Harvard University,FAS
Summer 2003

Mathematics Maths21a
Summer 2003

Multivariable Calculus

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu
News Syllabus Calendar Homework Exams Handouts Lab Project Faq Links

Syllabus

-  Math-S21a: Multivariable Calculus

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

-  Course assistant Brad Burns, bpburns@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 1-2 PM, Lecture Hall Emerson 104

-  Office hours: Oliver: Wednesday 14:00-15:30, SC-434
                                Monday    10:00-11:00, SC 434 and by appointment
                        Brad:   Mondays   16:00-17:00 Math common room.

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

-  Text: 
      Handouts, other material and homework will be distributed in each class.
      This allows to follow the course without book. We recommend to read besides
      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 the fundamental
         equations of nature (e.g. weather, heat, planetary motion,
         waves, finance, epidemiology, quantum mechanics, 
         bioinformatics, etc.);
       - provides tools for describing curves, surfaces, 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. Homework is collected weekly 
         in class on Tuesdays at the beginning of the lecture.
        
- Computers: The use of computers and other 
         electronic aids is not permitted during exams. 
         A Mathematica project is optional and will teach you 
         the basics of a computer algebra system.

- Exams: 
         Two midterm exams and one final exam.

- Grades: 

         First and second hourly                   40 %
         Homework                                  25 %
         Project                                    5 %
         Final                                     30 %

         The higher-scoring mid-term will be worth 25%, the other mid-term 
         will be worth 15%. 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 grade by 
         up to 5%. 

- Calendar: (21 sessions: 19 lectures plus 2 midterms in 7 weeks)

       +----------+
  Su Mo| Tu We Th | Fr Sa
       |          |
  22 23| 24 25 26 | 27 28  June                     1      
  29 30|  1  2  3 |  4  5  July                     2
   6  7|  8  9 10 | 11 12                           3
  13 14| 15 16 17 | 18 19                           4
  20 21| 22 23 24 | 25 26                           5
  27 28| 29 30 31 |  1  2  August                   6
   3  4| 5  6  7  |  8  9                           7
  10 11| 12 13 14 | 15 16  [13'th 09:00 AM, Final]
       +----------+

- Day to day syllabus: 

1. Week:  Geometry and Space

   24. June: introduction, space, coordinates, distance
   25. June: vectors, dot product, projections
   26. June: cross product, lines

2. Week:  Functions and Graphs

   1. July:  planes, distance formulas
   2. July:  functions, graphs, quadrics
   3. July:  parametric surfaces

3. Week:  Curves and Surfaces

   8. July:  curves, velocity, acceleration
   9. July:  arclength, curvature
  10. July:  first midterm (week 1-2)

4. Week:  Extrema and Lagrange Multipliers

  15. July:  pde's, gradient, chain rule, tangents
  16. July:  extrema, second derivative test
  17. July:  extrema with constraints

5. Week:  Double Integrals and Surface Area

  22. July:  double integrals, type I,II regions
  23. July:  general regions, polar coordinates
  24. July:  surface area

6. Week:  Triple Integrals and line integrals

  29. July:  triple integrals, other coordinates
  30. July:  line integrals, fundamental thm of lineintegrals
  31. July:  second midterm (week 3-5)

7. Week:  Vector Fields and Integral Theorems

  5. August: curl and Greens theorem
  6. August: curl and Stokes theorem
  7. August: div and divergence theorem

 13. August: Final exam (week 1-7)



Please send comments to maths21a@fas.harvard.edu


Sun Aug 17 20:11:50 EDT 2003