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 advanceded 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.
Lectures:	CA's lecture and CA problem sessions are listed on the section page
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 17 to Wednesday, Sep 19 2007. On the sectioning page.
Introductory Meeting:	Tuesday, Sept 18, 2007, Sci Center C, 8:30 AM.
Lectures start:	Mon Sep 24 for MWF sections, and on Tue Feb 25 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" by James Stewart. We will use the third edition. This book is used by all sections.
Math Question Center MQC	The Math question center (MQC) is open Sundays - Thursdays 8:30 - 10:30 pm (with occasional breaks for holidays). Note that this semester, the MQC for Math21a and Math21b is in Science Center 216.
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. We will use Mathematica 6 this fall which has gotten fantastic new features. Note that computers and other electronic aids can not be permitted during exams.
Exams:	First Hourly: Wednesday, Oct 17. 2007, Hall A and D, 7-8:30 PM Second Hourly: Thursday , Nov 15, 2007, Hall A and E, 7-8:30 PM Final Examination: TBA
Grades:	First and second hourly 30 % Homework 25 % Mathematica project 5 % Final exam 40 % ---------------------------------------------- Final grade A 100 % Final grade B () Final ---------------------------------------------- For students which are seen regularly in class and which turn in HW regularly (all but 5 HW are turned in), the grade is computed as follows (resurrection). ---------------------------------------------- Final grade: max(A,B) ---------------------------------------------- () if the final average is more than 10% of midterm average, B will be lineary curved for all students to get within 10% of the midterm mean. We do not expect the final to be off more than 10% however so that B will be the final grade. For students who do not qualify, grade A is the final grade as before.
Calendar:	---------------------+--------------------------------------- Su Mo Tu We Th Fr Sa \| week special dates month ---------------------+--------------------------------------- 9 10 11 12 13 14 15 Sep 10: freshmen regist. Sep 16 17 18 19 20 21 22 Sep 19: intro meeting 23 24 25 26 27 28 29 1 Sep 24/25: lectures start 30 1 2 3 4 5 6 2 Oct 7 8 9 10 11 12 13 3 Oct 8: Columbus day 14 15 16 17 18 19 20 4 1. hourly 21 22 23 24 25 26 27 5 28 29 30 31 1 2 3 6 Nov 4 5 6 7 8 9 10 7 11 12 13 14 15 16 17 8 Nov 12: Veteransday, 2. hourly 18 19 20 21 22 23 24 9 Nov 22-25 thanksgiving 25 26 27 28 29 30 1 10 Dec 2 3 4 5 6 7 8 11 9 10 11 12 13 14 15 12 16 17 18 19 20 21 22 13 Dec 18: last day of class 23 24 25 26 27 28 29 30 31 1 2 3 4 5 Jan 2-12: reading period Jan 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Jan 15: Martin Luther day 20 21 22 23 24 25 26 Final exam ---------------------+---------------------------------------
Day to day syllabus:	Hour Topic Book section Tue Thu 1. Geometry of Space 9/24-9/28 1 - coordinates 9.1 \| 1 - distance \| 2 - vectors 9.2 -+ - dot product 9.3 \| 2 3 - cross product and planes 9.4 \| 2. Functions and Graphs 10/1-10/5 1 - lines and planes 9.5 \| - distance formulas \| 1 2 - functions 9.6 -+ graphs \| 3 - level curves \| 2 - quadrics \| 3. Curves 10/8-10/12 - Columbus day, no class 1 - curves in space 10.1 \| 1 - velocity \| - acceleration 10.2 \| 2 - arc length 10.3 -+ 2 - curvature 10.4 \| 4. Surfaces 10/15-10/19 1 - review for first hourly \| 1 first Midterm (week 1-3) 2 - cylindrical coordinates 9.7 \| 1 - spherical coordinates -+ 3 - parametric surfaces 10.5 \| 2 5. Functions 10/22-10/26 1 - functions 11.1 \| 1 - continuity 11.2 \| 2 - partial derivatives 11.3 -+ solutions to PDE's \| 2 3 - linear approximation 11.4 \| tangent planes 6. Gradient 10/29-11/2 1 - chain rule 11.5 \| 1 implicit differentiation \| 2 - gradient 11.6 -+ gradient and level curves \| 2 3 - directional derivative 11.6 \| direction of steepest decent \| 7. Extrema 11/5-11/9 1 - maxima, minima, saddle points 11.7 \| 1 2 - Lagrange multipliers 11.8 -+ 3 - Global extremal problems 11.8 \| 2 8. Double Integrals 11/12-11/16 1 - Veterans day (no class) \| 2 - Review for second midterm \| 2 second Midterm (week 4-7) 3 - Double integrals 12.1-3 \| 9. Surface area 11/19-11/23 1 - polar coordinates 12.4 \| 1 - applications of double integrals 12.5 \| 2 - surface area 12.6 \| Thanksgiving break 10. Triple and line Integrals 11/26-11/30 1 - triple integrals 12.7 \| 1 2 - cylinder, spherical coordinates 12.8 -+ 3 - vector fields 13.1 + - line integrals 13.2 \| 2 11. Integral Theorems I 12/3-12/7 1 - fundamental thm line integrals 13.3 \| 1 2 - Greens theorem 13.4 -+ 3 - curl and divergence 13.5 \| 2 12. Integral Theorems II 12/10-12/14 1 - flux integrals 13.6 \| 1 2 - Stokes theorem 13.7 -+ 3 - Gauss theorem 13.8 \| 2 - Applications 13.9 \| 13. Free and review 12/17-12/18 1 - Review or free topic. \| 1 Mathematica project due.