Fall 2019

Harvard Extension School
Mathematics E-21a - Fall 2019
Multivariable Calculus

Professor:
Robert Winters

Teaching Assistants:
Renée Chipman
Jeremy Marcq

Calendar:
Weekly topics, HW assignments, and supplements
Solutions
(requires username/password)
Canvas site


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). PLEASE buy a used copy of either edition using the links below.

 

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 Final Exam will take place on Thursday, December 19, from 8:00pm to 10:00pm in Science Center Hall C. The topics will be drawn from the entire course with added emphasis on the most recent topics, i.e. integration on curves and surfaces and the major theorems: Fundamental Theorem of Line Integrals, Green's Theorem, Divergence Theorem, and Stokes' Theorem.

This will be a two hour exam. There will be no special arrangements for alternate times or locations for the Final Exam except for students with disabilities. Any medical exceptions must be requested directly via the Extension School. Distance students should make the necessary arrangements through the Exams Office.

A Practice Exam and Solutions will be posted soon.


HW #14 problems (PDF) - Do these problems, but don't turn them in (solutions will be posted)

Lecture #14 Notes


HW #13 problems (PDF) - Due Dec 12: [Online deadline Dec 14]

Lecture #13 Notes


A mandatory questionnaire is now posted on Canvas (look under "Quizzes"). We're trying to get a sense of how many high school students (or earlier) are in the course, what school, and what grade. This is purely to satisfy the curiosity of your professor and will be used for no other purpose. Please respond to this questionnaire at your convenience but no later than November 30. The survey has now been edited to allow you to enter the requested information, so if you tried it before and were unable to enter responses, try it again now. Thanks! - RW


HW #12 problems (PDF) - Due Dec 5: [Online deadline Dec 7]

Lecture #12 Notes


Approximate letter grades for Exam #1
Total points on exam was 50. Median score was 45 (90%).
Mean score was 42.6 (85.1%). Standard deviation was 8.1.
Scores are available on Canvas.
score grade   score grade
46+ A 31+ C+
43+ A– 28+ C
40+ B+ 25+ C–
37+ B 23+ D
34+ B– 0-22 E
Practice Exam #1     Solutions
Exam #1 solutions
     
Approximate letter grades for Exam #2
Total points on exam was 50. Median score was 47 (94%).
Mean score was 43.9 (87.9%). Standard deviation was 8.1.
Scores are available on Canvas.
score grade   score grade
46+ A 31+ C+
43+ A– 28+ C
40+ B+ 25+ C–
37+ B 23+ D
34+ B– 0-22 E
Exam #2 Practice     Solutions
Exam #2 solutions

Exam #2 took place during the latter part of class on Thurs, Nov 21. Because of the larger attendance, both the lecture (8pm-9pm) and the exam (9pm-10pm) took place in Science Center Hall C. The topics covered on the exam are primarily optimization (uncontrained and constrained) and integration (multiple integrals and applications).

Please be aware that the only academic relationship here is between the student and the staff and, of course, the Harvard Extension School. Parents and/or guardians of students in the course should not be contacting staff directly - only students in the course.


Note: Exam #1 took place during the last hour of class on Thurs, Oct 10 [covering Lecture #1 - Lecture #5].


Please be aware that a variety of email messages have been sent to everyone in the course regarding exam arrangements and other topics such as access to HW solutions, Practice Exams, etc. If you have not received these messages, please check any Spam folders you may have and take the necessary steps to ensure that you receive these messages without delay. The staff will not be responsible for your failure to heed messages sent to all students in the course.

Please also be aware that the only academic relationship here is between the student and the staff and, of course, the Harvard Extension School. Parents and/or guardians of students in the course should not be contacting staff directly - only students in the course.


Lectures will meet weekly from 8:00pm to 10:00pm in Maxwell-Dworkin G115 and online for distance students beginning Thurs, Sept 5. The recorded lectures should be available within 24 hours of the lecture.

