Fall 2011

Harvard Extension School

Mathematics E-21a - Fall 2011

Multivariable Calculus

Professor:
Robert Winters

Course Assistants:
John Tsai
Renée Chipman
Calendar:
Weekly topics, HW assignments, and supplements
Solutions
(requires username/password
given out in class)

The recommended text for this course is Stewart's "Multivariable Calculus: Concepts and Contexts". Either the 4th Edition or the 3rd Edition is acceptable (or an even earlier edition).

 

4th Edition:
ISBN-10: 0-495-56054-5
ISBN-13: 978-0-495-56054-8
(published 2010, Brooks-Cole)

Click on the image
to compare prices.

OR

3rd Edition:
ISBN-10: 0-534-41004-9
ISBN-13: 978-0-534-41004-9
(published 2005, Brooks-Cole)

Click on the image
to compare prices.

Homework assignments are now keyed to the 4th Edition, but all assignments will be made available as PDFs.

A key matching HW exercises in different editions is available on request.

 

Announcements:

The Math E-21a Final Exam took place on Thursday, December 15. The exams are graded and course grades will soon be submitted.

Final Exam Information from the Harvard Extension School
Final exams are administered in on-campus courses at regular class meetings during the exam period listed in the calendar. Instructors inform students of the date and location of their exams. Students who are unable to take their exams at the scheduled times may not make separate arrangements with their instructors to take the exam early or at a later date; grades will not be accepted for students who do this. Students who cannot take their exams at the scheduled time must appeal for a make-up final exam.

Exam #1 took place during the latter part of class on Thursday, Oct 6. Graded exams were returned on Oct 13.

Exam #2 took place during the latter part of class on Thursday, Nov 17. Graded exams were returned on Dec 1.

Approximate letter grades for Exam #1
Total points on exam was 50. Median score was 41.5.
Mean score was 39.3. Standard deviation was 9.7.
score grade   score grade
46+ A 30+ C+
43+ A– 27+ C
39+ B+ 25+ C–
36+ B

22+

 D
33+ B– 0-21 E
Exam #1 solutions
Practice Exam #1        Solutions
    
Approximate letter grades for Exam #2
Total points on exam was 40. Median score was 35.5.
Mean score was 32.7. Standard deviation was 7.3.
score grade   score grade
37+ A 24+ C+
34+ A– 22+ C
31+ B+ 20+ C–
28+ B

18+

 D
26+ B– 0-17 E
Exam #2 solutions
Exam #2 Topics and Practice Exam    Solutions

Due to the Occupants in Harvard Yard, please note the following:

Extension courses will meet as scheduled
Extension courses scheduled to meet this week in Harvard Yard will meet in their regular classrooms.

Five Harvard Yard gates will be open
The following five Harvard Yard gates will be open on their regular schedule: Johnston, Lamont, Thayer, Wadsworth, and Widener. The one exception is Johnston Gate, which will close at 10pm. Please note that the Sever Hall Gate on Quincy Street will be closed.

Harvard identification for entrance to Harvard Yard
Harvard Police and Security Guards will be posted again this week at all open Harvard Yard gates to check the Harvard identification of all persons entering the Yard.

Extension students may enter Harvard Yard through any open gate by presenting to the security guards either your Harvard ID card, if you have one, or the following identification:

A copy of your Fall 2011 Registration Schedule, which you print from your secure Extension School online services account AND

Your government-issued photo ID – e.g., your driver’s license or passport.

Please carry this identification until further notice for entrance to Harvard Yard.

To print your Fall 2011 registration schedule
Log in to online services. From the main menu, select “Course Registration and Schedule” and then “View Course Schedule.” Print your schedule and carry it with you to Harvard. You may print your schedule at these Harvard DCE locations: at 51 Brattle Street, 1st floor, Information Services Lobby; or at 53 Church Street.

If you have questions about these protocols, call Susan McGee, Registrar, Harvard Division of Continuing Education at 617-495-4024.

Classes meet Thursdays from 7:35pm to 9:35pm in Harvard Hall 202.

Note: The Math Placement Exam is NOT required for registration in this course. It is still a good idea to take the exam in order to better assess which mathematics course is most appropriate for you. At a minimum, you should have successfully completed a full year of Calculus prior to taking Multivariable Calculus. Some topics from first-year Calculus (sequences and series, differential equations) are not essential for this Multivariable Calculus course, but you should be comfortable with all facets of differentiation and integration and their applications.

