Fall 2009

Harvard Extension School
Mathematics E-21a - Fall 2009
Multivariable Calculus

Professor:
Robert Winters
(click here to contact me)

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", 3rd Ed.
 ISBN:  0534410049.
It should be available at the Harvard Coop and may also be purchased online, generally at a much lower price. Click on the image to compare prices.

A copy of this text will be placed on reserve in the Extension School Library in Sever Hall.

If you can get a copy of the new 4th Edition of the text or the 2nd Edition of the text for a good price, it will work OK. Homework assignments will be made available as PDFs.

Announcements: 

HW #14 (do the problems, but don't turn them in) is now posted in the Calendar.

All homework solutions are now posted. New homework will no longer be accepted unless prior arrangements have been made.

The Final Exam will take place on Thursday, December 17 from 7:35pm to 9:35pm in Emerson Hall Room 105. Please note that this is not our usual lecture hall.

Practice Final Exam problems     Solutions

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

There have been an unprecedented number of requests from students to take the Final Exam at some time other than the scheduled time on Thursday, Dec 17 from 7:35pm to 9:35pm. This exam date has been known and clearly posted on the course website since before the course began.

Here's what the Harvard Extension School has to say about make-up exams:

Make-up exams

Students who cannot take their final exams as scheduled because of documented serious illness or compelling, unexpected circumstances may appeal for a make-up final exam. Students must provide documentation of the reason for missing the exam and be able to successfully complete the course for which the make-up exam is requested. They also must have records of good attendance and participation.

Students may appeal for make-up exams within 3 days of the missed exams by submitting make-up final exam forms. Forms must be submitted by December 24 for fall courses or May 19 for spring courses.

Original documentation explaining the reason for missing the final exam must accompany the appeal. Documentation must be on official letterhead and include specific dates. Medical documentation must be based on a physical examination within 3 days of the missed exam and must include an explanation of the illness relevant to the student’s inability to take the exam.

A $25 nonrefundable processing fee for each make-up exam requested must be included with the appeal. Students are advised to call Academic Services before submitting appeals. Make-up exams are not available for Institute for English Language courses.

The make-up exams are administered at 51 Brattle Street on Saturday, January 23, 2010, for fall courses and Saturday, May 26, 2010, for spring courses. A student who does not take the exam as scheduled is assigned a failing grade for the exam.

Exam #2 took place on Thursday, Nov 19.

Approximate letter grades for Exam #1
Total points on exam was 50. Median score was 40.
Mean score was 37.8. Std. dev. was 11.0.
score grade      score grade
45+ A 28+ C+
41+ A- 25+ C
37+ B+ 23+ C-
33+ B 21+ D
30+ B- 0-20 E
Exam 1 Topics and Practice Exam #1     Solutions 
Exam #1 solutions
    
Approximate letter grades for Exam #2
Total points on exam was 60. Median score was 51.
Mean score was 48.2. Std. dev. was 11.7.
score grade      score grade
55+ A 36+ C+
51+ A- 32+ C
48+ B+ 28+ C-
45+ B 25+ D
40+ B- 0-24 E
Exam #2 topics and Practice Exam #2      Solutions
Exam #2 solutions

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

There are 89 students now registered in the course (as of Thursday, November 26).

Click on the image of the textbook (to the left and down) for the best online deals. We're using the 3rd edition of the Stewart text, but I want to emphasize that it is not necessary to have a current edition of the text for this course and, in truth, almost any multivariable calculus text will suffice. Though almost all of the assigned homework problems will be taken from Stewart's Multivariable Calculus: Concepts and Contexts, 3rd Edition, all assignments will be posted as PDF's on the course website.

Class meets Thursday evenings from 7:35pm to 9:35pm, in Harvard Hall 201 (next to Johnson Gate).

A pre-class problem session will take place each week starting shortly after 6:30pm in our regular lecture hall (Harvard Hall 201) before class. This session is for last-minute questions on the weekly homework. This session is purely optional, but students have found it helpful in the past.

Course Assistant Umang Shukla has a problem session each Monday evening from 7:30pm until 8:30pm in Science Center Room 109. Our other Course Assistant is Renee Chipman. Additional details may follow.

If you are unable to turn in your homework during class, there is 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.

Calendar [Topics and homework assignments will posted here.]

Math E-21a syllabus 

Printable Math E-21a syllabus (PDF)

Note: The Math Placement Exam is NOT required for registration in this course. It is still a good idea to take it in order to better assess which mathematics course is most appropriate for you.

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:  Monday, December 14, 2009