Course: MATH 32B, Calculus of Several Variables, Lecture 3,
Prerequisite: MATH 31B and MATH 32A, with grades of C- or
Course Content: Introduction to integral calculus of several
variables, line and surface integrals.
Last update: 25 February 2015
Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Mondays, 10AM-12PM, Wednesdays, 1PM-2PM, MS
Lecture Meeting Time/Location: Monday, Wednesday and Friday,
2PM-250PM, Rolfe 1200
TA: Ohrt, C. J., cohrt(@-symbola)ucla.edu; Shani, A.,
assafshani(@-symbol)ucla.edu; Keneda, J., jkeneda(@-symbol)math.ucla.edu
TA Office Hours: Ohrt: Tuesdays 12PM-1PM, Thursdays 3PM-4PM, MS
3915E; Keneda: Tuesdays and Thursdays, 11AM-12PM, MS 2951; Shani: Thursdays
3PM-4PM, MS 2344
Discussion Session Meeting Time/Location:
Required Textbook: J. Rogawski, Multivariable Calculus,
Second Edition, W.H. Freeman & Co.
- 3A, Tuesday, 2PM-250PM, MS 5137. Ohrt, C. J. www.math.ucla.edu/~cohrt
- 3B, Thursday, 2PM-250PM, Royce 160. Ohrt, C. J. www.math.ucla.edu/~cohrt
- 3C, Tuesday, 2PM-250PM, PAB 1749. Shani, A. www.math.ucla.edu/people/grad/assafshani
- 3D, Thursday, 2PM-250PM, PAB 1749. Shani, A. www.math.ucla.edu/people/grad/assafshani
- 3E, Tuesday, 2PM-250PM, PAB 1434A. Keneda, J. T. www.math.ucla.edu/~jkeneda/teaching.html
- 3F, Thursday, 2PM-250PM, PAB 1434A. Keneda, J. T. www.math.ucla.edu/~jkeneda/teaching.html
Other Textbooks (not required): Calculus, Thomas
First Midterm: Monday, January 26th, 2PM-250PM. If your last
name begins with the letter A through O, come to Rolfe 1200. If your
last name begins with the letter P through Z, come to Haines 118.
Second Midterm: Friday, February 27th, 2PM-250PM, Broad 2160E
Final Exam: March 20, 3PM-6PM, Broad 2160E
The Student Math Center in MS 3974 offers group study and
tutorials. See their schedule here.
Applets from Monroe CC
Exam Procedures: Students must bring their UCLA ID cards to the
midterms and to the final exam. Phones must be turned off. Cheating on
an exam results in a score of zero on that exam. Exams can be
regraded at most 15 days after the date of the exam.
- My email address for this course is heilman(@-symbol)ucla.edu.
- It is your responsibility to make sure you are receiving emails from
heilman(@-symbol)ucla.edu, and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.
- Homework questions sent to me by email will be answered altogether in the form
of a "digest." I will get to every question, but I cannot reply to every email.
This digest will be sent out typically two days before the homework is due.
Exam Resources: Here
is a page containing old exams
for a similar multivariable course. (Exams 3A,3B,4A,4C are
most relevant.) Here
is another page containing old exams
for a similar multivariable course. (Here I would recommend the Spring
2001 Midterm Exam 2, which should correspond closely to our second exam.)
Also, for our second exam, try out this
exam, (problems 2 through 9); see also this
exam with solutions
(and maybe skip Question 8). For the final exam, here is a page
containing several practice finals with solutions.
Occasionally these exams will cover
slightly different material than this class, or the material will be in a
slightly different order, but generally, the concepts should be close if
- Late homework is not accepted.
- You may not use the internet to try to find answers to homework problems.
- The lowest two homework scores will be dropped. This policy is meant
to account for illnesses, emergencies, etc.
- Do not submit homework via email.
- There will be 9 homework assignments, assigned weekly on Friday
in at the beginning of class on the following Friday. In the
second and eighth week of the quarter, the homework will not be turned in,
instead there will be quiz in the discussion section.
