# MATH-2080-ES31

Welcome to the permanent home page for Section ES31 of MATH-2080 (Calculus 3) at Southeast Community College in the Spring term of 2020. I am Toby Bartels, the instructor.

• Canvas page (where you must log in for full access, available while the course is in session).
• Help with DjVu (if you have trouble reading the files below).
• Course policies (DjVu).
• Class hours: Mondays through Thursdays from 1:00 PM to 1:50 in ESQ 100C.
Information to contact me:
• Name: Toby Bartels, PhD;
• Canvas messages.
• Email: TBartels@Southeast.edu.
• Voice mail: 1-402-323-3452.
• Text messages: 1-402-805-3021.
• Office hours:
• Mondays and Wednesdays from 9:30 to 10:30,
• Tuesdays and Thursdays from 2:30 PM to 4:00, and
• by appointment,
in ESQ 112 and online. (I am often available outside of those times; feel free to send a message any time and to check for me in the office whenever it's open.)

The official textbook for the course is the 4th Edition of University Calculus: Early Transcendentals by Hass et al published by Addison Wesley (Pearson). There is also a packet of course notes (DjVu):
1. General review:
• Date due: January 14 Tuesday.
• Reading from the textbook: As needed: Review §§11.1–11.5.
• Reading from my notes: Optional: Chapter 1 (the handout on vectors).
• Online notes: Required: Vector operations.
• Exercises due:
1. Give a formula for the vector from the point (x1, y1) to the point (x2, y2).
2. If u and v are vectors in 2 dimensions, then is u × v a scalar or a vector?
3. If u and v are vectors in 3 dimensions, then is u × v a scalar or a vector?
2. Parametrized curves:
• Date due: January 15 Wednesday.
• Reading from the textbook: Chapter 12 through Section 12.1 (pages 662–668).
• Reading from my notes: Chapter 2 through the first half of Section 2.1 (through the first two lines of page 2 in the handout on parametrized curves).
• Exercises due:
1. If C is a point-valued function, so that P = C(t) is a point (for each scalar value of t), then what type of value does its derivative C′ take?; that is, is dP/dt = C′(t) a point, a scalar, a vector, or what?
2. If c is a vector-valued function, so that r = c(t) is a vector (for each scalar value of t), then what type of value does its derivative c′ take?; that is, is dr/dt = c′(t) a point, a scalar, a vector, or what?
3. Integrating parametrized curves:
• Date due: January 16 Thursday.
• Reading from the textbook: Section 12.2 (pages 671–675).
• Reading from my notes: The second half of Section 2.1 (the rest of page 2 in the handout on parametrized curves).
• Exercises due: If f is a vector-valued function, so that v = f(t) is a vector (for each scalar value of t), then:
1. What type of value can its definite integrals take?; that is, can ∫bt=af(t) dt = ∫bt=av dt (where a and b are scalars) be a point, a scalar, a vector, or what?
2. What type of value can its indefinite integrals take?; that is, can ∫ f(t) dt = ∫ v dt be a point, a scalar, a vector, or what?
4. Arclength:
• Date due: January 21 Tuesday.
• Reading from the textbook: Section 12.3 (pages 678–680).
• Reading from my notes: Section 2.4 (pages 5&6 in the handout on parametrized curves).
• Exercises due: Section 12.3 of the textbook uses several variables, including r, s, t, T, and v, to describe various quantities on the path of a parametrized curve. Fill in the right-hand side of each of these equations with the appropriate one of these variables:
1. dr/dt = ___.
2. v/|v| = ___.
3. dr/ds = ___.
5. Functions of several variables:
• Date due: January 22 Wednesday.
• Reading from my notes: Chapter 3 through Section 3.1 (pages 1–3 in the handout on functions of several variables).
• Chapter 13 through Section 13.1 "Domains and Ranges" (pages 697&698);
• Section 13.1 "Graphs, Level Curves, and Contours of Functions of Two Variables" through the end of Section 13.1 (pages 700–702).
• Exercises due:
1. If f(2, 3) = 5, then what number or point must belong to the domain of f and what number or point must belong to the range of f?
2. If f(2, 3) = 5, then what point must be on the graph of f?
6. Topology in several variables:
• Date due: January 23 Thursday.
• Reading from the textbook: Section 13.1 "Functions of Two Variables" (pages 698&699).
• Reading from my notes: Sections 3.2&3.3 (pages 3&4 in the handout on functions of several variables).
• Exercises due: Let R be a (binary) relation, thought of as a set of points in Rn. Recall that a point P is in the boundary (or frontier) of R if, among the points arbitrarily close to P (including P itself), there are both at least one point in R and one point not in R. For each of the following examples, state whether R is open (Yes or No) and whether R is closed (Yes or No):
1. There is at least one point in the boundary of R, and all of them are in R.
2. There is at least one point in the boundary of R, and none of them are in R.
3. There are points in the boundary of R, and at least one of them is in R and at least one of them is not.
4. There are no points in the boundary of R.
7. Limits in several variables:
• Date due: January 27 Monday.
• Section 13.2 (pages 705–711).
• Reading from my notes: Section 3.4 (pages 4&5 in the handout on functions of several variables).
• Exercises due:
1. Suppose that the limit of f approaching (2, 3) is 5 (in symbols, lim(x,y)→(2,3)f(x, y) = 5), and the limit of g approaching (2, 3) is 7 (so lim(x,y)→(2,3)g(x, y) = 7). What (if anything) is the limit of f + g approaching (2, 3)? (so lim(x,y)→(2,3) (f(x, y) + g(x, y)) = ___).
2. Suppose that the limit of f approaching (0, 0) horizontally is 4 (in symbols, lim(x,y)→(0,0),y=0f(x, y) = 4), and the limit of f approaching (0, 0) vertically is 6 (so lim(x,y)→(0,0),x=0f(x, y) = 6). What (if anything) is the limit of f approaching (0, 0)? (so lim(x,y)→(0,0)f(x, y) = ___).
8. More to come!

This web page and the files linked from it were written by Toby Bartels, last edited on 2020 January 23. Toby reserves no legal rights to them.

The permanent URI of this web page is `http://tobybartels.name/MATH-2080/2020SP/`.