Maths21a, Summer 2009, Multivariable Calculus,

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)