Calculus of Functions of One and Several Variables

Math 8 Winter 2026

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 sequences and series (including Taylor series) in one-variable calculus. 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.

Instructors

Instructor Stoyan Dimitrov
Section 1 		Anne Gelb
Section 2 		Anne Gelb
Section 3
Class (10A) TTh: 10:10 am - 12:00 pm (10) MWF: 10:10 am - 11:15 am (11) MWF: 11:30 am - 12:35 pm
X-Hour F: 3:30 pm - 4:20 pm Th: 12:15 pm - 1:05 pm Tu: 12:15 pm - 1:05 pm
Classroom Kmeny 006 Kemeny 007 Kemeny 006
Contact Stoyan.Dimitrov@dartmouth.edu Anne.E.Gelb@dartmouth.edu Anne.E.Gelb@dartmouth.edu
Office Kemeny 320 Kemeny 207 Kemeny 207
Office Hours M: 3pm - 6pm
W: 2pm - 3pm
F: 2pm - 3pm 		W: 2pm - 3pm
F: 2pm - 3pm

Links

General Information

Please see Lecture Plan for detailed information.

Classroom 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 not to come to class, please get in touch with the instructor prior to class. In this case, the instructor will try to arrange to have a classmate take notes for you. Lectures may be rescheduled to the X-hour if needed.

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.

Tutorial Sessions

Tutorial sessions run Sundays, Tuesdays and Thursdays from 7:00-9:00pm in Kemeny 007, focusing on answering your questions on the homework and class material. For maximal benefit, we strongly recommend that you try all the homework problems ahead of time and come with your questions to the tutorial. Tutorials are open to all Math 8 students. You don't need an appointment.

Textbook

Calculus, (8th Edition) by James Stewart

Grading

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, although from time to time will also include material from the Monday and Wednesday (or Tuesday for the 10A) lecture.

Homework grading policy: The goal of homework is to learn to work through problems. Therefore each problem set will be assigned a grade on a 10 point scale based on the following percentage of correct results as submitted through webwork: 85% or higher = 10; 81-85% = 9; 71-80% = 8; 61-70% = 7; 50-60% = 6; 30-49% = 5; 20-29% = 3; 10-19% = 2; 5-9% = 1; below 5% = 0. The lowest homework score will be dropped, and the combination of the remaining scores will be scaled out of 80 points.

AI assisted homework solving:It can be very useful to use open AI resources to help understand some of the concepts in this course. There is a difference between having AI solve the problem and reasonably using it for assistance. It is your responsibility to know Dartmouth's policy on the use of AI.

Attendance (20 points)

Attendance is a crucial aspect of this course, and students are expected to attend, be engaged with, and contribute in class. Students should keep track of their attendance and report the number of unexcused absences to their instructor on the last day of class. If you need to miss a class, please let your instructor know beforehand so that your absence is excused and so that your instructor can provide guidance for learning the missed material.

Honor Principle

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

Prerequisite:

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.