Calculus of Functions of One and Several Variables

Math 8 Spring 2024

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.


Instructor Shiang Tang
Section 1
Alice Schwarze
Sections 2

Class (10) MWF 10:10 - 11:15 Kemeny 105 (2) MWF 2:10 - 3:15 Kemeny 008
x-hour Th 12:15 - 1:05 Kemeny 105 Th 1:20 - 2:10 Kemeny 008
Office Hours Mon, 3-4 pm in Kem 320; Thu, 12:15-1:10 pm in Kem 105 Mon 3:15-4:15 pm and Thu 2:10-3:10 pm in Kem 342


General Information

Please see Lecture Plan for detailed information.

In person lectures

All lectures will be held in person unless otherwise stated. They will not be recorded, nor will slides or lecture notes be available. If you are not feeling well or have been instructed to not come to class, please contact the instructor prior to class. In this case, the instructor will try to arrange to have a classmate take notes for you.

In person and remote office hours

Office hours will generally be held in person. From time to time, it may be announced in class or on CANVAS that office hours will be conducted via zoom. Individual appointments with instructors may be held remotely via zoom, especially those made for late afternoon.

Math 8 tutorial sessions

Weekly tutorial sessions Tuesday and Thursday 7-9 pm in Kemeny 120. There will be additional tutorial sessions on Sun Apr 14 and Sun May 5.


The course grade will be based upon on weekly homework (total 80 points), class attendance (total 20 points) exam 1 (125 points), exam 2 (125 points), exam 3 (150 points). Total points possible: 500.

Exams 400 points

Homework 80 points

We will be using webwork (through canvas). We will also suggest textbook problems which will be posted Homework. Homework reinforces concepts and skills while challenging students to extend what they have learned to other types of problems. Because it is important for students to have this experience, instructors will not solve assigned homework problems during office hours before the due date. We will of course answer questions you may have in approaching problems that give you difficulty. It is therefore essential to begin homework sets early so that you may get help if difficulties do arise.

Homework is due each Tuesday at 11:59 pm. We are using webwork , which will be administered through your CANVAS website. As all homework is posted well in advance, no late homework will be accepted. Homework typically covers course material through the past week.

The lowest homework score will be dropped.

Honor Principle

We will strictly enforce Dartmouth's Academic Honor Principle. Please be advised of especially

  • Exams: Giving and/or receiving assistance during an examination violates the Academic Honor Principle.
  • Homework: Collaboration is both permitted and encouraged, but it is a violation of the honor code for someone to provide the answers for you.


Calculus, Volumes 2 and 3 by E. Herman, et. al., OpenStax (available online):
Volume 2
Volume 3


Math 3 or advanced placement into Math 8.

Student Religious Observances

Some students may wish to take part in religious observances that fall during this academic term. Should you have a religious observance that conflicts with your participation in the course, please come speak with your instructor before the end of the second week of the term to discuss appropriate accommodations.