Calculus of Functions of One and Several Variables-ALL SECTIONS (FA22)

Welcome to Math 8 Fall 2022!

Course Description

This course is a sequel to MATH 3, appropriate for students who have successfully completed an AB Calculus curriculum (or equivalent). The course splits roughly into two parts: the first devoted to topics in single-variable calculus and the second covering topics in differential multivariable calculus.

The single-variable portion includes techniques of integration, convergence tests for sequences and series, and Taylor series and remainder estimates.

The multi-variable portion studies three-dimensional vector geometry; lines, planes, and space curves (velocity, acceleration, arc length); limits and continuity of multivariable functions; partial derivatives, tangent planes and differentials; the multivariable Chain Rule; directional derivatives and applications; and optimization problems and Lagrange multipliers.


(10) MWF 10:10-11:15

Kemeny 006

Instructor: Zhen Chen

X-hour: Thursday 12:15-1:05 pm

Office Hours: T, Th 3:30pm-5:00pm, Kemeny 200

(11) MWF 11:30-12:35

Kemeny 006

Instructor: Matthew Ellison

X-hour: Tuesday 12:15-1:05 pm

Office Hours: T, Th 9:30-11am, Kemeny 221

(12) MWF 12:50-1:55

Kemeny 006

Instructor: Melanie Ferreri

X-hour: Tuesday 1:20-2:10 pm

Office Hours: M, T, W 2:30-3:30 pm, Kemeny 247


Calculus, Volumes 2 and 3 by E. Herman, et. al., Openstax (available for free on OpenStax: Vol 2, Vol 3)


Tutorials are a place where you can drop in for help with homework, exam review, or anything else related to Math 8 material! They will be run by our Graduate TAs --- Anna Vasenina and Beth Anne Castellano  --- on Tuesdays, Thursdays, and Sundays from 7-9 pm in Kemeny 007. The first tutorial will take place on Thursday September 15th.


There will be two midterms and one final exam. All exams will be in-person.

The exams are scheduled as follows. If you have a scheduled conflict with these exam times (such as a conflict with another class or a game if you are a student-athlete), please bring this up to your instructor at least two weeks in advance.

Midterm 1: October 5th (4:00 pm - 6:00 pm/Life Sciences Center 100 Arvo J. Oopik '78 Auditor)

Midterm 2: October 26th (4:00 pm - 6:00 pm/Life Sciences Center 100 Arvo J. Oopik '78 Auditor)

Final Exam: November 22nd (11:30 am - 2:30 pm/Life Sciences Center 100 Arvo J. Oopik '78 Auditor)

If you have a question about how your exam was graded, you can ask your instructor; to have your exam regraded, please submit your question in writing to your instructor.


Each week, you will typically be assigned two kinds of homework: WebWork and written homework, both will be posted on Canvas. Links for both will be on the Canvas course calendar.

WebWork is intended as a set of shorter review problems. Most weeks, there will be 3 Webwork assignments ---  due Monday, Wednesday, and Friday before class meeting.

Written homework will typically be released each Wednesday and due the following Wednesday at the beginning of class. Written homework will be collected via Gradescope. We will not accept any late homework, but will drop your lowest score.  On written homework, you must show all of your work by hand; in particular, your solution write up should not depend on the use of a calculator or computer (unless otherwise indicated). For full credit, your work should be explained with full English sentences.

Collaboration Policy: We encourage you to work together and discuss problems on both the WebWork and written homework. For the WebWork, the software will often give you unique constants to work with. Sometimes, though, you will have exactly the same problem as your classmates --- in which case it is up to you to make sure that you are staying on top of the material and able to solve each problem by yourself. For the written homework, you may discuss problems with others but your writeup must be your own. You must list everyone you worked with at the top of each written homework submission.

Academic Integrity

Our collaboration policy for homework is above.

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

Dartmouth's Academic Honor Principle applies to all courses, including this one. If you are not famililar with the policy, you should review it at the following link: Violations of the Academic Honor Principle will be referred to the Committee on Standards. Please note that the college takes such violations seriously, for example the following is an excerpt from the Principle linked above:

"Given the fundamental nature of the Academic Honor Principle in an academic community, students should expect to be suspended if they engage in acts of academic dishonesty. Any student who submits work which is not his or her own, or commits other acts of academic dishonesty, violates the purposes of the College and is subject to disciplinary action, up to and including suspension or separation."


The grade breakdown for the course is as follows:

Written homework


WebWork 10%
Participation 5%
Midterm 1 20%
Midterm 2 20%
Final Exam 25%


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

Students who need academic adjustments or alternate accommodations for this course are encouraged to see their instructor privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (Carson Suite 125, 646-9900, Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their professor. As a first step, if students have questions about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.


Tentative Course Schedule

Day Lectures Sections in Text Brief Description
1 12 Sep (M) V2, 1.1-1.5, 3.1 Review of Math 3; Riemann sums and the Fundamental Theorem of Calculus
2 14 Sep (W) V2, 3.1; 5.1-5.2 Integration by parts; Infinite sequences and infinite series; geometric series
3 16 Sep (F) V2, 5.3 The divergence test and integral test
4 19 Sep (M) V2, 5.4-5.5 Comparison tests; alternating series test
5 21 Sep (W) V2, 5.6, 6.1 Remainder of alternating series; Conditional and absolute convergence; Ratio test.
6 23 Sep (F) V2, 6.1, 6.2 Power series (incl. differentiation and integration)
7 26 Sep (M) V2, 6.3 Taylor and Maclaurin series, I
8 28 Sep (W) V2, 6.4 Taylor and Maclaurin series, II
9 30 Sep (F) V2, 6.3 Taylor polynomials; remainder estimates
10 3 Oct (M) Review
11 5 Oct (W) V3, 2.1, 2.2 Coordinates in R^n as a vector space; distance formula; simple surfaces
5 Oct (W) Midterm 1
12 7 Oct (F) V3, 2.3 Dot products and projections, I
13 10 Oct (M) V3, 2.3 Dot products and projections, II
14 12 Oct (W) V3, 2.4 Cross products and geometry; relation to volume/area
15 14 Oct (F) V3, 2.5 Lines in R^3: parametric and symmetric equations
16 17 Oct (M) V3, 2.5 Planes in R^3: vector and scalar equations
17 19 Oct (W) V3, 3.1-3.3 Derivatives and integrals along curves, arc length
18 21 Oct (F) No class: Day of Caring
19 24 Oct (M) V3, 4.1-4.2 Limits and continuity in 2- and 3-D
20 26 Oct (W) Review
26 Oct (W) Midterm 2 
21 28 Oct (F)

V3, 4.3

Partial derivatives
22 31 Oct (M) V3, 4.4 Tangent planes and normal lines
23 2 Nov (W) V3, 4.5 Chain Rule and Implicit Differentiation
24 4 Nov (F) V3, 4.6 Gradients and directional derivatives
25 7 Nov (M) V3, 4.7 Extreme values, I
26 9 Nov (W) V3 4.7-4.8 Extreme values, II; Lagrange multipliers, I
27 11 Nov (F) V3, 4.8 Lagrange multipliers, II
28 14 Nov (M) Wrap up
22 Nov Final Exam


Course Summary:

Date Details Due