# Math 241 Section AL2:

## Course diary and homework assignments, Spring 2019

Note: Lecture notes will generally be available before class. I recommend having these available with you during lecture (e.g. printed or on an electronic device). Make sure you refresh the page regularly, as I may update it several times a day.

#### WEEK 1

Lecture M 1/14: Introduction (§12.1) Rn. Notes (by C. Leininger).
HW 0 due W 1/16!!
HW 1 due F 1/18 (at 8:00am, as always).
Section Tu 1/15: Review of parts of Calc I and II. Worksheet. Solutions.

Lecture W 1/16: Vectors (§12.2) and the dot product (§12.3). Notes (by C. Leininger).
HW 2 due W 1/23 (because of MLK Day).
Section Th 1/17: Parametric curves via vector arithmetic. Worksheet. Solutions.
Lecture F 1/18: Dot product applications (§12.3) and equations for planes (§12.5). Notes (by C. Leininger).
HW 3 due F 1/25.
Notes: Make sure you visit course website, https://faculty.math.illinois.edu/~ecliff/S19-241/S19-241.html, especially if you were not in class Monday.
Homework is completed online at http://www.webassign.net/uiuc/login.html

#### WEEK 2

Lecture M 1/21: MLK Day.
Section Tu 1/22: Projections, distances, and planes. Worksheet. Solutions.
Lecture W 1/23: Cross product (§12.4). Notes. i-clicker slides (and solutions).
HW 4 due M 1/28
Section Th 1/24: Vectors and the geometry of 3-space discussion. Quiz on HW 1-3.
Lecture F 1/25: Functions of several variables (§14.1). Notes (and correction to an example). i-clicker slides (and solutions). Hopf fibration video.
HW 5 due W 1/30
Notes: Make sure you are reading the sections in the book, and looking at any of the notes we don't get to in class---I write longer notes than I expect to cover so I don't run out of things to say! If you have a laptop or tablet, please bring it to discussion section next Tuesday.

#### WEEK 3

Lecture M 1/28: Level sets in 3d (§14.1); quadric surfaces (§12.6); intro to limits (§14.2).
HW 6 due F 2/1
Notes. i-clicker slides (and solutions). Interactive guide to quadrics. More on limits.

Section Tu 1/29: Visualizing quadrics. Worksheet. Solutions.
If you have a laptop or tablet, please bring it today.
Lecture W 1/30: Limits in several variables (§14.2). Today's lecture is cancelled due to the cold weather.
Please read the lecture notes and watch the following videos: first, second, and third. (There is overlap between the notes and videos, so one idea is to watch the videos with the notes in front of you, pausing whenever there is additional material in the notes to read and understand that, and then continuing. The videos have total length of only about 20 minutes.)
HW 7 due M 2/4
Section Th 1/31: Functions of several variables. Worksheet. Solutions.
Lecture F 2/1: Limit laws (§14.2); Continuity in several variables (§14.2); partial derivatives (§14.3).
HW 8 due W 2/6
Notes. i-clicker slides (and solutions).
Notes: The first midterm will be Tuesday, 2/12, 7:00-8:15pm. See here for complete details, including how to register for the conflict exam.

#### WEEK 4

Lecture M 2/4: Applications of partial derivatives (§14.3 and §14.4).
HW 9 due F 2/8
Notes. i-clicker slides and solutions.
The deadline to sign up for a conflict exam for Midterm 1 is tomorrow, Tuesday, 5 February.
Section Tu 2/5: Partial derivatives and differentiability. Worksheet. Solutions.
Lecture W 2/6: Chain rule (§14.5).
HW 10 due M 2/11
Notes. i-clicker slides and solutions.
Section Th 2/7: Practice exam for Midterm 1. (More practice exams and solutions, and all information relevant to Midterm one, can be found here.)
Lecture F 2/8: More on the chain rule (§14.5), directional derivatives and the gradient (§14.6).
HW 11 due F 2/15
Notes. i-clicker slides and solutions.
The first midterm will be next Tuesday, 2/12, 7:00-8:15pm. See here for complete details.

#### WEEK 5

Lecture M 2/11: More on the gradient (§14.6) and overview of optimization (§14.7-14.8).
HW 12 due M 2/18
Notes. i-clicker slides and solutions.
Section Tu 2/12: Review for midterm 1.
Midterm 1, 7:00-8:15pm
Lecture W 2/13 No class
Section Th 2/14: Midterm discussed.
Lecture F 2/15: Local min and max (§14.7).
HW 13 due W 2/20
Notes. i-clicker slides and solutions.

#### WEEK 6

Lecture M 2/18: Absolute min and max (§14.7).
HW 14 due F 2/22
Notes. i-clicker slides and solutions.
Section Tu 2/19: Taylor series, the second derivative test, and changing coordinates. Worksheet. Solutions.
Lecture W 2/20: Constrained min/max (§14.8).
HW 15 due M 2/25
Notes. i-clicker slides and solutions.
Section Th 2/21: Constrained min/max via Lagrange multipliers. Worksheet. Solutions.
Lecture F 2/22: Introduction to space curves (§13.1-4).
HW 16 due W 2/27
Notes. i-clicker slides and solutions
Note that in the lecture notes, there is a mistake in the example at the bottom of page 2. I lost the z component when calculating the speed, and ended up with the square root of 1 instead of the square root of 2.