Math E-21a syllabus - Fall 2019     Printable Math E-21a syllabus (PDF) - Fall 2019

TA Renee Chipman will conduct an optional online Q&A session (web conference) on Mondays from 2:00pm to 3:00pm plus an extra half-hour from 3:00pm to 3:30pm if there are additional questions. The link is https://harvard-dce.zoom.us/j/9702143672 (Zoom). This should be accessible via the Canvas site. A recording will be available on the Canvas site. Please contact Renee directly for additional options.

TA Jeremy Marcq will conduct an optional weekly (web conference) on Thursday from 12:00pm to 1:00pm. This should be accessible via the Canvas site. A recording will be available on the Canvas site. Please contact Jeremy directly for additional options.

In addition, starting Sept 12, Robert Winters will hold an informal pre-class Q&A session in Maxwell-Dworkin 119 (upstairs from our lecture hall) starting ~7:00pm [if attendance is low we might meet more informally at the tables in the lobby area outside the lecture hall]. 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.


Regarding Homework: Your worked solutions should be submitted either in class or online via the Canvas site (primarily for distance students but available to all). We prefer that assignments be submitted on paper for those who attend class in person. Other students may submit their assignments as scanned PDF files. We will establish limits on file size, but a basic standard is that you should not scan at resolution greater than about 120dpi. Anything beyond that is not necessary for handwritten work and dramatically increases file size. Black & White scans are preferred unless there is a good reason to scan using color. Please also make sure that the contrast is adjusted properly so that all work is legible. Photographs of HW assignments will not be accepted - scans only. Based on class size and practical limits, we may select a subset of each assignment for grading. Solutions to all problems will be posted after the deadline.

Note: Starting with HW #2, there will be a zero tolerance policy for late HW (unless justified by personal or medical reasons). If you cannot submit HW in class you should scan and submit it no later than Saturday at midnight (Eastern time). You are advised not to wait until midnight just in case you have scanning troubles or other computer troubles. Staying current with the assigned HW is strongly advised.

HW #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13
Total points 50 50 50 50 50 50 50 50 50 50 50 50 50
Median score 48 48 46 48 48 50 49 48 48 50 50 - -
Mean score 47.1 45.9 44.4 46.5 46.0 47.9 47.6 45.9 45.8 47.6 47.4 - -

Your lowest HW score will be dropped when determining course grades.


Lecture #1 Notes Lecture #2 Notes Lecture #3 Notes Lecture #4 Notes
Lecture #5 Notes Lecture #6 Notes Lecture #7 Notes Lecture #8 Notes
Lecture #9 Notes Lecture #10 Notes Lecture #11 Notes Lecture #12 Notes
Lecture #13 Notes Lecture #14 Notes Note: These Lecture Notes may be edited as the course proceeds.

Teaching Assistant Renée Chipman will also be available for small group sessions and individual assistance on request (if agreeable times can be arranged).

Note: The "Graduate" credit option is primarily for students enrolled in certain Extension School graduate programs such as the "Math for Teaching" program. All other students (including high school students) should register for the "Undergraduate" option or the Noncredit option (if you will not be submitting homework or taking exams).


Calendar [Topics and homework assignments are posted here.]

Note: 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.

This course covers the following topics: Calculus of functions of several variables; vectors and vector-valued functions; parameterized curves and surfaces; vector fields; partial derivatives and gradients; optimization; method of Lagrange multipliers; integration over regions in R2 and R3; integration over curves and surfaces; Green's Theorem, Stokes's Theorem, Divergence Theorem.

Please take note that the pace of this course is quite fast and you will be required to do a substantial amount of homework. You should plan accordingly.


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.


The Harvard Extension School is committed to providing an accessible academic community. The Accessibility Office offers a variety of accommodations and services to students with documented disabilities.

Please visit https://www.extension.harvard.edu/resources-policies/resources/disability-services-accessibility for more information.


