Calculus of Functions of One and Several Variables-01-02 (SP23)

General Information



Math 3 or advanced placement into Math 8.



This course is a sequel to Math 3 and provides an introduction to Taylor series and functions of several variables. The first third of the course is devoted to approximation of functions by Taylor polynomials and representing functions by Taylor series. The second third of the course introduces vector-valued functions. It begins with the study of vector geometry, equations of lines and planes, and space curves. The last third of the course is devoted to studying differential calculus of functions of several variables.


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


Kameron McCombs

Lectures: MWF  10:10 am - 11:15 am

Office: Kemeny 214 

Office hours: M 11:30-12:30pm, F 1:00-2:00pm

Jack Petok

Lectures: MWF 11:30 am - 12:35 pm

Office: Kemeny 320

Office hours: Tu 12:45-1:45pm, W 9:45-10:45am


TA and Tutorial


Tutorials: The tutorial schedule is 5-7pm Monday, in Kemeny 105; and Tuesday and Thursday in Kemeny 108. This is an excellent studying resource! Our graduate TAs are Lucy Knight and Jay Chen


COVID 19 Information

You are expected to attend class in person unless you have made alternative arrangements due to illness, medical reasons, or the need to isolate due to COVID-19. For the health and safety of our class community, please: do not attend class when you are sick, nor when you have been instructed by Student Health Services to stay home. Sick days will not count against your participation score.



There will be two timed in-person midterm exams and one in-person final during the final exam period.

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: Wednesday, April 26, 4:00 pm - 6:00 pm (room TBA)

Midterm 2: Monday, May 15, 4:00 pm - 6:00 pm (room TBA)

Final Exam: Friday, June 2, 8:00 am - 11:00 am (room TBA)

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.



The only way to really figure this stuff out is to work out some exercises on your own. In a typical week, you will be assigned two kinds of homeworks: online homework and written homework, both will be posted on Canvas (see the Canvas course calendar for links).

Online homework will be administered via WebWork. You do not need to signup for webwork, all webwork assignments will be linked to our Canvas page. 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. If you are experiencing an illness with severe symptoms, we will accept a high-quality scan by email. We will not accept any late homeworks, but we will drop your lowest score.

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, you should explain your work with full English sentences.

Collaboration is an important part of learning and doing mathematics. You are encouraged to discuss these problems amongst each other, but the final write-up must be your own. Solutions to problems must be written up in a self-contained way and the write up must contain all crucial steps and not just the final answer. You are allowed to use textbooks and notes from class, and you are allowed to use other online reference and educational sources such as Wikipedia, but you are not allowed to specifically look up solutions of the homework problems as a means to avoid thinking about the problem yourself . You are also not allowed to ask for the solution by posting a particular problem on any online Q & A site or help forum.

The Academic Honor Principle

Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously. We also believe in working and learning together.

Cooperation on homework is permitted and encouraged, but if you work together, try not take any paper away with you—in other words, you can share your thoughts (say on a blackboard), but try to walk away with only your understanding. In particular, you must write the solution up individually, in your own words. This applies to working with tutors as well: students are welcome to take notes when working with tutors on general principles and techniques and on other example problems, but must work on the assigned homework problems on their 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.

Plagiarism, collusion, or other violations of the Academic Honor Principle will be referred to the Committee on Standards.



The course grade will be based upon reading and class participation, the scores on the exams, homework, and the final exam as follows:

Written homework


WebWork 10%
Participation 5%
Midterm 1 20%
Midterm 2 20%
Final Exam 30%


Other Considerations

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.



Day Lectures Sections in Text Brief Description
1 27 Mar (M) V2, 1.1-1.5 Review of Math 3: Riemann sums and the Fundamental Theorem of Calculus. Substituion
2 29 Mar (W) V2, 2.4, 3.1 Arc length. Integration by parts. Trig substitution
3 31 Apr (F) V2 2.2, 2.3 Volume by slicing, volume of solid of revolution.
4 3 Apr (M) V2, 5.1-5.2 Infinite sequences.  Infinite series.
5 5 Apr (W) V2, 5.3-5.6 Divergence and convergence. Divergence test, p-series, comparison test, alternating series test, ratio test.
6 7 Apr (F) V2, 6.1, 6.2 Power series (incl. differentiation and integration)
7 10 Apr (M) V2, 6.3 Taylor and Maclaurin series, I
8 12 Apr (W) V2, 6.4 Taylor and Maclaurin series, II
9 14 Apr (F) V2,, 6.3 Taylor polynomials; remainder estimates
10 17 Apr (M) V3, 2.1, 2.2 Coordinates in R^n as a vector space; distance formula; simple surfaces
11 19 Apr (W) V3, 2.3 Dot products and projections, I
12 21 Apr (F) V3, 2.3 Dot products and projections, II
13 24 Apr (M) Review
14 26 Apr (W) V3, 2.4 Cross products and geometry; relation to volume/area
26 Apr (W) Midterm 1 (4:00 pm - 6:00 pm)
15 28 Apr (F) V3, 2.5 Lines in R^3: parametric and symmetric equations
16 1 May (M) V3, 2.5 Planes in R^3: vector and scalar equations
17 3 May (W) V2, 3.1-3.3 Derivatives and integrals along curves, arc length
18 5 May (F) V3, 4.1-4.2 Limits and continuity in 2- and 3-D
19 8 May (M) V2, 4.3 Partial derivatives
20 10 May (W) V3, 4.4 Tangent planes and normal lines
21 12 May (F) Review
22 15 May (M) V3, 4.5 Chain rule
15 May (M) Midterm 2 (4:00 pm - 6:00 pm)
23 17 May (W) V3, 4.6 Gradients and directional derivatives, I
24 19 May (F) V3, 4.6 Gradients and directional derivatives, II
25 22 May (M) V3, 4.7 Extreme values, I
26 24 May (W) V3 4.7-4.8 Extreme values, II; Lagrange multipliers, I
27 26 May (F) V3, 4.8 Lagrange multipliers, II
28 31 May (W) Wrap up
2 Jun (F) Final Exam (8:00 am - 11:00 am)


Course Summary:

Date Details Due