Ma 1c-an:  Calculus of One and Several Variables and Linear (Spring 2016-17)



Final Exam Review

Final exam review sessions will be held in your recitations this week, in class on Friday and with Nathan on Saturday June 10 at 11am in 151 Sloan.


Request Section Change

Please use this online request form if you want to change your recitation section.


This page was last updated:   .


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 - 10:55, 151 SLN


Alexander Kechris
386 Sloan


Section 11 - Jim Tao
Office Hours: Sunday, 1-2 pm
307 Kellogg, 626-395-5762
Thursdays, 9:00 AM
119 DWN
Section 12 - Nathan Lawless
Office Hours: Friday, 4-5 pm
280 Sloan, 626-395-3733
Thursdays, 10:00 AM
119 DWN
Section 13 - Victor Zhang
Office Hours: Saturday 3-4 pm
155 Sloan, 626-395-4081
Thursday, 1:00 PM
119 DWN
Section 14 - Siqi He
Office Hours: Sunday, 10-11 pm
356 Sloan, 626-395-1732
Thursday, 2:00 PM
119 DWN


Dr. A Kechris
386 Sloan
Wednesday 11:00 am - 12:00 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 Policy

Homework is due Mondays at 3:00pm 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 note 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
4/7/17 Week 1
4/13/17 Week 2
4/20/17 Week 3
4/27/17 Week 4
5/11/17 Week 6
5/18/17 Week 7
5/25/17 Week 8
6/1/17 Week 9


Due Date Homework Solutions
 Monday, April 10
at 10:00 am
HW #1
 Monday, April17
at 10:00 am
 HW #2  Solutions
 Monday, April 24
at 10:00 am
 HW #3  Solutions
 Monday, May 1
at 10:00 am
 HW #4  Solutions
 Monday, May 15
at 3:00 pm
 HW #5  Solutions
 Monday, May 22
at 3:00 pm
 HW #6  Solutions
 Tuesday, May 30
at 3:00 pm
(note change in date)
 HW #7  Solutions
 Monday, June 5
at 3:00 pm
 HW #8 (last HW)  Solutions



Midterm Solutions


Final Solutions