Harvard University,FAS
Summer 2005

Mathematics Maths21a
Summer 2005

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 2005


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

- Course assistant: Benjamin Bakker, bakker@post.harvard.edu

- Lectures: Every Tuesday, Wednesday, and Thursday at 9:30-11:00, lectures start 9:30 sharp. - Place: Lecture Hall Emerson 101 Google map centered at Emerson 101, marked local version. - Sections: Thursday 8-9 Emerson Hall 307 1-2 PM, Emerson Hall 106 - Office hours: Oliver: Monday 11:00-12:00, SC 434 and by appointment Ben: - Website: http://www.courses.fas.harvard.edu/~maths21a/ - Text: The book "Multivariable Calculus: Concepts and Contexts" by James Stewart is recommended in addition to following the lectures. Both the newest edition or the older edition are ok. Homework will be distributed in each class and not assigned from the book. - 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 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 21 sessions: 19 lectures plus 2 midterms during 7 weeks from June 28, 2005 to August 11, 2005. This is followed by a final examination week ending August 19. You might want to check out the Official Summerschool Calendar +----------+ +-------------------+ Su Mo| Tu We Th | Fr Sa Events |Week|Exam|Quiz|Proj| -----+----------+------ ----------+-------------------+ 26 27| 28 29 30 | 1 2 June | 1 | | * | | 3 4| 5 6 7 | 8 9 July | 2 | | | | 10 11| 12 13 14 | 15 16 14. hourly| 3 | * | | | 17 18| 19 20 21 | 22 23 | 4 | | * | | 24 25| 26 27 28 | 29 30 28. hourly| 5 | * | | | 31 1| 2 3 4 | 5 6 August | 6 | | * | | 7 8| 9 10 11 | 12 13 | 7 | | | * | 14 15| 16 17 18 | 19 20 16. final | | * | | | +----------+ +-------------------+ - Day to day syllabus: 1. Week: Geometry and Space 28. June: introduction, space, coordinates, distance 29. June: vectors, dot product, projections 30. July: cross product, lines 2. Week: Functions and Surfaces 5. July: planes, distance formulas 6. July: functions, graphs, quadrics 7. July: implicit and parametric surfaces 3. Week: Curves and Partial Derivatives 12. July: curves, velocity, acceleration, chain rule 13. July: arclength, curvature, partial derivatives 14. July: first midterm (on week 1-2) 4. Week: Extrema and Lagrange Multipliers 19. July: gradient, linearization, tangents 20. July: extrema, second derivative test 21. July: extrema with constraints 5. Week: Double Integrals and Surface Integrals 26. July: double integrals, type I,II regions 27. July: polar coordinates, surface area 28. July: second midterm (on week 3-4) 6. Week: Triple Integrals and Line Integrals 2. August: triple integrals, cylindrical coordinates 3. August: spherical coordinates, vector fields 4. August: line integrals, fundamental thm of lineintegrals 7. Week: Exterior Derivatives and Integral Theorems 9. August: curl and Green theorem 10. August: curl and Stokes theorem 11. August: div and Gauss theorem 15 August: Final Review 16 August: Final exam (on week 1-7) Exam: 1:30 PM Tuesday, August 16


Please send comments to maths21a@fas.harvard.edu
Maths21a, Multivariable Calculus, Summer 2005, Department of Mathematics, Faculty of Art and Sciences, Harvard University


Fri Aug 19 20:56:00 EDT 2005