Message from CA John Tsai:
I'm John, and I'll be one of the course assistants for the class this semester. I'll be running an optional weekly problem session to go over topics, examples, and homework questions; feel free to come to any or all of these as you like. The sessions will tae place each Sunday, 7:00-8:00PM, in Science Center 101b. If you have any other questions on the homework or any of the material, please feel free to email me at jtsai@college.harvard.edu. I'm also happy to meet with any of you individually by appointment if you ever need more hands-on assistance with a difficult topic or homework assignment; please email me to arrange a time.

I'd also like to outline the homework policies for this course; feel free to let me know if you have any questions about them.
Due dates: Homework assignments must be submitted either in class a week after they are assigned, or to the dropbox in the Science Center before 9:30PM the day they are due. In case of emergency, please let me know by email so we can arrange something.
Late penalties: Homework assignments submitted after the due dates outlined above but before the following Sunday at 8PM will receive a five-point (one problem's worth) deduction, and any assignments turned in after that will receive a 50% deduction. (However, at no point will any assignment be un-submittable, so it is in your best interest to do all of the assignments.) Your first late homework is a "freebie" and will not be subject to penalty, but save this for when you need it!
Grading: Each problem on the homework will generally be marked out of 5 points. Be sure to show your work; answers alone are not acceptable. All assignments will likely be equally weighted. To be lenient, your lowest score will not be factored into your final course grade.

Thanks for reading all this, and hope you have an enjoyable semester! - John

Math E-21a syllabus - Fall 2011       Printable Math E-21a syllabus (PDF) - Fall 2011

Calendar [Topics and homework assignments are posted here.]

Textbook: Multivariable Calculus: Concepts and Contexts by James Stewart - either the 4th Edition (published 2010 by Brooks-Cole, ISBN: 0495560545) OR the 3rd Edition (published 2005 by Brooks-Cole, ISBN: 0534410049). The text should be available at The Coop or via the Internet. Note: If you can find an inexpensive copy of the 2nd Edition of the Stewart text or a comparable text, this should also work fine. Each homework assignment will be posted as a PDF for those with other editions of the text.

Click on the image of your choice of textbook (to the left) for the best online deals.

Classes meet every Thursday evening from 7:35pm to 9:35pm in Harvard Hall 202 (next to Johnson Gate). The first class meeting is on Thursday, September 1. The Course Assistants will also arrange an optional weekly problem session at a time to be determined.

In addition, starting Sept. 8 there will be an optional pre-class Q&A session each week on Thursday starting soon after 6:30pm in Harvard Hall 202 (our regular classroom, though this may change). The purpose of this session is to resolve questions raised after you have struggled mightily with the homework but were either unsuccessful on some problems or have some doubts. Please don't use this session simply to get answers without having dedicated some time on every homework problem.

Accommodations for students with disabilities must be approved and arranged by Rory Stein, Coordinator for Disability Services. Mr. Stein can be reached at 617-495-0977.

If you are unable to turn in your homework during class, there will be a mail slot on the 3rd floor of the Science Center diagonally across from the elevators. The Math E-21a slot is at the bottom of the black rack with an orange label, one slot for homework being turned in and another slot for graded homework to be returned. However, it is always best to turn in homework in class. Any other arrangements and all rules regarding lateness are at the discretion of the course assistants.

Mega-List of Math E-21a techniques       Math E-21a Useful Facts

Here's something: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html

Mathematica (optional, but worth investigating)
If you would like to experiment with Mathematica to graph parameterized curves and functions f(x, y), find level curves, and much more, here are a few labs that will introduce you to this software and show you how to do most of the basic things that are relevant to Math E-21a. You can also cut and paste images produced by Mathematica into other documents and print some pretty dazzling graphics.
Hands-On Start to Mathematica (Flash presentation from Wolfram.com)

Mathematica Lab #1     Mathematica Lab #2     Mathematica Lab #3
[Right-click to save these files, then open them with Mathematica.]

Download your free Adobe Acrobat Reader for reading and printing PDF formatted documents.

Please send comments to Robert Winters.
URL: http://math.rwinters.com/E21a
Last modified: Saturday, December 24, 2011 8:38 PM