Harvard University,FAS
Summer 2002

Mathematics MathS21a
Summer 2002

Multivariable Calculus

Daniel Goroff and Oliver Knill

Email: smath21a@math.harvard.edu
 
Mainpage Syllabus Announcements Calendar Homework Exams Supplements Links

Syllabus

- Math-S21a: Multivariable Calculus

- Instructors: Daniel Goroff and Oliver Knill

- Course Assistants: Jonathan Kaplan (jkaplan@math.harvard.edu) and
                   Izzet Coskun    (coskun@math.harvard.edu)

- Office hours: 
                  Wednesday 11-12:30 for Goroff in SC-427
                  Mondays   11-12:30 for Knill  in SC-434
                  Tuesdays  13-14:00 for Kaplan in SC-428b

- Website: http://www.courses.fas.harvard.edu/~maths21a/

- Time: Every Tuesday, Wednesday, and Thursday 9:30-11 except 7/4
     The lectures start at 9:30 sharp. 

- Place: Emerson 101 (beginning Thursday 6/27/2002)

- Problem sessions: Thursdays 1-2 in SC-110
                    Thursdays 8-9 in SC-112

- Homework: Weekly HW assigned in three parts, one in each lecture.
            All three parts are due Tuesdays at the start of class.
            No late homework is accepted.  You are encouraged to
            discuss solution strategies with classmates, but you
            must write up answers yourself in your own words.  As
            with any academic work, please cite sources consulted.

- Project: As an optional 8th homework, you may choose to hand in:

         - a computer laboratory project
         - challenge problems you have completed 
         - certain projects and problems from the book 

  If you do decide to work on an 8th assignment, only the best 7 of
  your 8 HW scores will count.  Projects are due on 8/12 at 9:30 am.
  Graduate students are expected to do 2/3 of the 8'th homework to get
  credit for this course. 

- Text: James Stewart, "Multivariable Calculus, Concepts and
  Contexts" can be purchased on line or at the Harvard Coop. Student
  solution manuals are also available.  Please read relevant
  sections of the textbook before you come to class.

- Calendar: (18 lectures in 7 weeks)

       +----------+
  Su Mo| Tu We Th | Fr Sa
       |          |
  23 24| 25 26 27 |28 29   June                     1
  30  1|  2  3 -  | 5  6   July                     2
   7  8|  9 10 11 |12 13                            3
  14 15| 16 17 18 |19 20                            4
  21 22| 23 24 25 |26 27                            5
  28 29| 30 31  1 | 2  3   August                   6
   4  5|  6  7  8 | 9 10                            7
  11 12|    14    |16 17                            8
       +----------+

- Exams: Two Midterms 
              Thursday 7/11 at 9:30, in usual room.
              Thursday 7/25 at 9:30, in usual room. 
  One cumulative Final Examination on Wednesday 8/14 at 9:15am.
  These three exams are required.  Please note the dates and times.
  In general, we expect roughly a third of each test to consist
  of True/False or Conceptional Questions directly from the text,
  and another third to consist of assigned or unassigned 
  exercices directly from the book. 

- Grades: There is a total target of T=1000 points for this course.
  Roughly, we expect people who end up with over 900 points to
  receive some kind of A, people who have 800-900 points to receive
  some kind of B, etc.  A maximum of 820 points can be obtained
  during the term:

             7 Homeworks, each 60 points       420 points
             2 Midterms, each 200 points       400 points

  If you earn N points during the term, your final exam will be worth
  a possible T-N points.  For example,

     1) If you enter the final with all 820 points and get
     50% correct on the final, your course total will be:
     820 + (1000-820) * 50/100 = 910 (probably a low A or high B).

     2) If you enter the final with 430 points and get
     70% correct on the final, your course total will be:
     430 + (1000-430) * 70/100 = 839 (probably a low B).

   Notice this means you can earn back on the final any point you
   miss during the term, so you always have an incentive to keep
   working.  This grading system is very kind to anyone who
   eventually masters the material by the day of the final, but very
   risky for anyone who tries to wait until then.  Please keep up,
   work lots of problems, go over everything you did not get right
   the first time, ask lots of questions, and you will do fine.


- About this course: 

       - extends single variable calculus to higher dimensions;
       - provides vocabulary for understanding the fundamental
         equations of nature (e.g., weather, heat, planetary
         motion, waves, profit maximization, quantum world);
       - provides tools for describing curves, surfaces, and other
         graphical objects in three dimensions;
       - develops methods for solving optimization problems with and
         without constraints;
       - prepares you for further study in many other fields of
         mathematics and its applications;
       - improves thinking skills, problem solving skills,
         visualization skills, and computing skills.

- Syllabus:

Date      Topic                        Book section

        I)    Geometry of Space

6/25    Tue - coordinates                       9.1
            - distance
6/26    Wed - vectors                           9.2
            - dot product                       9.3
6/27    Thu - cross product                     9.4
            - lines and planes                  9.5

        II)   Functions and Graphs

7/2     Tue - functions, graphs                 9.6
            - level curves, quadrics
7/3     Wed - cylindrical coordinates           9.7
            - spherical coordinates
7/4     Thu - holiday

        III)  Curves and Surfaces

7/9     Tue - curves in space                  10.1
            - velocity,acceleration            10.2
7/10    Wed - arc length, curvature            10.3
              parametric surfaces              10.5

7/11    Thu - First Midterm  (chapters 9-10)

        IV)   Partial Derivatives

7/16    Tue - functions                        11.1
            - continuity                       11.2
            - partial derivatives              11.3
            - linear approximation             11.4
7/17    Wed - chain rule                       11.5
            - gradient, directional deriv.     11.6
7/18    Thu - maxima, minima, saddle points    11.7
            - Lagrange multipliers             11.8

        V)    Multiple Integrals

7/23    Tue - double integrals                 12.1
            - iterated integrals               12.2
            - general regions                  12.3
            - polar coordinates                12.4
7/24    Wed - surface area                     12.6
            - triple integrals                 12.7
            - polar, spherical coordinates     12.8
            - change of variables              12.9

7/25    Thu - Second Midterm   (until chapter 12)

        VI)   Line Integrals

7/30    Tue - vector fields                    13.1
            - gradient fields
7/31    Wed - line integrals                   13.2
            - fundamental thm line integrals   13.3
8/1     Thu - application: work
              application: electrostatics

        VII)  Integral Theorems

8/6     Tue - Greens theorem                   13.4
            - curl and divergence              13.5
8/7     Wed - surface integrals                13.6
            - Stokes theorem                   13.7
8/8     Thu - Gauss theorem                    13.8
            - Applications

8/14    Wed   Final Examination 9:15 (chapters 9-13)

Please send comments to maths21a@fas.harvard.edu