Harvard University,FAS
Summer 2004

Mathematics Maths21a
Summer 2004

Multivariable Calculus

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu

Syllabus

-  MathS21a: Multivariable Calculus, of the Harvard Summerschool 2004

-  Instructor: Oliver Knill, SC-434, knill@math

-  Course assistant: Benjamin Bakker
   bakker@fas

-  Lectures: Every Tuesday, Wednesday, and Thursday at 9:30-11:00, 
      lectures start 9:30 sharp. 

-  Place: Lecture Hall Emerson 101

-  Sections: Thursday 8-9 and/or 1-2 PM, Lecture Hall Emerson 104

-  Office hours: Oliver: Monday    10:00-12:00, SC 434 and by appointment
                 Ben:   Monday  19:00-20:00  Math common room (near SC 434) 

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

-  Text: 
      Students who commit to follow this course will be handed out a preliminary 
      lecture notes package during the first week. Final versions of the notes,
      handouts, class material and homework sheets will be distributed during 
      lectures. This allows to follow the course without a book. We recommend 
      however to read in a book like "Multivariable Calculus: Concepts and Contexts" 
      by James Stewart in addition to following the lectures.

-  About this course:

       - extends single variable calculus to higher dimensions;
       - provides vocabulary for understanding fundamental
         equations of nature like weather, planetary motion,
         waves, heat, finance, epidemiology, or quantum mechanics. 
       - teaches important background needed for statistics, 
         computergraphics, bioinformatics, etc;
       - provides tools for describing curves, surfaces, solids 
         and other geometrical objects in three dimensions;
       - develops methods for solving optimization problems with 
         and without constraints;
       - prepares you for further study in other fields of
         mathematics and its applications;
       - improves thinking skills, problem solving skills,
         visualization skills as well as computing skills;

- Homework: Weekly HW will be assigned in three parts, 
         one in each lecture. You will receive a handout for
         each problem set. Problems will not be assigned from books. 
        
- Computers: The use of computers and other 
         electronic aids is not permitted during exams. 
         Mathematica projects are optional and will 
         teach you the basics of a computer algebra system.
         Harvard has a site licence for Mathematica. Using
         this software does not lead to any additional expenses. 
         The total time for doing the lab is 1-3 hours. 
         For people who prefer not to use any computers, there
         will be the possibility to work on some challenge problems or
         to write a little paper on your own. As experience has
         shown, the later options require much more time resources 
         but they can be rewarding too. The project will be handed 
         in during the last lecture.  

- Graduate Credit: This course can be taken for graduate credit. 
         The course work is the same. To fulfill the graduate credit, 
         a minimal 2/3 score has to be reached for the final project. 
         The project can also be chosen in the field of interests of 
         the student. 

- Exams: 
         Two midterm exams and one final exam. The midterms
         will be administered during class time in the usual lecture hall. 
         The final will take place during the examination period. 
         Online quizes are offered during nonexamination weeks 1,2,4,6. 
         They are "light", are of multiple choice nature and will help you to 
         gauge your progress in knowing the basic concepts. The score in 
         the quizzes will allow you to balance the scores in the midterms. 

- Grades: 

         First and second hourly     40 % weighted according to quizz
         Homework                    25 %
         Project                      5 %
         Final                       30 %

         The higher-scoring mid-term will be worth 20+X%, the other mid-term 
         will be worth 20-X%, where X is the total score in the online quizzes 
         scaled from 0 to 8. If the grade on the final exam is higher than 
         the grade from the composite score, then the final grade for the 
         course will be equal to the grade on the final exam. Active class 
         participation and attendence can boost your final grade by up to 5%. 

- Calendar: we have 21 sessions: 19 lectures plus 2 midterms
         during 7 weeks from June 28, 2004 to August 12, 2004. This is 
         followed by a final examination week ending August 20. You might
         want to check out the Official Summerschool Calendar

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

- Day to day syllabus: 

1. Week:  Geometry and Space

  29. June: introduction, space, coordinates, distance
  30. June: vectors, dot product, projections
   1. July: cross product, lines

2. Week:  Functions and Surfaces

   6. July: planes, distance formulas
   7. July: functions, graphs, quadrics
   8. July: implicit and parametric surfaces

3. Week:  Curves and Partial Derivatives

  13. July: curves, velocity, acceleration, chain rule
  14. July: arclength, curvature, partial derivatives
  15. July: first midterm (on week 1-2)

4. Week:  Extrema and Lagrange Multipliers

  20. July: gradient, linearization, tangents 
  21. July: extrema, second derivative test
  22. July: extrema with constraints

5. Week:  Double Integrals and Surface Integrals

  27. July: double integrals, type I,II regions
  28. July: polar coordinates, surface area
  29. July: second midterm (on week 3-4)

6. Week:  Triple Integrals and Line Integrals

   3. August: triple integrals, cylindrical coordiantes
   4. August: spherical coordinates, vector fields
   5. August: line integrals, fundamental thm of lineintegrals

7. Week:  Exterior Derivatives and Integral Theorems

  10. August: curl and Green theorem
  11. August: curl and Stokes theorem
  12. August: div  and Gauss theorem

  17. August: Final exam (on week 1-7)
  1:30 PM.  



Please send comments to maths21a@fas.harvard.edu
Maths21a, Multivariable Calculus, Summer 2004, Department of Mathematics, Faculty of Art and Sciences, Harvard University


Fri Aug 20 15:22:36 EDT 2004