Calculus of Vector-Valued Functions (FA23)

General Information

 

Prerequisite

Math 8 or advanced placement into Math 13.

 

Content

This course is a sequel to Math 8. Following the introduction of differential theory of vector-valued functions and space curves in 3-dimensional space, this course will focus on the corresponding integration theory. We will learn how to make sense of integrals for the types of functions we learned about in Math 8. Then we will discuss how these integrals transform under changes in coordinates. Finally, we will will extend the Fundamental Theorem of Calculus to line integrals and discuss two very important integration theorems: Green's Theorem and Stokes' Theorem.

Textbook

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

Instructors

Kameron McCombs kameron.t.mccombs.gr@dartmouth.edu Lectures: MWF 11:30am - 12:35pm Office: Kemeny 214  Office hours: tba (For now see me W 12:45-1:45)

 

TA and Tutorial

Tutorials: The tutorial schedule is 7:00-9:00pm on Tuesdays, Thursdays, and Sundays in Kemeny 242. Our TA this term is David Shuster!

 

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.

 

Exams

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, Oct 4, 4:00 pm - 6:00 pm (room TBA)

Midterm 2: Friday, Oct 27, 4:00 pm - 6:00 pm (room TBA)

Final Exam: Sunday, Nov 19, 3:00 pm - 6:00 pm (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.

 

Homework 

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.

AI Use

In this course, we will allow you to use things like ChatGPT as long as you do not use its responses as your own work. Think of AI like this as a collaborator; you may ask any questions you like and receive helpful guidance, but you should write all your work down on your own time by yourself. If you decide to use such a resource, please provide all chat logs along with your assignments.

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.

 

Grades

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	15%
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, Student.Accessibility.Services@Dartmouth.edu). 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	11 Sept(M)	4.1-4.2	Review of functions of several variables and definite integrals
2	13 Sept (W)	5.1	Double integrals over rectangular regions
3	15 Sept (F)	5.2	Double Integrals over general regions
4	18 Sept (M)	5.3	Integration in polar coordinates
5	20 Sept (W)	5.3-5.4	Integration in polar coordinates and triple integrals
6	22 Sept (F)	5.4-5.5	Triple integration, cylindrical coordinates
7	25 Sept (M)	5.5	Spherical coordinates
8	27 Sept (W)	2.3, 2.5, 4.3	Review of vectors, dot product, cross product, determinants, planes
9	29 Sept (F)	5.7	Change of variables, the Jacobian
10	2 Oct (M)	5.7	Change of variables, the Jacobian (continued)
11	4 Oct (W)	3.1-3.2	Review of vector functions
	4 Oct (W)		Midterm Exam (4:00pm-6:00pm)
12	6 Oct (F)	4.3-4.4, 4.6	Review of partial and directional derivatives, gradients, tangent planes
13	9 Oct (M)		Vector Fields
14	11 Oct (W)	6.1	Line integrals of vector fields
15	13 Oct (F)	6.2	Line Integrals, The Fundamental Theorem of Calculus for line integrals
16	16 Oct (M)	6.3	Line Integrals, The Fundamental Theorem of Calculus for line integrals (continued)
17	18 Oct (W)	6.3	The Fundamental Theorem of Calculus for line integrals (continued)
18	20 Oct (F)	6.4	Green's Theorem
19	23 Oct (M)	6.4	Green's Theorem (continued)
20	25 Oct (W)	6.5	Curl and Divergence
21	27 Oct (F)	6.5	Curl and Divergence (continued), Parametrizing surfaces
	27 Oct (F)		Midterm Exam (4:00pm-6:00pm)
22	30 Oct (M)	6.6	Parameterizing a surface and surface area
23	1 Nov (W)	6.6	Surface integrals of scalar functions
24	3 Nov (F)	6.7	Stokes' Theorem
25	6 Nov (M)	6.7	Stokes' Theorem (continued)
26	8 Nov (W)	6.8	The Divergence Theorem
27	10 Nov (F)	6.8	The Divergence Theorem (continued)
28	13 Nov (M)		Wrap up
	19 Nov (Sun)		Final Exam (3:00pm-6:00pm)