Math 8: Calculus of Functions of One and Several Variables

General Information

Instructors and Scheduled Lectures

Instructor Sam Schiavone (Section 01) Samantha Allen (Section 02)
Lecture MWF 10:10 - 11:15 MWF 11:30 - 12:35
x-Hour Th 12:15 - 1:05 Tu 12:15 - 1:05
Classroom Kemeny 007 Kemeny 007
Email AT dartmouth DOT edu samantha.g.allen AT dartmouth DOT edu
Office Hours Wednesday: 2 - 3:30pm
Thursday: 1:15 - 2:15pm
Monday: 2 - 3pm
Wednesday: 9:30 - 11am
Thursday: 1 - 2pm
Office Kemeny 219 Kemeny 311
Canvas Section 1 Section 2

Course Description

This course is a sequel to MATH 3 and is appropriate for students who have successfully completed an AB calculus curriculum (or the equivalent) in secondary school. Roughly half of the course is devoted to topics in one-variable calculus, selected from techniques of integrations, areas, volumes, numerical integration, sequences and series including Taylor series, ordinary differential equations and techniques of their solution. The second half of the course studies scalar-valued functions of several variables. It begins with the study of vector geometry, equations of lines and planes, and space curves (velocity, acceleration, arclength). The balance of the course is devoted to studying differential calculus of functions of several variables. Topics include limits and continuity, partial derivatives, tangent planes and differentials, the chain rule, directional derivatives and applications, and optimization problems including the use of Lagrange multipliers.
Prerequisites: MATH 3


We will be using volumes 2 and 3 of Openstax calculus series, which are available for free at the links below.


There will be two midterm exams and a cumulative final exam. The exams are scheduled as follows:

Exam 1 Tuesday, April 16, 4:30 - 6:30 pm Silsby 028
Exam 2 Tuesday, May 7, 4:30 - 6:30 pm Silsby 028
Final Exam Saturday, June 1, 11:30 am Carpenter 013

If you have a conflict with one of the midterm exams because of a religious observance, scheduled extracurricular activity such as a game or performance [not practice], scheduled laboratory for another course, or similar commitment, please see your instructor as soon as possible. If you must miss a class, it is your responsibility to submit all homework on time.

Homework Policy 

  • WeBWorK. WeBWork online assignments can be found on the WeBWorK page for this class. Assignments are due at 10 am every Monday, Wednesday and Friday unless otherwise announced. The WeBWorK system will not accept late submissions unless you have made arrangements with your instructor. Please plan ahead. More information on WeBWorK (and how to enter mathematical notation) is listed here.
  • Written homework. Written homework assignments will be assigned weekly and will be posted on the homework page. Homework will be due at 4 pm each Friday, a week from the day it is assigned, and is to be turned in to the homework boxes outside Kemeny 008. No late homework will be accepted. (Practice problems are not to be turned in, but you may be asked to present solutions in class.)

The Honor Principle

Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously.

Cooperation on homework is permitted and encouraged, but if you work together, do not take any paper away with you; in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, you must write the solution up on your own. Please acknowledge any collaborators at the beginning of each assignment.

On exams, you may not give or receive help from anyone. Exams in this course are closed book, and no notes, calculators or other electronic devices are permitted.


Our graduate teaching assistant, Yao Xiao, will run tutorials Sunday, Tuesday, and Thursday at 7 - 9 pm in Kemeny 105, focusing on answering your questions as you work through the homework problems. Past students have found these tutorials immensely helpful!

Other Outside Help

  • Office Hours: Please feel free to meet with us during office hours (or by appointment) with questions regarding homework problems or any other aspect of the course.
  • Peer Tutoring: The Tutor Clearinghouse of the Academic Skills Center provides one-on-one peer tutoring.


The course grade will be based upon the scores on the midterm exam, homework, and the final exam as follows:

WeBWorK 10%
Written homework 15%
Exam 1 22.5%
Exam 2 22.5%
Final Exam 30%


Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see their instructor as soon as possible. For further information on the available support services, please contact Student Accessibility Services.