You are responsible for understanding Harvard Extension School policies on academic integrity (https://www.extension.harvard.edu/resources-policies/student-conduct/academic-integrity) and how to use sources responsibly. Not knowing the rules, misunderstanding the rules, running out of time, submitting the wrong draft, or being overwhelmed with multiple demands are not acceptable excuses. There are no excuses for failure to uphold academic integrity. To support your learning about academic citation rules, please visit the Harvard Extension School Tips to Avoid Plagiarism (https://www.extension.harvard.edu/resources-policies/resources/tips-avoid-plagiarism), where you'll find links to the Harvard Guide to Using Sources and two free online 15-minute tutorials to test your knowledge of academic citation policy. The tutorials are anonymous open-learning tools.


Questions, questions, questions..... and some answers

1) I usually post announcements and assignments initially on the working course website: http://math.rwinters.com/E21a/
I also then post them on the Canvas Site which is linked from there, but it's best to first check on this (non-Canvas) site.

2) All of the lectures will be live-streamed and recorded and made available within about one day. All of the lectures will be available via a link on the course's Canvas Site for the duration of the course and for a few weeks thereafter.

3) The main materials of the course are the lectures, the weekly Lecture Notes, the Stewart text (best to get an inexpensive one online - links for best deals on the course website), and, of course, the homework assignments.

4) People who attend class in person can submit HW on paper in class. Distance students will be able to submit HW as a single scanned PDF (easily readable and with a reasonable file size, i.e. not scanned at an unnecessarily high resolution). Since classes are on Thursday and the recorded lectures are available on Friday (usually), assignments are usually due no later than the following Saturday night. All students have the option to submit their assignments online, including those who regularly attend the lectures.

5) We will have two midterm exams and a final exam. The Calendar is given at: http://math.rwinters.com/E21a/calendar.htm. Most students who can take exams in person will do so on the scheduled date of the exam. Distance students are responsible for finding a qualified proctor near their home who will administer and monitor them throughout the duration of their exam. The proctor must be approved by the Distance Exams Office at least a week prior to the exam. Proctors scan and send the completed exams to the Exams Office, and they then make them available to the Instructor for grading. Students can find more information at the Extension School website here: https://www.extension.harvard.edu/exams-online-courses

6) There is an optional Math Placement Test to see for yourself if you're ready for the course. It is not required for registration. There is also a Math Question Center online and in Sever Hall, available to students in a range of math classes.

7) The "Graduate" credit option is primarily for students enrolled in certain Extension School graduate programs such as the "Math for Teaching" program. All other students (including high school students) should register for the "Undergraduate" option or the Noncredit option (if you will not be submitting homework or taking exams).


We prefer that assignments be submitted on paper for those who attend class in person. Other students should submit their assignments as a single scanned PDF file, but this option is also open to local students for any given assignment.

A basic standard is that you should not scan at resolution greater than about 120dpi. Anything beyond that is not necessary for handwritten work and dramatically increases file size. Black & White scans are preferred unless there is a good reason to scan using color. Please also make sure that the contrast is adjusted properly so that all work is clearly legible.

Photographs of assignments will not be accepted - scans only.

Based on class size and practical limits, we will select a subset of each assignment for grading. Solutions to all problems will be posted after the due date.

Important Dates - Harvard University Extension School - Fall 2019

Registration opens for degree candidates Thurs, July 25
Registration opens for all students Mon, July 29
Registration ends Thurs, Aug 29
Classes begin (Math E-21a) Thurs, Sept 5
Course adds and credit status changes deadline Mon, Sept 9
Course drop deadline for full-tuition refund Mon, Sept 9
Course drop deadline for half-tuition refund   Mon, Sept 16
Withdrawal for WD/WN grade deadline (no refund)     Fri, Nov 22
Final Exam (Math E-21a) Thurs, Dec 19
Grades available online Tues, Jan 7, 2020

Notes on dot products and cross products

Supplement on parameterized curves

Supplement on the Chain Rule and Implicit Differentiation

Supplement on Conservative Vector Fields and the Fundamental Theorem of Line Integrals


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: Thursday, December 12, 2019 11:38 PM