## Class Summaries and Homework Assignments

Note: Lecture notes will generally be available before class. I recommend have 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.

# THIS COURSE ENDED IN MAY 2019

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### WEEK 1

Lecture M 1/14: Introduction (§12.1) Rn.
Notes.
HW 0 due W 1/16 HW 1 due F 1/18 (both 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 and i>clicker questions.
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 and i>clicker questions.
HW 3 due F 1/25.
Notes: Make sure you visit course website, https://faculty.math.illinois.edu/~clein/classes/2019/241.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 and i>clicker questions.
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 i>clicker questions. 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). Notes and i>clicker questions.
HW 6 due F 2/1
Notes 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). Notes
No class or help room today due to weather. Instead, read the notes and/or watch lecture videos:
Review of limits in one variable,
First definitions and examples for limits in 2 variables,
More examples, and strange behavior.
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). Notes and i>clicker questions.
HW 8 due W 2/6
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.
There will be additional help room hours, this Friday, February 1, 4-6pm in 241 Altgeld Hall to make up for missed hours on Tuesday and Wednesday.

### WEEK 4

Lecture M 2/4: Applications of partial derivatives (§14.3 and §14.4). Notes and (corrected) i>clicker questions.
HW 9 due F 2/8
Section Tu 2/5: Partial derivatives and differentiability. Worksheet. Solutions.
Lecture W 2/6: Chain rule (§14.5). Notes (w/ minor edits 2/7) and i>clicker questions.
HW 10 due M 2/11
Section Th 2/7: Practice exam for Midterm 1.
Lecture F 2/8: More on the chain rule (§14.5), directional derivatives and the gradient (§14.6). Notes and i>clicker questions.
HW 11 due F 2/15
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). Notes and i>clicker questions.
HW 12 due M 2/18
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). Notes and i>clicker questions.
HW 13 due W 2/20

### WEEK 6

Lecture M 2/18: Absolute min and max (§14.7). Notes and i>clicker questions.
HW 14 due F 2/22
Section Tu 2/19: Taylor series, the second derivative test, and changing coordinates. Worksheet. Solutions.
Lecture W 2/20: Constrained min/max (§14.8). Notes and i>clicker questions.
HW 15 due M 2/25
Section Th 2/21: Constrained min/max via Lagrange multipliers. Worksheet. Solutions.
Lecture F 2/22: Introduction to space curves (§13.1-4). Notes and i>clicker questions.
HW 16 due W 2/27

### WEEK 7

Lecture M 2/25: More on arc length (§13.3) and integrating functions on curves (§16.2, pages 1063-1065). Notes and i>clicker questions.
HW 17 due F 3/1
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). Notes and i>clicker questions. Wind map.
HW 18 due M 3/4
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). Notes and i>clicker questions.
HW 19 due W 3/6

### WEEK 8

Lecture M 3/4: Conservative vector fields I (§16.3). Notes and i>clicker questions.
HW 20 due F 3/8
Section Tu 3/5: Integrating vector fields. Worksheet. Solutions.
Lecture W 3/6: Conservative vector fields II (§16.3). Notes and i>clicker questions.
HW 21 due M 3/11
Section Th 3/7: Discussion of line integral problems. Quiz on HW 16-19.
Lecture F 3/8: Intro to multiple integrals (§15.1). Notes and i>clicker questions.
HW 22 due F 3/15
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). Notes and i>clicker questions.
HW 23 due M 3/25
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). Notes and i>clicker questions.
HW 24 due W 3/27
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). Notes and i>clicker questions.
HW 25 due F 3/29
Section Tu 3/26: Transformations of the plane. Worksheet. Solutions.
Lecture W 3/27: Review of triple integrals, introduction to chainging coordinates (§15.6-§15.9). Notes and i>clicker questions.
HW 26 due M 4/1
Section Th 3/28: Discussion of multivariable integral problems. Quiz on HW 22-24.
Lecture F 3/29: Changing coordinates I (§15.9). Notes and i>clicker questions.
HW 27 due W 4/3

### WEEK 11

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

### WEEK 12

Lecture M 4/8: Green's Theorem (§16.4). Notes and i>clicker questions.
HW 31 due F 4/12
Section Tu 4/9: Parametrizations and integrals. Worksheet. Solutions.
Lecture W 4/10: Curl and divergence, conservative vector fields in R3(§16.5). Notes.
HW 32 due M 4/15
Section Th 4/11: Green's Theorem. Worksheet. Solutions.
Lecture F 4/12: Vector versions of Green's theorem and the geometric meaning of divergence and curl (§16.5). Notes and i>clicker questions.
HW 33 due F 4/19
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). Notes and i>clicker questions.
HW 34 due M 4/22
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). Notes and i>clicker questions.
HW 35 due W 4/24
Friday morning office hours reschedule 8:45-9:30am.

### WEEK 14

Lecture M 4/22: Stokes' Theorem, part II (§16.8). Notes (with additional calculations added) and i>clicker questions.
HW 36 due F 4/26
Section Tu 4/23: Stokes' Theorem. Worksheet. Solutions.
Lecture W 4/24 Divergence Theorem, part I (§16.9). Notes and i>clicker questions.
HW 37 due M 4/29
Section Th 4/25: More on Stokes' Theorem. Worksheet. Solutions.
Lecture F 4/26: Divergence Theorem, part II (§16.9). Notes and i>clicker questions.
HW 38 due W 5/1

### WEEK 15

Lecture M 4/29: Conservative vector fields in R3 revisited and Topology 101. Notes and i>clicker questions.
No HW
Section Tu 4/30: Surface integrals of vector fields. Worksheet. Solutions.
Lecture W 5/1: Review. Notes and iclicker.
No HW
No class Th 5/2: Reading day. Help room in 445 and 447 Altgeld Hall, 12:00 noon until 8:00pm.
Finals begin F 5/3 I will hold additional office hours: 8:10am to 11:00am in 343 Altgeld Hall and 2:00pm to 3:00pm in 366 Altgeld Hall. The help room will be in 445 and 447 Altgeld Hall 11:00am to 3:00pm.
FINAL EXAM. Information for the final exam is found here.
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