Math 233: Multivariable Calculus, Spring 2008

Course Chair

Robert Gardner
1430 LGRT
Ph: 5-0029
e-mail: gardner@math.umass.edu
Office hours: TBA
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Textbook: 

Calculus: Early Transcendentals (5th Edition) by James Stewart. The text book annex now has a small packet with chapter 10 which costs $7.75; if you have the "big" book then it has this chapter in it.



Section meetings


update 1/29: office hours: Instructors of m233 have agreed to pool office hours.  You may attend the office hours of any m233 instructors, regardless of section.
update 2/11 End of add-drop period: dropping and adding can no longer be completed through Spire.  The procedure after the add-drop deadline is that  students should obtain and complete the appropriate form from the registrar's office, obtain their instructor's  approval by having them sign the form, and return the form to the registrar after it is completed.

Han: Section 1 Class number (58654)
MoWeFr 10:10AM - 11:00AM    Lederle Grad Res Tower rm 113  
Office hours: Mon 2:30-4:30pm; Wed 9:00-10:00am, 12:30-1:30pm

Gardner :  Section 2 Class number (58656)
MoWeFr 11:15AM - 12:05PM    Lederle Grad Res Tower rm 323
Office hours: M 12:15-2:15, W 9-10 and by appointment

Materov:  Section 3 Class number (58658)
MoWe 2:30-3:45PM   Lederle Grad Res Ctr A203
Office hours: MWF 11-12 in LGRT 1238

Fedorov: Section 4 Class number (58660)
MoWeFr 12:20PM - 1:10PM    Lederle Grad Res Tower rm 119    
Office Hours: Monday, 1:30 - 2:45, Wednesday, 2:45 - 4


Ridgdill: Section 5 Class number (58662)
TuTh 11:15AM - 12:30PM    Lederle Grad Res Ctr rm A205  

Fenn: Section 06 Class number (58782)
TuTh 1:00PM - 2:15PM    Lederle Grad Res  Ctr rm A201
Office hours: Tues 3:30-5 (Blue Wall), Thurs 2:30-4 (1323D LGRT) (after February 14)


Norkin: Section  7 Class number (58664)
TuTh 2:30PM - 3:45PM    Lederle Grad Res Tower rm 119
Office Hours: Mon 10-11, Wed 3-4 (1624 LGRT)

Tentative Exam Schedule

The following dates and times are likely to be correct, but are contingent upon
room assignments from the scheduling office. Further information will be posted as
soon as it becomes available.

Exam 1: March 5 (Wednesday), Time 7:00-9:00 pm.  , room: TBA
Exam 2: April 16  (Wednesday).  Time 7:00-9:00 pm. , room: TBA
Final Exam: TBA

Exam policies:

Make-up policies:  please familiarize yourself with the procedures for granting requests for make-up exams.

Grading

The final grade will be 25% Exam 1, 25% Exam 2, 25% Final Exam and 25% from Instructor. All scores will be scaled to a 0-100 scale before averaging. The final grading scale is

A: 88% - 100%         C: 66% - 71%        
A-: 85% - 88% C-: 63% - 66%
B+: 82% - 85% D+: 60% - 63%
B: 77% - 82% D: 55% - 60%
B-: 74% - 77% F: 0% - 55%
C+ 71% - 74%

Weekly Schedule (Tentative)

Week of Sections Remarks
Jan 28
12.1, 12.2 First class Monday
Feb 4
 12.3, 12.4, 12.5
Feb 11
 12.6, 10.1, 13.1 Add/drop deadline Feb 11
Feb 19
 13.2, 13.3
  18th: President's day; Monday schedule on the 19th
Feb25
 13.4, 14.1, 14.2
March 3
 14.3, 14.4  Exam I: March 5, 7-9pm
March 10
 14.5, 14.6
March 24
 14.7, 14.8 Spring recess: Mar 15-23; Witdrawal deadline: Apr 25
March 31
 15.1, 15.2
April 7
 15.3, 10.3
April 14
 15.4, 15.5 Exam II: April 16, 7-9pm
April 22
 16.1, 16.2 April 21: Patriot's day (usual scedule Tuesday)
April 28
 16.2, 16.3
May  5
 16.4
May 12
 Catch-up and review Last day of class on Tuesday, May 13

