## 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.

`
### WEEK 1

**Lecture M 1/14:** Introduction (§12.1) **R**^{n}.
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

Interactive guide to quadrics.

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 **R**^{3} (§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 **R**^{3}(§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 **R**^{3} 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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