Syllabus

Math21a: Multivariable Calculus	This course 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 also teaches important background needed for statistics, computer science, bioinformatics, etc. You learn tools to describe curves, surfaces, solids and other geometrical objects in three dimensions and develops methods for solving optimization problems with and without constraints. The course prepares you for advanced study in other fields of mathematics and its applications. Furthermore it sharpens your abstract thinking and problem solving as well as visualization and computing skills. Math21a together with Math21b gives a solid background in multivariable calculus, linear algebra and differential equations.
Lectures:	These course offers lectures at MWF 9 AM, MWF 10 AM, MWF 11 AM, TTh 10-11:30 AM, TTH 11:30-1 PM. This course is taught in sections rather than in a large lecture. This allows you to get involved more and to ask questions during lecture. CA's lecture and CA problem sessions will be listed here.
Prerequisites:	Math 1b or equivalent
Course change fees:	All course change fees are waved for students who change between Math 21a, Math 23a, Math 25a and Math 55a until the 5'th Monday of the term.
How to Sign Up:	Input your time preferences from Monday, Sep 15 to Wednesday, Sep 17 2008. On the sectioning and advising page from the Mathematics department
Introductory Meeting:	Tuesday, Sept 16, 2008, Sci Center C, 8:30 AM.
Lectures start:	Mon Sep 22 for MWF sections, and on Tue Feb 23 for TTh sections
Course Head	Oliver Knill Office: Science Center SC-434 Email: knill@math.harvard.edu Office hours: Tue/Thu 4:30 to 5:30
Text	Multivariable Calculus: Concepts and Contexts.3" by James Stewart: we use the third edition. This book is used by all sections. The ISBN of the book is 0-534-41004-9. You find a copy also in the Cabot library on reserve.
Math Question Center MQC	The Math question center (MQC) is open Sundays - Thursdays 8:30 - 10:30 pm (with occasional breaks for holidays). starting September 23 and ending December 15. The MQC will be closed for holidays on October 12, November 10, November 26 and November 27. Place: Sunday nights, in SC 112; on Monday-Thursday nights, in SC 222.
Homework:	Homework is assigned each lecture and due the next lecture. In this course, no late homework is accepted but a fraction of the HW score with weight of a week can be discarded and used as "jokers", for example, in case of sickness. You are encouraged to discuss solution strategies with classmates, your section leader or your CA but you must write up answers yourself in your own words. As with any academic work, external sources which were consulted should be cited. For example, if you use Mathematica for a computation, acknowledge it and add the output.
Computers:	The course features a Mathematica project, which introduces you to an advanced and industrial strength computer algebra system. Mathematica 6. At the end of the semester you submit a short project. The actual lab will be posted here later in the semester. The workload for the lab is not too large, a couple of hours.
Exams:	First Hourly: Tuesday, Oct 21. 2008, Hall B, 7-8:30 PM Second Hourly: Tuesday, Nov 18, 2008, Hall B, 7-8:30 PM Final Examination: TBA Computers and other electronic aids are not permitted during exams.
Grades:	First and second hourly 30 % Homework 25 % Mathematica project 5 % Final exam 40 % ---------------------------------------------- Final grade 100 % ----------------------------------------------
Calendar:	---------------------+--------------------------------------- Su Mo Tu We Th Fr Sa \| week special dates month ---------------------+--------------------------------------- 7 8 9 10 11 12 13 Sep 9: freshmen registr. Sep 14 15 16 17 18 19 20 Sep 16: intro meeting 21 22 23 24 25 26 27 1 Sep 22/23: lectures start 28 29 30 1 2 3 4 2 Oct 5 6 7 8 9 10 11 3 12 13 14 15 16 17 18 4 Oct 13: Columbus day 19 20 21 22 23 24 25 5 Oct 21: First hourly 26 27 28 29 30 31 1 6 Nov 2 3 4 5 6 7 8 7 9 10 11 12 13 14 15 8 Nov 11: Veterans day 16 17 18 19 20 21 22 9 Nov 18: Second hourly 23 24 25 26 27 28 29 10 Nov 27-30 Thanksgiving 30 1 2 3 4 5 6 11 Dec 7 8 9 10 11 12 13 12 14 15 16 17 18 19 20 13 Dec 16: Last day class 21 22 23 24 25 26 27 28 29 30 31 1 2 3 Jan 2-12 Reading period Jan 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Jan 13-22 Final exams 18 19 20 21 22 23 24 Jan 19: Martin Luther
Day to day syllabus:	Hour Topic Book section Tue Thu 1. Geometry of Space 9/22-9/26 1 - coordinates 9.1 \| - distance \| 2 - vectors 9.2 -+ - dot product 9.3 \| 3 - cross product and planes 9.4 \| 2. Functions and Graphs 9/29-10/3 1 - lines and planes 9.5 \| - distance formulas \| 2 - functions 9.6 -+ graphs \| 3 - level curves \| - quadrics \| 3. Curves 10/6-10/10 1 - curves in space 10.1 \| - velocity \| - acceleration 10.2 \| 2 - arc length 10.3 -+ - curvature 10.4 \| 3 - cylindrical coordinates 9.7 \| - spherical coordinates -+ 4. Surfaces 10/13-10/17 1 - Columbus day, no class 2 - parametric surfaces 10.5 \| 3 - functions 11.1 \| - continuity 11.2 \| 5. Functions 10/20-10/26 1 - review for first hourly \| first Midterm (week 1-4) 2 - partial derivatives 11.3 -+ solutions to PDE's \| 3 - linear approximation 11.4 \| 6. Gradient 10/27-19/31 1 - chain rule 11.5 \| implicit differentiation \| 2 - gradient 11.6 -+ tangent spaces \| 3 - directional derivative 11.6 \| 7. Extrema 11/3-11/7 1 - maxima, minima, saddle points 11.7 \| 2 - Lagrange multipliers 11.8 -+ 3 - Global extremal problems 11.8 \| 8. Double Integrals 11/10-11/14 1 - Double integrals 12.1-2 \| TTh do 2 - Double integrals 12.3 \| 12:1-4 3 - polar coordinates 12.4 \| Thursday 9. Surface area 11/17-11/21 1 - Review for second midterm \| second Midterm (week 5-8) 2 - applications of double integrals 12.5 \| - surface area 12.6 \| 3 - triple integrals 12.7 \| 10. Triple and line Integrals 11/24-11/28 2 - cylinder, spherical coordinates 12.8 -+ 3 - vector fields 13.1 + - line integrals 13.2 \| Thanksgiving break 11. Integral Theorems I 12/1-12/5 1 - fundamental thm line integrals 13.3 \| 2 - Greens theorem 13.4 -+ 3 - curl and divergence 13.5 \| 12. Integral Theorems II 12/8-12/12 1 - flux integrals 13.6 \| 2 - Stokes theorem 13.7 -+ 3 - Gauss theorem 13.8 \| - Applications 13.9 \| 13. Free and review 12/15-12/16 1 - Review or free topic. \| Mathematica project due.