Maths21a, Summer 2007, Multivariable Calculus,

Maths21a: Multivariable Calculus of the Harvard Summerschool 2007	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: Emil Pitkin (pitkin@fas.harvard.edu).	TBA
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.
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. Instead of the computer algebra project, a student can work on some challenge problems or write a paper on a subject. The project will be handed in at the start of the last lecture.
Calendar:	+----------+ +--------------+ Su Mo\| Tu We Th \| Fr Sa Events \|Week\|Exam\|Proj\| -----+----------+------ ----------+--------------+ 24 25\| 26 27 28 \| 29 30 June \| 1 \| \| \| 1 2\| 3 4 5 \| 6 7 July \| 2 \| \| \| 8 9\| 10 11 12 \| 13 14 12. hourly\| 3 \| * \| \| 15 16\| 17 18 19 \| 20 21 \| 4 \| \| \| 22 23\| 24 25 26 \| 27 28 26. hourly\| 5 \| * \| \| 29 30\| 31 1 2 \| 3 4 August \| 6 \| \| \| 5 6\| 7 8 9 \| 10 11 \| 7 \| \| * \| 12 13\| 14 15 16 \| 17 18 final \| \| * \| \| +----------+ +--------------+
Day to day syllabus:	1. Week: Geometry and Space 26. June: introduction, Eulidean space 27. June: vectors, dot product, projection 28. July: cross product, lines, planes, distances 2. Week: Functions and Surfaces 3. July: functions, graphs, quadrics 4. July: independence day, no class 5. July: implicit and parametric surfaces 3. Week: Curves and Partial Derivatives 10. July: curves, velocity, acceleration, chain rule 11. July: arclength, curvature, partial derivatives 12. July: first midterm (on week 1-2) 4. Week: Extrema and Lagrange Multipliers 17. July: gradient, linearization, tangents 18. July: extrema, second derivative test 19. July: extrema with constraints 5. Week: Double Integrals and Surface Integrals 24. July: double integrals, type I,II regions 25. July: polar coordinates, surface area 26. July: second midterm (on week 3-4) 6. Week: Triple Integrals and Line Integrals 31. July: triple integrals, cylindrical coordinates 1. August: spherical coordinates, vector fields 2. August: line integrals, fundamental thm of lineintegrals 7. Week: Exterior Derivatives and Integral Theorems 7. August: curl and Green theorem 8. August: curl and Stokes theorem 9. August: div and Gauss theorem 12 August: Final review 14 August: Final exam (on week 1-7) Exam: