[Ma 1c Analytical]: Vector Calculus (2014-15)


The last homework #8 is due on Monday, June 1 at 10:00 am.

If you received an extension for any homework, please turn it in
by Friday, June 5, 10:00 am at the latest. We will not accept any
homeworks beyond this date.

The final will be handed out in class on Friday, June 5 and will be
available in the math office afterwards. It will be due on
Wednesday, June 10 at noon.

There will be final review sessions in the recitation sections on
Thursday, June 4 and in class on Friday, June 5. Moreover, Brian
Hwang will hold a final review session on Monday, June 8 at
10:00 am in Sloan 151.

Section Change


The lectures will take place on Mondays, Wednesdays and Fridays in 151 Sloan at 10:00 AM. The course will not follow any text, but will present a large chunk of the material covered in Chapters 8-12 in the second volume of T. Apostol's Calculus. Supplementary notes on Vector Calculus (by D. Ramakrishnan) will be also posted weekly on the course web site. We will cover the following topics in the course:

  1. Subsets of Euclidean Space, Vector Fields and Continuity
  2. Differentiation in Higher Dimensions
  3. Tangent Spaces, Normals and Extrema
  4. Multiple Integrals
  5. Line Integrals
  6. Green's Theorem
  7. Div, grad and curl
  8. Change of Variables, Parametrizations, Surface Integrals
  9. The Theorems of Stokes and Gauss


The only prerequisites are Ma 1a, 1b.


MWF 10:00 AM, in 151 Sloan


Alexander Kechris
386 Sloan


Section 7 - Brian Hwang
Office Hours: Sundays, 9 PM
158 Sloan, 626-395-4373
Thursdays, 9:00 AM
153 Sloan
Section 8 - Gaurav Sinha
Office Hours: Saturdays, 2 PM
385 Sloan, 626-395-1732
Thursdays, 10:00 AM
257 Sloan
Section 9 - Andrei Frimu
Office Hours: Sundays, 5 PM
155 Sloan, 626-395-4081
Thursday, 11:00 AM
159 Sloan
Section 10 - Pooya Vahidi Ferdowsi
Office Hours: Saturdays, 11 AM
155 Sloan, 626-395-4081
Thursday, 1:00 PM
159 Sloan
Section 11 - Gaurav Sinha
Office Hours: Saturdays, 2 PM
385 Sloan, 626-395-1732
Thursday, 2:00PM
159 Sloan
Section 12 - Nathan Lawless
Office Hours: Sundays, 4 PM
155 Sloan, 626-395-4081
Thursday, 10:00 AM


Dr. Kechris

Wednesdays, 11 - 12:00

Lead TA

Brian Hwang
Sundays, 9 - 10 PM



There will be weekly homework assignments, a Midterm and a Final examination. The final grade will depend on a composite of these factors; to be precise, the homework will be worth 40 percent, while the final and midterm will each be worth 30 percent. No one will be excused from the final.


Please go to the recitations. Each week, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the instructor will not have time to present in class. In general, get to know your TA and bug him/her with your questions, and try to fill in all the holes in your understanding.


Homework is due Mondays at 10am and will be posted on the course web site at least a week before it is due. All problems may be done in collaboration with others. However, each student must write down the solution in his/her own individual way and there should be no two identical solutions to any problem. Do not consult the solution sets from previous years in working this year's problems. Collaboration is not allowed in the exams. The following table gives more details on what is and what is not allowed.

  Homework Exams
You may consult:    
Course textbook (including answers in the back) YES YES
Other books YES NO
Solution manuals NO NO
Internet YES NO
Your notes (taken in class) YES YES
Class notes of others YES NO
Your hand copies of class notes of others YES YES
Photocopies of class notes of others YES NO
Electronic copies of class notes of others YES NO
Course handouts YES YES
Your returned homework / exams YES YES
Solutions to homework / exams (posted on webpage) YES YES
Homework / exams of previous years NO NO
Solutions to homework / exams of previous years NO NO
Emails from TAs YES NO
You may:

Discuss problems with others YES NO
Look at communal materials while writing up solutions YES NO
Look at individual written work of others NO NO
Post about problems online NO NO
For computational aids, you may use:

Calculators YES* NO
Computers YES* NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

At most one late homework set will be accepted, and only at your TA's discretion, if arrangements have been made in advance with your TA, and if the work is less than a week late. Beyond this, late homeworks will NOT be accepted, except with a letter form the health center or from the Dean's office. Every week, graded homeworks can be picked up from the TA during the recitation on Thursday.




Apostol, Tom M.  Calculus, Vol. II, Multi-Variable Calculus and Linear Algebra with Applications, 2nd Ed., John Wiley, 1967, ISBN:  0-471-00007-8.


Date Description
4/3/2015 Week 1
4/9/2015 Week 2
4/16/2015 Week 3
Week 4, 5
Week 6
Week 7

Week 7a
Week 8
Week 9


Due Date Homework Solutions
 Monday, April 6 at 10:00 am
 Homework #1  
 Monday, April 13 at 10:00 am
 Homework #2  
 Monday, April 20 at 10:00 am
 Homework #3  
 Monday, April 27 at 10:00 am
 Homework #4  
 Monday, May 11 at 10:00 am
 Homework #5  
 Monday, May 18 at 10:00 am
 Homework #6  
 Tuesday, May 26 at 10:00am
 Homework #7  
 Monday, June 1 at 10:00 am
(last homework)
 Homework #8  


Midterm exam   Solutions

Final exam         Solutions