Harvard Extension School 
Professor: Teaching Assistants: 

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: 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: Thank you for attending the course! The Final Exam took place on Thursday, December 20. All but one of the exams are graded. Final Exam scores are posted on the Canvas site. Approximate letter grades for the Final Exam are given below. Course grades have been submitted to the Extension School. Course grades will be available online on Tuesday, January 8. Please do not send email regarding exam scores or course grades. You will not receive a response until after all exams are done and all course grades have been submitted. Great care has been taken to ensure accuracy in grading and in the determination of course grades and these are not subject to negotiation.
HW #14 problems (PDF)  Do them, but don't turn in. Solutions are posted. HW #13 problems (PDF)  due Thurs, Dec 13 in class or online via Canvas no later than Sat, Dec 15) HW #12 problems (PDF)  due Thurs, Dec 6 in class or online via Canvas no later than Sat, Dec 8) Exam #2 took place during the latter half of class on Thursday, Nov 29. Exam #1 took place on Oct 11 during the latter half of class. The exam covered topics through Lecture #5. Distance students and other students choosing to take their exam using the distance option MUST make arrangements through the Distance Exams Office at the Harvard Extension School. This means finding a qualified proctor approved by the Distance Exam Office. Those taking a proctored exam using this option will have a 24 hour window during which the exam must be taken. [additional information here] HW #11 problems (PDF)  due Thurs, Nov 29 in class or online via Canvas no later than Sat, Dec 1) and Supplement HW #10 problems (PDF)  due Thurs, Nov 15 in class or online via Canvas no later than Sat, Nov 17) HW #9 problems (PDF)  due Thurs, Nov 8 in class or online via Canvas no later than Sat, Nov 10) 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.
Your lowest HW score will be dropped when determining course grades. Lectures will meet weekly from 8:00pm to 10:00pm in Harvard Hall 201 and online for distance students beginning Thurs, Sept 6. The recorded lectures should be available within 24 hours of the lecture. Math E21a syllabus  Fall 2018 Printable Math E21a syllabus (PDF)  Fall 2018 TA Renee Chipman will conduct an optional online Q&A session (web conference) on Mondays, 2:00pm3:00pm (this was changed). There will be time for additional questions from 3:003:30pm if needed. Recording will be available. TA Jeremy Marcq will conduct an optional weekly Q&A session at 53 Church St. #203 on Mondays, 8:009:00pm. You may attend this in person or participate online. Recording will be available. In addition, Robert Winters will hold an informal preclass Q&A session in Harvard Hall 103 starting ~7:00pm. 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.
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 firstyear 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 vectorvalued functions; parameterized curves and surfaces; vector fields; partial derivatives and gradients; optimization; method of Lagrange multipliers; integration over regions in R^{2} and R^{3}; 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 BrooksCole, ISBN: 0495560545) OR the 3rd Edition (published 2005 by BrooksCole, 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/resourcespolicies/resources/disabilityservicesaccessibility for more information. Important Dates  Harvard University Extension School  Fall 2018
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 MegaList of Math E21a techniques Math E21a Useful Facts Here's something: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html Mathematica (optional, but worth investigating) Mathematica Lab #1 Mathematica Lab #2 Mathematica Lab #3 Download your free Adobe Acrobat Reader for reading and printing PDF formatted documents. Please send comments to Robert Winters. 