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. |
Prerequisites: | Single variable calculus like 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 starting Monday, August 31, and no later than 12:00 pm (noon) on Thursday, September 3rd. See the sectioning and advising page from th e Mathematics department. |
Introductory Meeting: | Tuesday, Sept 3, 2009, Sci Center C, 8:30 AM. |
Lectures start: | Wed Sep 9 for MWF sections Thu Sep 10 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 |
Head CA: Anna Marie Wagner | |
Text | Multivariable Calculus: Concepts and Contexts, 4" by James Stewart: we use the fourth edition. This book is used by all sections. The newest Stewart Multivariable Calculus Edition 4E as the ISBN-13:978-0-495-56054-8. It is contained also in the "fat version" ISBN-10: 0-495-55742-0 which contains all single variable. 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). 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 work load for the lab is not too large, a couple of hours. |
Exams: |
First Hourly: Tuesday, Oct 6. 2009, Hall C, 7-8:30 PM Second Hourly: Tuesday, Nov 3, 2009, Hall C, 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: |
Calendar FAS --------------------------------------------------------------- Su Mo Tu We Th Fr Sa Event --------------------------------------------------------------- 1 2 3 4 5 Sep 3 Intro meeting 8:30 AM SC C 6 7 8 9 10 11 12 1 Sep 7 Labor day, Sep 9, first day 21a 13 14 15 16 17 18 19 2 20 21 22 23 24 25 26 3 27 28 29 30 1 2 3 4 4 5 6 7 8 9 10 5 Oct 6 First hourly 7 PM Hall C 11 12 13 14 15 16 17 6 Oct 12 Columbus day 18 19 20 21 22 23 24 7 25 26 27 28 29 30 31 8 1 2 3 4 5 6 7 9 Nov 3 Second hourly 7 PM Hall C 8 9 10 11 12 13 14 10 Nov 11 Veterans day 15 16 17 18 19 20 21 11 22 23 24 25 26 27 28 12 Nov 26-29 Thanksgiving 29 30 1 2 3 4 5 13 Dec 3 last day of classes 6 7 8 9 10 11 12 Fall reading period 13 14 15 16 17 18 19 Final Exam 20 21 22 23 24 25 26 Dec 21 Final exams end 27 28 29 30 31 1 2 Jan 3 end winter recess |
Day to day syllabus: |
Hour Topic Book section Tue Thu 1. Geometry of Space 9/9-9/12 1 - coordinates 9.1 | - distance | 2 - vectors 9.2 -+ - dot product 9.3 | 2. Functions and Graphs 9/14-9/19 1 - cross product and planes 9.4 | 2 - lines and planes 9.5 | - distance formulas | 3 - functions, graphs 9.6 -+ level curves, and surfaces | - quadrics | 3. Curves 9/21-9/26 1 - curves in space, velocity 10.1 | - acceleration 10.2 | 2 - arc length 10.3 -+ - curvature 10.4 | 3 - cylindrical coordinates 9.7 | - spherical coordinates -+ 4. Surfaces 9/28-10/3 1 - parametric surfaces 10.5 | 2 - functions and continuity 11.1 | 3 - continuity 11.2 | - partial derivatives 11.3 5. Functions 10/5-10/10 1 - review for first hourly | first Midterm (week 1-4) Oct 6 2 - Solutions to partial 11.3 -+ differential equations | 3 - linear approximation 11.4 | 6. Gradient 10/12-10/17 Columbus day (no class) Oct 12 1 - chain rule 11.5 | implicit differentiation | 2 - gradient, tangent spaces 11.6 -+ - directional derivative 11.6 | 7. Extrema 10/19-10/24 1 - maxima, minima, saddle points 11.7 | 2 - Lagrange multipliers 11.8 -+ 3 - Global extremal problems 11.8 | 8. Double Integrals 10/26-10/31 1 - Double integrals 12.1-2 | 2 - Double integrals 12.3 | 3 - Polar integration 12.4 | 9. Surface area 11/2-11/7 1 - Review for second midterm | second Midterm (week 5-8) Nov 3 2 - applications of double integrals 12.5 | - surface area 12.6 | 3 - triple integrals 12.7 | 10. Vector fields 11/9-11/14 1 - cylinder, spherical coordinates 12.8 -| 2 Veterans day, no class -+ 3 - vector fields and line integrals 13.1-2 | 11. Integral Theorems I 11/16-11/21 1 - fundamental thm line integrals 13.3 | 2 - Greens theorem 13.4 -+ 3 - curl and divergence 13.5 | 12. Integral Theorems II 11/23-11/28 1 - flux integrals 13.6 | 2 - Stokes theorem 13.7 -+ Thanksgiving break 13. Integral Theorems III 11/30-12/3 1 - Stokes theorem review 2 - Gauss theorem 13.8 | 3 - Overview over integral theorems | Mathematica project due. |