewey 1101
  • Midterm 2 20% of grade (here is the Practice Midterm #2 -- with solutions) -- Midterm 2 is in Dewey 1101
  • Final 40% of grade (here is the Practice Final -- with solutions) The final is in Strong Lower at 4 pm on Monday May 5

Solutions for Midterm#1

Solutions for Midterm#2

You may bring one piece of paper -- regular size, front and back -- with formulas on it to each exam.

Thus, the course grade will be determined on the basis of the total numerical score achieved on the WeBWorK sets and exams. You will be able to access your test scores at any time via BlackBoard. You can access your grades by loging in at http://my.rochester.edu. The program is being used by many instructors of large mathematics classes, so you may already be familiar with it.
WeBWorK:
You will need to read the textbook (do not make the mistake of heading straight for the homework problems armed with only your lecture notes) and do many different types of problems in order to reinforce your understanding of a particular concept or technique. To help you achieve these goals, we have combined WeBWorK problems (these are presented and graded electronically) with weekly practice problems. Each WeBWorK set is due Monday morning at 0500, one week after it was assigned. The solutions are posted each Tuesday at 1000. There will be approximately 13 WeBWorK sets, from which the best 10 scores will count toward your grade. The first WeBWorK set is meant to familiarize you with WeBWorK and will not count toward your grade. Here is the link for the webwork page.
Exams:
The exam schedule is as follows. (The exam locations will be announced in the next two weeks.)
  • Midterm 1, February 21, 0800-0930, Dewey 1101
  • Midterm 2, April 3, 0800-0930, Dewey 1101
  • Final, May 5, 1600-1900 Strong Auditorium Lower
See the Spring 2008 Exam Schedule at http://www.rochester.edu/registrar/examschedule.html. The final will be cumulative and about twice as long as a midterm. We do not give make-ups on exams. If you miss an exam, you will receive a score of 0.
Recitations:
There will be sign-up sheets for Recitations posted on the first floor of Hylan (on the walls near the elevators), by January 18. You must register for Recitations and attend the meetings regularly, starting the week of January 20. Apart from Recitations, we encourage you to take full advantage of your instructor's office hours and the free tutoring offered in the Department of Mathematics. The Math Study Hall in 1103 Hylan is staffed by graduate mathematics students who will answer your questions on a walk-in basis. It is open each Tuesday and Thursday. A schedule will be posted on the door.
We strongly encourage you to discuss with classmates and form a study group. Studying in groups has tremendous value and is most effective when the group takes responsibility for the learning of its members.
Calculator Policy:
While a few of the practice problems may require the use of a basic calculator, exam problems will be constructed such that calculators are not needed and would provide no benefit (and, in fact, may be a distraction). Therefore, calculators are not allowed in exams.
ADA Disability Statement:
If you have a disability and need assistance, special arrangements can be made to accomodate most needs. For information please contact Learning Assistance Services (10 Lattimore, telephone number (585)275-9049), or visit their web site http://www.rochester.edu/College/las/. Any accomodations for exams must be arranged a week in advance and will require a letter or e-mail from Learning Assistance Services.
Academic Integrity Statement:
You are responsible for knowing and abiding by the University of Rochester's academic integrity code. For a complete listing visit the College of Arts, Sciences, and Engineering's web site http://www.rochester.edu/College/honesty/. Any violation of academic integrity will be pursued according to the specified procedures.
Weekly Schedule:
The following weekly schedule has a list of practice problems assigned for each section covered in the lectures, and describes what will be discussed in Recitations.

Week of Topic WeBWorK Practice Problems (to be discussed in Recitations in the following week)
01/13 12.1-12.3 Set 0 12.1: 3, 9, 15, 17, 21; 12.2: 5, 19, 21, 25, 35; 12.3: 19, 23, 26, 31, 49, 59.
01/20 12.4-12.5 Set 1 12.4: 1, 3, 29, 33, 41; 12.5: 3, 5, 7, 21, 23, 35, 39, 53.
01/27 12.6-13.1 Set 2 12.7: 11, 15, 19, 39, 49, 51, 63; 13.1: 3, 5, 19-24, 25, 34.
02/03 13.1-4 Set 3 13.2: 3, 5, 9, 11, 17, 23, 33, 39; 13.3: 1, 3, 5, 7; 13.4: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25.
02/10 14.1-14.3 Set 4 14.1: 21, 23, 24, 30, 37, 39, 41, 45, 53-58; 14.2: 1, 3, 5, 11, 13; 14.3: 13, 15, 21, 35, 53, 57, 59.
02/17 (Midterm 1) 14.4-14.5 Set 5 14.4: 1, 3, 5, 11, 13, 31, 33.; 14.5: 1, 5, 7, 9, 11, 21, 23, 27, 29, 31, 47, 49; 14.6: 5, 7, 9, 11, 13, 15, 21, 25, 39, 41, 49, 55
02/24 14.6-14.7 Set 6 14.7: 1, 3, 5, 7, 11, 27, 29, 31, 41, 53; 14.8: 1, 3, 5, 7, 15, 17, 19, 21, 39.
03/02 14.7-14.8 Set 7 15.1: 1, 5, 11, 13; 15.2: 3, 5, 7, 11, 15, 19, 21, 27, 29.
03/16 15.1-15.3 Set 8 15.3: 3, 5, 9, 11, 15, 17, 25, 37, 39; 15.4: 1, 3, 5, 6, 7, 9, 11, 19, 23; 15.5: 1, 3, 9, 13, 21
03/23 15.4-15.5, 15.7 Set 9 15.7: 3, 5, 7, 9, 11, 15, 17, 19, 33, 37; 16.1: 5, 11-18, 21, 23.
03/30 (Midterm 2) 16.1-16.3 Set 10 16.2: 1, 3, 5, 9, 11, 15, 17, 19, 21, 23; 16.3: 3, 5, 7, 9, 11, 13, 15, 19, 21, 23,
04/06 16.4-16.5 Set 11 16.4: 1, 3, 7, 9, 13, 15, 19, 21, 27; 16.5: 1, 3, 5, 7, 9, 10, 11, 15, 17, 21, 25, 27, 31, 33.
04/13 16.5-16.6 Set 12 16.6: 1, 3, 11-16, 17, 19, 35, 37, 43, 53(a); 16.7: 5, 7, 9, 11, 13, 17, 21, 23, 27, 41, 43.
04/20 16.7-16.8 Set 13 16.8: 1, 3, 5, 7, 9, 13, 15, 17, 19, 20; 16.9: 1, 3, 5, 7, 9, 13, 21, 23, 25, 28.
04/27

Practice Midterm #1


Note: this one comes with answers so you can check that what you are doing is right.

Practice Midterm #2 (with solutions)


Practice Final (with solutions)