#### WEEK 7

Lecture M 2/25: More on arc length (§13.3) and integrating functions on curves (§16.2, pages 1063-1065).
HW 17 due F 3/1
Notes. i-clicker slides and solutions
Section Tu 2/26: Lagrange multipliers problem discussion. Quiz on HW 11-15.
Lecture W 2/27: Vector fields (§16.1) and integrating them along curves (§16.2).
HW 18 due M 3/4
Notes. i-clicker slides and solutions.
Section Th 2/28: Curves and integration. Worksheet. Solutions.
Lecture F 3/1: More on integrating vector fields along curves; the Fundamental Theorem of Line Integrals (§16.2 and §16.3).
HW 19 due W 3/6
Notes. i-clicker slides and solutions.

#### WEEK 8

Lecture M 3/4: Conservative vector fields I (§16.3).
HW 20 due F 3/8
Notes. i-clicker slides and solutions.
Section Tu 3/5: Integrating vector fields. Worksheet. Solutions.
Lecture W 3/6: Conservative vector fields II (§16.3).
HW 21 due M 3/11
Notes. i-clicker slides and solutions.
Section Th 3/7: Discussion of line integral problems. Quiz on HW 16-19.
Lecture F 3/8: Intro to multiple integrals (§15.1).
HW 22 due F 3/15
Notes. i-clicker slides (including some tips about what to expect on the midterm) and solutions.
Note: Last day to drop the course.
The second midterm will be next Tuesday, 3/12, 7:00-8:15pm. See here for complete details.

#### WEEK 9

Lecture M 3/11: Integrating over more complicated regions (§15.2 and §15.3).
HW 23 due M 3/25
Notes. i-clicker slides and solutions.
Section Tu 3/12: Review for midterm 2.
Midterm 2, 7:00-8:15pm
Lecture W 3/13: Polar coordinates (§15.3) and applications (§15.4).
HW 24 due W 3/27
Notes. i-clicker slides.
Section Th 3/14: Multivariable integrals. Worksheet. Solutions.
Lecture F 3/15: No class.

SPRING BREAK

#### WEEK 10

Lecture M 3/25: Triple integrals (§15.6).
HW 25 due F 3/29
Notes. i-clicker slides and solutions.
Section Tu 3/26: Transformations of the plane. Worksheet. Solutions.
Lecture W 3/27: Integrating in cylindrical and spherical coordinates (§15.7 and §15.8).
HW 26 due M 4/1
Notes. i-clicker slides and solutions.
Section Th 3/28: Discussion of multivariable integral problems. Quiz on HW 22-24.
Lecture F 3/29: Changing coordinates I (§15.9).
HW 27 due W 4/3
Notes. i-clicker slides and solutions.

#### WEEK 11

Lecture M 4/1: Changing coordinates II (§15.9).
HW 28 due F 4/5
Notes. i-clicker slides and solutions.
Section Tu 4/2: Integrating by changing coordinates. Worksheet.
Lecture W 4/3: Surfaces in R3 (§16.6).
HW 29 due M 4/8
Notes. i-clicker slides and solutions.
Section Th 4/4: Surface Parameterpolooza. Worksheet.
Lecture F 4/5: Area and integration on surfaces (§16.6-16.7).
HW 30 due W 4/10
Notes. i-clicker slides and solutions.

#### WEEK 12

Lecture M 4/8: Green's Theorem (§16.4).
HW 31 due F 4/12
Notes. i-clicker slides and solutions.
Section Tu 4/9: Parametrizations and integrals. Worksheet.
Lecture W 4/10: Curl and divergence, conservative vector fields in R3(§16.5).
HW 32 due M 4/15
Notes. i-clicker slides and solutions.
Section Th 4/11: Green's Theorem. Worksheet.
Lecture F 4/12: Vector versions of Green's theorem and the geometric meaning of divergence and curl (§16.5).
HW 33 due F 4/19
Notes. i-clicker slides and solutions.
Notes: The third midterm will be next Tuesday, 4/16, 7:00-8:15pm. See here for complete details.

#### WEEK 13

Lecture M 4/15: Integrating vector fields over oriented surfaces (§16.7).
HW 34 due M 4/22
Notes. i-clicker slides and solutions.
Section Tu 4/16: Review for midterm 3.
Midterm 3, 7:00-8:15pm
Lecture W 4/17: No class
Section Th 4/18: Midterm discussed.
Lecture F 4/19 Stokes' Theorem, part I (§16.8).
HW 35 due W 4/24
Notes. i-clicker slides and solutions.

#### WEEK 14

Lecture M 4/22: Stokes' Theorem, part II (§16.8).
HW 36 due F 4/26
Notes. i-clicker slides and solutions.
If you want to come to a review session, please indicate your availability using this form, so I can choose a good time.
Section Tu 4/23: Stokes' Theorem. Worksheet.
Lecture W 4/24 Divergence Theorem, part I (§16.9).
HW 37 due M 4/29
Notes. i-clicker slides and solutions.

Section Th 4/25: More on Stokes' Theorem. Worksheet.
Lecture F 4/26: Divergence Theorem, part II (§16.9).
HW 38 due W 5/1
Notes. i-clicker slides and solutions.

#### WEEK 15

Lecture M 4/29: Conservative vector fields in R3 revisited and Topology 101.
Notes. i-clicker slides and solutions.
No homework
Section Tu 4/30: Surface integrals of vector fields. Worksheet.
Lecture W 5/1: Review.
Notes. i-clicker slides.

No class Th 5/2: Reading day
Finals begin F 5/3
FINAL EXAM. Information for the final exam is found here.
Back to the main course page.