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Course 30189: Maths21A Summer 2009
Multivariable Calculus
Syllabus
Office: SciCtr 434
Maths21a: Multivariable Calculus of the Harvard Summerschool 2009 This is a standard multivariable calculus course. It extends single variable calculus to higher dimensions; It provides vocabulary for understanding fundamental equations of nature like weather, planetary motion, waves, heat, finance, epidemiology, or quantum mechanics. It teaches important background needed for statistics, computergraphics, bioinformatics, etc; It builds tools for describing curves, surfaces, solids and other geometrical objects in three dimensions; It develops methods for solving optimization problems with and without constraints; It makes you acquainted with a powerful computer algebra system. It prepares you for further study in other fields of mathematics and its applications; It improves thinking skills, problem solving skills, visualization skills as well as computing skills;
Lectures: Every Tuesday and Thursday at 8:30-11:30,
Sections: Thursday 1-2.
Course assistant: Chris Phillips
Office hours: Thursday 2 PM. 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 (current multivariable textbooks are all very similar). We cover the material which can be found in chapters 9-12 of Stewart or chapters 10-14 in Varberg Purcell Rigdon or chapters 10-15 in Smith Minton. 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 9 and July 23 will be administered during class time in the usual lecture hall. The final exam will take place during the examination period in the usual lecture hall.
Grades:
 First and second hourly     40 % total
 Homework                    25 %
 Project                      5 %
 Final                       30 %
 
Active class participation and attendance 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 Mathematica project.
Mathematica 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 license for Mathematica, a professional computer algebra system. 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 July 30.
Calendar:
       +----+    +----+
 Su Mo | Tu | We | Th | Fr Sa  Week Event       
 ------+----+----+----+------------------------
 21 22 | 23 | 24 | 25 | 26 27    1  23. June start
 28 29 | 30 |  1 |  2 |  3  4    2  July
  5  6 |  7 |  8 |  9 | 10 11    3  9.  hourly
 12 13 | 14 | 15 | 16 | 17 18    4
 19 20 | 21 | 22 | 23 | 24 25    5  23. hourly
 26 27 | 28 | 29 | 30 | 31  1    6  August,
  2  3 |  4 |  5 |  6 |  7  8    7  Exam on Aug 6
       +----+    +----+
 
Day to day syllabus:
 1. Week:  Geometry and Space
 
    June 23: space, vectors, 
              dot product, projection
    June 25: cross product, lines, 
              planes, distances
 
 2. Week:  Surfaces and Curves
 
    June 30: functions, graphs, 
              implicit and parametric surfaces
    July 2: curves, velocity, acceleration, 
              chain rule and curvature
 
  3. Week:  Linearization and Gradient
 
     July 7:  partial derivatives,
              partial differential equations, review
     July 9: first midterm    
             gradient, linearization
             tangent lines and planes
 
  4. Week:  Extrema and Lagrange Multipliers
 
    July 14: extrema, second derivative test, 
              Lagrange multiplier method
    July 16: double integrals, Type I and II regions
              polar integration, surface area
 
  5. Week:  Double Integrals and Triple Integrals
 
    July 21: triple integrals, cylindrical coordinates 
             integration in spherical coordinates
    July 23: second midterm (on week 3-4)
             vector fields and line integrals
 
  6. Week:  Vector fields and Integral Theorems
 
    July 28: 2d curl and Greens theorem
             3d curl and flux integrals
    July 30: Stokes theorem 
             Gauss theorem.
 
  7. Week:  Final exam (Aug 6)
 
Please send questions and comments to maths21a@fas.harvard.edu
Maths21A | Oliver Knill | Summer 2009 | Summer school | Department of Mathematics | Faculty of Art and Sciences | Harvard University QR code of this page