Here is material about the administration of the course:

- 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.

- 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,

- Chapter 1 (on vectors);
- Chapter 2 (on parametrized curves);
- Chapter 3 (on functions of several variables);
- The full set (TBA).

- 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:
- Give a formula
for the vector
from the point (
*x*_{1},*y*_{1}) to the point (*x*_{2},*y*_{2}). - If
**u**and**v**are vectors in 2 dimensions, then is**u**×**v**a scalar or a vector? - If
**u**and**v**are vectors in 3 dimensions, then is**u**×**v**a scalar or a vector?

- Give a formula
for the vector
from the point (

- 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:
- 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 d*P*/d*t*=*C*′(*t*) a point, a scalar, a vector, or what? - 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 d**r**/d*t*=**c**′(*t*) a point, a scalar, a vector, or what?

- If

- 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:- What type of value
can its definite integrals take?;
that is,
can
∫
^{b}_{t=a}**f**(*t*) d*t*= ∫^{b}_{t=a}**v**d*t*(where*a*and*b*are scalars) be a point, a scalar, a vector, or what? - What type of value
can its indefinite integrals take?;
that is,
can
∫
**f**(*t*) d*t*= ∫**v**d*t*be a point, a scalar, a vector, or what?

- What type of value
can its definite integrals take?;
that is,
can
∫

- 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:- d
**r**/d*t*= ___. **v**/|**v**| = ___.- d
**r**/d*s*= ___.

- d

- 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).
- Reading from the textbook:
- 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:
- 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*? - If
*f*(2, 3) = 5, then what point must be on the graph of*f*?

- If

- 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**R**^{n}. 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):- There is at least one point in the boundary of
*R*, and all of them are in*R*. - There is at least one point in the boundary of
*R*, and none of them are in*R*. - 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. - There are no points in the boundary of
*R*.

- There is at least one point in the boundary of

- 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:
- 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*)) = ___). - Suppose that
the limit of
*f*approaching (0, 0) horizontally is 4 (in symbols, lim_{(x,y)→(0,0),y=0}*f*(*x*,*y*) = 4), and the limit of*f*approaching (0, 0) vertically is 6 (so lim_{(x,y)→(0,0),x=0}*f*(*x*,*y*) = 6). What (if anything) is the limit of*f*approaching (0, 0)? (so lim_{(x,y)→(0,0)}*f*(*x*,*y*) = ___).

- Suppose that the limit of

- 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.

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