Harvard University,FAS
Summer 2006

Mathematics Maths21a
Summer 2006

Multivariable Calculus

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

Harvard Summer school

Syllabus

-  MathS21a: Multivariable Calculus, of the Harvard Summerschool 2006

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

-  Course assistant: Chris Phillips (phillips@fas)

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

-  Place: Lecture Hall Emerson 101 Google map, (marked local version).

-  Sections: Thursday 8-9 Emerson Hall 307 
      1-2 PM, Emerson Hall 106 

-  Office hours: Oliver: Monday  15:30-16:30, SC 434 and by appointment

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

-  Text: Reading a textbook gives you a second opinion on the material.
      We can recommend the new multivariable calculus book 
      by Brian Blank and Steven Krantz. It is available as a paperback edition 
      and is less than half the prize of other books like 
      "Multivariable Calculus: Concepts and Contexts" by James Stewart. 
      The Blank-Krantz book fits this summerschool syllabus beautifully (evenso 
      we treat some topics in other order). Alternatively, any multivariable text 
      works. Homework will be distributed each class during lecture. Homework 
      problems are not given from textbooks. 

-  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. 

- Quizes: We will have three short online multiple choice quizes.
         The quizes do not enter the grade directly but allow to weight
         the quiz score better. More details below. 
        
- 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
         and all three quizes have to be completed. The project can 
         also be chosen by the student. 

- Exams: 
         Two midterm exams and one final exam. The midterms on July 13 and July 27
         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 20 sessions: 18 lectures plus 2 midterms
         during 7 weeks from June 27, 2006 to August 10, 2006. This is 
         followed by a final examination week ending August 18. You might
         want to check out the Official Summerschool Calendar

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

- Day to day syllabus: 

1. Week:  Geometry and Space

  27. June: introduction, Eulidean space, vectors in the plane
  28. June: vectors in space dot product, projection and component
  29. July: cross product, lines, planes, distances, triple product

2. Week:  Functions and Surfaces

   4. July: independence day
   5. July: functions, graphs, quadrics
   6. July: implicit and parametric surfaces

3. Week:  Curves and Partial Derivatives

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

4. Week:  Extrema and Lagrange Multipliers

  18. July: gradient, linearization, tangents 
  19. July: extrema, second derivative test
  20. July: extrema with constraints

5. Week:  Double Integrals and Surface Integrals

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

6. Week:  Triple Integrals and Line Integrals

   1. August: triple integrals, cylindrical coordinates
   2. August: spherical coordinates, vector fields
   3. August: line integrals, fundamental thm of lineintegrals

7. Week:  Exterior Derivatives and Integral Theorems

   8. August: curl and Green theorem
   9. August: curl and Stokes theorem
  10. August: div  and Gauss theorem

  14  August: Final Review
  15  August: Final exam (on week 1-7)
  Exam: 1:30 PM Tuesday, August 15
   


Please send comments to maths21a@fas.harvard.edu
Maths21a, Multivariable Calculus, Summer 2006, Department of Mathematics, Faculty of Art and Sciences, Harvard University


Fri Aug 18 10:21:21 EDT 2006