harvard logo
Course 30189: Maths21A Summer 2008
Multivariable Calculus
Syllabus
Office: SciCtr 434
Maths21a: Multivariable Calculus of the Harvard Summerschool 2008 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; Learn a powerful computer algebra system; 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;
Lectures: Every Tuesday, Wednesday, and Thursday at 9:30-11:00, lectures start at 9:30 sharp.
Sections: Thursday 8-9 Emerson Hall 307 and 1-2 PM, Emerson Hall 106. Every student choses one section.
Course assistant: Chris Phillips
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. A widely used textbook is "Multivariable Calculus: Concepts and Contexts" by James Stewart. but any multivariable text works. Homework will be distributed each class during lecture. Homework problems are handed out in class.
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. Homework is due on Tuesdays except for the last week, where the homework is due daily.
Exams: Two midterm exams and one final exam. The midterms on July 12 and July 26 will be administered during class time in the usual lecture hall. The final will take place during the examination period. The place and time will be a announced.
Grades:
 First and second hourly     40 % total
 Homework                    25 %
 Project                      5 %
 Final                       30 %
 
Active class participation and attendence can boost your final grade by up to 5%.
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 must be reached for the final project.
Computer project; The use of computers and other electronic aids can not permitted during exams. A Mathematica project 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 a few hours. The project will be handed in at the beginning of the lecture on August 6.
Calendar:
       +----------+                   +--------------+
 Su Mo | Tu We Th | Fr Sa  Events     |Week|Exam|Proj|
 ------+----------+------  -----------+--------------+
 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  10. hourly |  3 |  * |    |
 13 14 | 15 16 17 | 18 19             |  4 |    |    |
 20 21 | 22 23 24 | 25 26  24. hourly |  5 |  * |    |
 27 28 | 29 30 31 |  1  2             |  6 |    |    |
  3  4 |  5  6  7 |  8  9  August     |  7 |    | *  |
 10 11 | 12 13 14 | 15 16  12. final  |    |  * |    |
       +----------+                   +--------------+
 
Day to day syllabus:
 1. Week:  Geometry and Space
 
   24. June: introduction, Eulidean space
   25. June: vectors, dot product, projection
   26. July: cross product, lines
 
 2. Week:  Functions and Surfaces
 
    1. July: planes distances
    2. July: functions, graphs 
    3. July: implicit and parametric surfaces quadrics
 
 3. Week:  Curves and Partial Derivatives
 
    8. July: curves, velocity, acceleration, chain rule
    9. July: arclength, curvature, partial derivatives
   10. July: first midterm (on week 1-2)
 
 4. Week:  Extrema and Lagrange Multipliers
 
   15. July: gradient, linearization, tangents
   16. July: extrema, second derivative test
   17. July: extrema with constraints
 
 5. Week:  Double Integrals and Surface Integrals
 
   22. July: double integrals, type I,II regions
   23. July: polar coordinates, surface area
   24. July: second midterm (on week 3-4)
 
 6. Week:  Triple Integrals and Line Integrals
 
   29. July: triple integrals, cylindrical coordinates
   30. July: spherical coordinates, vector fields
   31. July: line integrals, fundamental thm of lineintegrals
 
 7. Week:  Exterior Derivatives and Integral Theorems
 
    5. August: curl Green and Stokes theorem
    6. August: div and Gauss theorem
    7. August: final review
 
   12  August: Final exam (on week 1-7)
 
 
Please send questions and comments to maths21a@fas.harvard.edu
Maths21A | Oliver Knill | Summer 2008 | Summer school | Department of Mathematics | Faculty of Art and Sciences | Harvard University