- A random subset of the homework problems will be graded each week. However, it is strongly recommended that you
try to complete the entire homework assignment.
- Collaboration on the homeworks is allowed and encouraged.
- All homework assignments must be written by you, i.e. you cannot copy someone else's solution verbatim.
- Label your homework with the lecture number and discussion
- Homework solutions will be posted ... (time)
- Reading the syllabus
counts as one homework grade. In order to
receive credit for reading the syllabus, you must read the
syllabus by January 9th, noon, PST.
- There will be two quizzes, administered in the second and sixth weeks
of class. In the second and sixth weeks of class, the homework will not
be turned in, and instead, the quiz will count for the homework grade.
The problems from the quiz will closely resemble or be identical to
problems from the homework from that particular week.
- Quizzes will be administered in your discussion section, which is on
either Tuesday or Thursday. Each quiz
last about 15 minutes.
- The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the
first midterm (20%), the second midterm (25%), and the final (40%).
Scheme 2: homework (15%), largest
midterm grade (35%), final (50%).
The grade for the semester will be curved. However, anyone who exceeds my
expectations in the class by showing A-level performance on the exams and
homeworks will receive an A for the class.
- We will use the MyUCLA
- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests
for rescheduling will most likely be denied.
- You must attend the final exam to pass the course.
Tentative Schedule: (This schedule may change slightly during the course.)
|Week|| Monday || Tuesday || Wednesday || Thursday || Friday |
|1||Jan 5: 16.1, Integrals in two variables||
||Jan 7: 16.2, Integrals over general regions||Jan 8
||Jan 9: Homework 1 due. 16.3, 12.3, Polar coordinates|
|2||Jan 12: 16.4, 13.7, Integrals in polar
||Quiz in section
||Jan 14: 16.2, 16.3, Triple integrals||Quiz in section
||Jan 16: Homework 2 (ungraded). 16.4, Cylindrical and spherical
||Jan 19: No class
||Jan 21: 16.5, Applications of multiple
integrals|| Jan 22
||Jan 23: Homework 3 due, 16.6, Change of variables
||Jan 26: Midterm #1
||Jan 28: 16.6, Change of vars, 17.1, Vector Fields||Jan
29 ||Jan 30: Homework 4 due. 17.2, Scalar line integrals|
|5||Feb 2: 17.2, Vector line integrals|| ||Feb
4: 17.3, Conservative Vector Fields||Feb 5 ||Feb 6: Homework
5 due. 17.3, Conservative Vector Fields|
|6||Feb 9: 17.4, Parametric
Surfaces||Quiz in section||Feb
11: 17.4, Surface Area, Surface Integrals||Quiz in
Homework 6 (ungraded). 17.5, Surface Integrals of Vector
|7||Feb 16: No class||
||Feb 18: 18.1, Green's Theorem||Feb
20: Homework 7 due, 18.1, Green's Theorem|
|8||Feb 23: 18.2, Stokes' Theorem
||Feb 25: 18.2, Stokes' Theorem
||Feb 27: No homework due. Midterm #2|
|9||Mar 2: 18.2, 18.3, Stokes' Theorem, Divergence
Theorem|| ||Mar 4:
18.3, Divergence Theorem||Mar 5 ||Mar 6: Homework
8 due. 18.3, Divergence Theorem|
|10||Mar 9: Leeway/review|| || Mar 11:
12||Mar 13: Homework 9 due. Review of course|
Advice on succeeding in a math class:
Homework Digest (email questions answered in batch form)
- Review the relevant course material before you come to lecture.
course material a week or two before the semester starts.
- When reading mathematics, use a pencil and paper to sketch the
calculations that are performed by the author.
- Come to class with questions, so you can get more out of the
lecture. Also, finish your homework at
least two days before it is due, to alleviate deadline stress.
- Write a rough draft and a separate final draft for your homework.
This procedure will help you catch mistakes.
- If you are having difficulty with the material or a particular homework problem, review Polya's
Strategies, and come to office hours.