Homework Assignments / Syllabus

Section Topic Recommended Homework
12.1 Three-dimensional coordinate systems 3, 7, 11, 13, 17, 23, 31, 41
12.2 Vectors 1, 3, 5, 11, 15, 19, 21, 25, 31, 37
12.3 The dot product 5, 7, 9, 11, 17, 19, 21, 23, 27, 37, 39, 43, 51
12.4 The cross product 1, 3, 5, 11, 13, 15, 25, 29, 39, 45
12.5 Equations of lines and planes 1, 3, 5, 7, 13, 19, 23, 27, 31, 35, 39, 45, 65
12.6 Cylinders and quadric surfaces 3, 5, 11, 13, 21-28, 41, 43
10.1 Curves defined by parametric equations
    (omit Examples 4 and 7)		 1, 3, 5, 7, 19, 21
13.1 Vector functions and space curves 3, 5, 7, 11, 13, 15, 17, 19-24, 33, 35, 39
13.2 Derivatives and integrals of vector functions 1, 3, 5, 9, 11, 13, 19, 25, 33, 37, 49
13.3 Arc length (omit curvature) 1, 3, 5
13.4 Motion in space: velocity and acceleration 3, 5, 9, 11, 15, 19, 23
14.1 Functions of several variables 11, 13, 23, 25, 29, 37, 39, 41, 53, 53-58
14.2 Limits and continuity 7, 9, 11, 27, 31
14.3 Partial derivatives 3, 13, 15, 17, 19, 21, 35, 37, 41, 47, 49, 81
14.4 Tangent planes and linear approximations 1, 3, 5, 17, 19, 23, 25, 29, 31
14.5 The chain rule 1, 3, 5, 7, 9, 11, 13, 17, 21, 23, 27, 29, 39
14.6 Directional derivatives and the gradient vector 1, 5, 7, 9, 11, 13, 21, 23, 39, 41, 53, 59
14.7 Maximum and minimum values 5, 7, 9, 11, 27, 29, 31
14.8 Lagrange multipliers 3, 5, 7, 9, 11, 19
15.1 Double integrals over rectangles 1, 5, 11, 13
15.2 Iterated integrals 3, 5, 7, 9, 11, 13, 15, 21, 23, 27, 33
15.3 Double integrals over general regions 1, 3, 5, 7, 9, 11, 13, 19, 21, 23, 37, 39, 43, 45, 49
10.3 Polar coordinates (omit tangents) 1, 3, 5, 7, 9, 15, 21, 23, 29, 31, 39
15.4 Double integrals in polar coordinates 9, 11, 13, 19, 21, 25, 29, 31
15.5 Applications of double integrals 3, 5
16.1 Vector fields 1, 3, 5, 11-18, 21, 25
16.2 Line integrals 1, 3, 5, 7, 11, 17, 19, 23, 25
16.3 The fundamental theorem for line integrals 3, 5, 7, 9, 11, 13, 19, 21, 23
16.4 Green's theorem 1, 3, 7, 9, 11, 13, 15, 19

Practice Exams:


Below are some practice exams and review problems offered in previous semesters. While these can be useful in preparing for exams,  you should be aware that there may be signifcant variation  in the choice of topics and the difficulty of the questions in various exams from different terms and years. You should not assume a particular topic or type of problem on a practice exam will necessarily appear on  the exams during the present term. The choice often depends on the pace and timing of lectures in different years, and the decisions made by different groups of Math 233 instructors.  The recomended homework problems above are suitable material for exam questions,  whether or not a similar topic or question was included in an exam from a previous semester. There will be further announcements about the particular exams on this web page throughout the term. You should also consult with your instructor. The exams for Math 233 for Spring 2008 will be written and reviewed  by all Math 233 instructors.

Exam 1 : The mean score for exam I was 75  (out of a possible 100 points), and the mean scores
for individual sections ranged between 71 and 82. The overall results  and the results for indivdiual sections were  consistent with the expectations about performance used to devise the letter-equivalent grading scale (above). Your exam I score will determined 25% of your final course average
The answers and and grading scheme for awarding partial credit can be obtained from the following
links.
entire exam
problem 1  problem 2  problem 3 problem 4 problem 5
 

  • Note that in the following practice exams there are questions concerning linear approximations, partial derivatives, and describing the tangent plane at some point on a graph and other material from section 14. 

  • Practice Problems for Exam 1
  • Answers
  • Exam 1 from Fall 2006
  • Answers
  • Formula Sheet (to be included in Exam 1)
  • Exam 1 from Spring 2007 with answers
  • Exam 1 from Fall 2007 with answers.


    • Exam 2  Wednesday, April 16, 7-9 pm


    calculators are permitted
    cheat sheets are not permitted
    there will be no formula sheet provided with this exam.


    Results for exam II
    The median and median scores for the various sections (in no particular order) were
    (mean   ) 63  74   64 63  71 76 70
    (median) 72  73   70 71  71 82 76
    The median scores for all sections were all comparable and at a level indicating that
    the exam presented a fair collection of problem that at least half the students in each
    section were well prepared for. There is therefore no basis for scaling the exams  scores
    and the numerical scores on this exam are final, with the exeption of possible errors in grading.
    Exam and makeup solutions are provided below, with a rough indication of how
    partial credit was awarded on each problem. Students with questions about how particular
    problems were graded should consult with their instructor. Furthermore, since there were so many
    students taking the makeup exam, a comparison between scores on the makeup and
    the regular exam was also made. The was no indication in terms of the overall numbers
    that one exam was more or less difficult than the other, and students, on average, performed
    in a comparable manner over the entire course.

    regular exam solutions:
    1 2 3 4 5
    makeup exam solutions:
    1 2 3 4 5



    \\\
  • Practice problems: exam II
  • Problem problem answers: exam II
  • Problems from Exam 2 Fall 2006 (no answers)
  • Exam 2 Spring 2007 with answers
  • Exam 2 from Fall 2007 with answers  

  •   Final Exam

    The final exam will be cumulative, but the majority covers the material in chapters 15 and 16 covered after Exam II.  Below are some practice problems offered in previous semesters, as well as the Finals from Fall 2006 and Spring 2007.

  • Practice Problems for Final Exam
  • Answers
  • Final Exam from Fall 2006 (no answers)
  • Final Exam from Spring 2007 (no answers)