Math 8: Calculus of Functions of One and Several Variables

Winter 2015

Every differentiable (or even continuous) function can be integrated. In fact, the Fundamental Theorem of Calculus beautifully connects differentiation and integration, guaranteeing the existence of antiderivatives. Nevertheless, in most cases, there is no simple expression for the antiderivative of a given function! By giving a method of approximating functions by polynomials, Taylor series not only provide a way of approaching this difficulty, but also provide a general framework for approximating functions in a computationally tractable way. For example, have you ever wondered how your calculator determines the exact value of sine or cosine for angles that are not special? In the first part of the course we learn about sequences, series and convergence in order to understand Taylor series and how to use them.

In the second part of course, we begin extending calculus to functions of several variables. First we will develop the language of vectors to describe multidimensional space, motion through it, and functions defined on it. During the 17th century, Johannes Kepler and subsequently Isaac Newton formulated their famous laws of planetary motion and universal motion. The ease with which both sets of laws can be stated and understood in the language of vectors is evidence of its power. Finally, we will carry out in the setting of multiple variables one of the fundamental aims of calculus: the linear approximation of differentiable functions.


Announcements will be posted here throughout the term.
  • (12/16/14) If you would like familiarize yourself with WeBWork, you can log on as "practice1" with password "practice1" and try out Problem Set 0. If somebody else is using practice1, practice2 through practice10 are also available.
  • (1/6/15) A copy of the FERPA waiver is available here.
  • (1/8/15) Please read the guidelines for written homework.
  • (1/10/15) Please note that section 7.4 has been replaced by Applications of Integration. A handout with the content that will be covered is available here.
  • (1/13/15) Monday January 19 is MLK Day and there will be no class. Instead we will use the x-hour that week. In addition the tutorial of Sunday January 18 is cancelled, and the written homework that would normally be due Monday at 11am will be due Wednesday January 21 at 11am. Also check individual WeBWork assignments for adjusted due dates.
  • (1/21/15) The review session for the first midterm will be held on Monday (1/26) 7-9pm in Kemeny 008.
  • (1/24/15) You can find a collection of practice problems for the exam this week here, and solutions to the problems here here. Please keep in mind that this document is not indicative of the length of the actual exam, or the distribution of problems on the actual exam.
  • (2/2/15) Class on Friday (2/6) is cancelled due to Winter Carnival and moved to x-hour instead. Also tutorial on Thursday (2/5) is cancelled. Check individual WeBWork assignments for respective due dates.
  • (2/7/15) An in-class worksheet on power series that was distributed in Prof. Groszek's section is available here.
  • (2/10/15) Solutions to the first exam can found here.
  • (2/14/15) A collection of practice problems for the second exam can be found here, and the same document with solutions can be found here. Please note that unlike the practice problems, the exam will be roughly 50% on Taylor series and 50% on vector geomtery.
  • (3/9/15) A collection of practice problems for the final exam can be found here, and the same document with solutions can be found here. Although the final exam will be cumulative, these problems are only on the materical covered since the second exam. As usual, these problems are not an indicative of the length of the actual final exam, or distribution of problems on it.
  • (3/9/15) There is a WeBWork set on section 14.8 and Lagrange multipliers. Since it is not required and not graded, you can access it via the practice1, practice2, etc. accounts.
  • (3/10/15) Solutions to the second midterm can be found here.
  • (3/11/15) Melanie will be running a review session for final exam on Friday, 7-9pm, in Moore Hall room B03.
  • (3/18/15) Solutions to the final exam can be found here.

Instructors and Meeting Times

Jonathan Epstein Marcia Groszek
Office: 245 Kemeny Hall Office: 330 Kemeny Hall
Office hours:
M 2-3
T 10-11
F 9-10
and by appointment
Office hours:
T 10:30-11:45
R 10:30-11:45
R 2:30-3:30
and by appointment
Lecture: MWF 11:15--12:20 Lecture: MWF 1:45--2:50
X-hour: T 12:00--12:50 X-hour: Th 1:00--1:50
Location: Kemeny 008
Location: Kemeny 105

Note that you do not need an appointment to attend regularly-scheduled office hours. If you have a conflict you may make an appointment to meet outside those times.


Calculus, 7th edition, by James Stewart.


There are three scheduled exams: two midterms, held outside of class time, and the final exam.

Midterm 1 Midterm 2 Final Exam
Wednesday, January 28
4:00--6:00 pm
Wednesday, February 18
4:00--6:00 pm
Monday, March 16
Filene Auditorium, Moore Hall Filene Auditorium, Moore Hall Steele 006

If you have a conflict with a scheduled exam contact your instructor as soon as possible.

Homework Policy

Homework consists of two components. The first is WeBWork assigned after each class and due at 11:00am the day of the following class. The second is weekly problem sets (see Written Homework page) to be written up and turned in on Mondays by 11:00am.

Late policy for the written homework: If the written homework is turned in by the end of the day it's due and the instructor has been notified via email, then it's worth 75% of what it would have been. If the written HW is turned in by 11am of the next class day (usually Wednesday) and the instructor has been notified via email, then it's worth 50% of what it would have been. Any written homework turned in after this is counted as zero.


Tutorials will be held on Sunday, Tuesday, and Thursday evenings, from 7 PM to 9 PM, in 006 Kemeny. Our graduate TA is Melanie Dennis. Tutorials are a chance to ask questions and discuss the material.


You final grade will be calculated according to one of the following schemes:

  1. If the grade on the final exam is greater than the average on the two midterms
    • WeBWork (10%)
    • Written Homework (10%)
    • Midterm Exam 1 (20%)
    • Midterm Exam 2 (20%)
    • Final Exam (40%)
  2. If the grade on the final exam is less than the average on the two midterms
    • WeBWork (10%)
    • Written Homework (10%)
    • Midterm Exam 1 (25%)
    • Midterm Exam 2 (25%)
    • Final Exam (30%)

The Honor Principle

Academic integrity and intellectual honesty are an integral part of academic practice. This does not mean that you can't work on homework together or get ideas and help from other people. It does mean that you can't present somebody else's work or ideas without giving them due credit.

Feel free to discuss homework problems with other people and to work together to answer them. You must write up the answers yourself without copying from anybody. (This means you cannot copy down a joint solution arrived at by a group working together, even if you were part of the group. You must write up the solution in your own words.) You must also acknowledge all sources your consulted and people you worked with. Working with other people or consulting other sources will not lower your grade.

Caclulators are not allowed on exams, and, of course, no help may be given or received on exams.

Special Considerations

Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, they should stop by Student Accessibility Services in Collis Center to register for support services.

Students who expect to need schedule adjustments for religious reasons or because of commitments to jobs, athletics, or other extracurricular activities, should see the instructor as soon as possible. Such adjustments are not always possible, but may be possible with sufficient advance notice.

Students with any other concerns about the course are likewise encouraged to see the instructor as soon as possible. Students with no concerns are also invited to come to office hours to introduce themselves.

Last modified 7 December 2014.