Syllabus
Course name
Multivariable Calculus Math 21a,, Harvard College/GSA: 6760, Fall 2011/2012, Exam group 1This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.
Course head
Oliver Knill, knill@math.harvard.edu, SC 432, Harvard UniversityMeeting time
After a short intro meeting Thursday September 1 at 8:30 AM in Sci Center B, classes are taught in sections on MWF 9,MWF 10,MWF 11, MWF 12, TuTh 1011:30, TuTh 11:301. The classes start on Wednesday, September 7.Problem sessions
Course assistants will run additional problems sessions.Office hours
Office hours of all the crew teaching this course will be posted. You are welcome to join any of the office hours.MQC
The Math question center (MQC) is a place where you can hang out to work on your course work. The MQC takes place SunThu 8:3010:30 PM in SC 309.Prerequisite
A solid single variable calculus background is required. The mathematics department provides advising if you are unsure. You can also check with the course head of this course.The course
It extends single variable calculus to higher dimensions. You will see that the structures are much richer than in single variable and that the fundamental theorem of calculus generalizes to higher dimensions.It provides vocabulary for understanding fundamental processes and phenomena. Examples are planetary motion, economics, waves, heat, finance, epidemiology, quantum mechanics or optimization.
It teaches important background needed in social sciences, life sciences and economics. But it is rigorous enough that it is also suited for students in core sciences like physics, mathematics or computer science.
It builds tools for describing geometrical objects like curves, surfaces, solids and intuition which is needed in other fields like linear algebra or data analysis.
It develops methods for solving problems. Examples are optimization problems with and without constraints, geometric problems, computations with scalar and vector fields, area and volume computations.
It makes you acquainted with a powerful computer algebra system which allows you to see the mathematics from a different perspective. No programming experience is required however.
It prepares you for further study in other fields. Not only in mathematics and its applications, but also in seemingly unrelated fields like game theory, probability theory, discrete mathematics or number theory, where similar structures and problems appear.
It improves thinking skills, problem solving skills, visualization skills as well as computing skills. You will see the power of logical thinking and deduction and why mathematics is timeless.
Lectures:
The lecture times are MWF 9, MWF 10, MWF 11, MWF 12, TuTh 1011:30, TuTh 11:301. The sections are all coordinated and teach the same material. Learning it in a smaller class helps you to absorb it better and to learn more efficiently. You will section for this course online. The actual lectures start on Wednesday, September 7 after labor day. Tuesday/Thursday sections start on Thursday, September 8.Text
We use the Multivariable Calculus: Concepts and Contexts, 4 book by James Stewart: it the fourth edition. This book is used by all sections. The newest Stewart Multivariable Calculus Edition 4E has the ISBN number ISBN13:9780495560548. It is contained also in the "fat version" ISBN10: 0495557420 which contains all single variable. A copy also in the Cabot library on reserve.Exams
There are two midterm exams and one final exam.First hourly: Tuesday, October 4, 2011 HALL C 7:00  8:30PM.
Second hourly: Tuesday, November 1, 2011 HALL C 5:30  7PM
The final exam date will be determined by the registrar later in the semester.
Grades
First and second hourly 30 % total Homework 25 % Mathematica project 5 % Final 40 %  Final grade 100 % 
Mathematica project
The course features a Mathematica project, which introduces you to the advanced and industrial strength computer algebra system. Mathematica 8.0 for which Harvard has a site license. At the end of the semester you submit a short project. The actual lab will be posted later in the semester. This software does not lead to any additional expenses and the total time for doing the lab is of the order of a homework problem.Calendar
FAS Calendar
Day to day lecture
We cover chapters 913 in the book.

Hour Topic Book section Tue Thu 1. Vector geometry 9/79/10 1 Labour day (no class) Sep 5 2  coordinates and distance 9.1 3  vectors and dot product 9.23 2. Functions 9/129/17 1  cross product and planes 9.4 2  lines and planes, distances 9.5 3  level surfaces and quadrics 9.6 3. Curves 9/199/24 1  curves, velocity, acceleration 10.12 2  arc length and curvature 10.34 3  other coordinates 9.7 4. Surfaces 9/2610/1 1  parametric surfaces 10.5 2  functions and continuity 11.12 3  differentiation and gradient 11.3 5. Partial derivatives 10/310/8 1  review for first hourly on Oct 4 2  partial differential equations 11.3 3  linear approximation 11.4 6. Gradient 10/1010/15 1 Columbus day (no class) Oct 10 2  chain rule,implicit different. 11.5 3  tangent, directional deriv. 11.6 7. Extrema 10/1710/22 1  maxima, minima, saddle points 11.7 2  Lagrange multipliers 11.8 3  Global extremal problems 11.8 8. Double Integrals 10/2410/29 1  double integrals 12.13 2  polar integration 12.4 3  surface area 12.6 9. Triple integrals 10/3111/5 1  review for second hourly on Nov 1 2  triple integrals 12.7 3  spherical integration 12.8 10. Line integral theorem 11/711/12 1  vector fields and line integrals 13.12 2  line integral theorem 13.3 3 Veterans day, (no class) Nov 11 11. Greens theorem 11/1411/19 1  Greens theorem 13.4 2  curl and divergence 13.5 3  flux integrals 13.6 12. Stokes theorem 11/2111/26 1  Stokes theorem 13.7 2 Thanksgiving break (no class) Nov 2327 3 Thanksgiving break (no class) 13. Divergence theorem 11/2812/1 1  Stokes review 13.7 2  divergence theorem 13.8 3  overview over integral theorems 