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Course 30189: Maths21A Summer 2009
Multivariable Calculus
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.
 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.
       +----+    +----+
 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