Homeworks:

Homeworks are due in your section on Monday of the listed week.

Homework from Week One: Due Week of Sept 1st (this is Labor Day--so the next day)

Section 10.1: 1, 2, 3, 5, 7, 11, 12, 24, 37, 38
Section 10.2: 1, 2, 3, 4, 5, 11, 13, 17, 18, 19, 29, 30, 32, 33, 41, 42, 43, 44, 48, 51, 52, 53, 73, 74
For Tuesday: Read 10.3, 10.4 ,10.5, 12.1, and 12.2.
For Thursday: Read 12.3, 12.4, and 12.5.

Lecture 1: Aug 28, 2025

Homework Work from Week Two: Due Week of Sept 8th

Section 10.3: 1a-c, 3a-c(*), 7, 9(*), 11, 15(*), 16, 17, 18(*), 19, 20, 29(*), 33, 35(*), 43, 45, 57(*), 60, 63(*)
Section 10.4: 1, 3(*), 9, 11(*), 17, 45(*), 47(*)
Section 10.5: 1, 3, 5(*), 11, 13(*), 17, 19(*), 21(*)
Section 12.1: 1, 3, 5, 7(*), 10, 11(*), 12, 13(*), 15, 16, 19a-b(*), 22,
Section 12.2: 1a-d, 5(*), 13(*), 14, 15(*), 18, 19(*), 24, 25(*), 26, 27(*), 32, 35(*), 41
Section 12.3: 3(*), 4, 5(*), 6, 9, 10, 11(*), 13(*), 14, 15(*), 17, 19(*), 23, 25(*), 26, 35(*), 36, 37(*), 41, 43, 49(*), 50, 51(*), 53(*), 58
Section 12.4: 1, 3, 5(*), 13, 20, 21(*), 22, 29(*), 31, 38, 45(*), 49(*)
Section 12.5: 1, 2, 3(*), 6, 7, 8, 12, 13(*), 14, 17(*), 23, 27, 43(*), 46, 49(*), 51(*), 62, 63(*), 73 (this one involves the distance from a point to a plane--you can save it for the next homework if you want).
READ 13.1, 13.2, 14.1, and 14.2 (these will be covered on Tuesday)
Lecture 2: Sept 2, 2025

Lecture 3: Sept 4, 2025

Homework for Week Three: Due Week of Sept 15th

Section 13.1: 1(*), 2, 3, (*)5, 7, 15(*), 18, 1(*)9, 20, 2(*)1, 22, 2(*)3, 24, 4(*)1, 42,

Section 13.2: 9, 11, 1(*)3, 15, 1(*)7, 19, 24, 2(*)5, 3(*)3, 3(*)5

Section 14.1: 9(*), 11, 13(*), 15, 17, 19(*), 21, 23(*), 31, 32, 33(*), 35(*), 36, 41, 43(*), 6(*)7

Section 14.2: 1(*), 5, 7(*), 9(*), 13(*), 19(*), 21, 25(*), 26, 29, 31(*), 37(*), 44(*) (this last one is interesting, and not so easy)

Section 14.3: 5(*), 8, 9, 15(*), 17(*), 19(*), 21, 23(*), 31, 37(*), 39, 42

Section 14.4: 1(*), 3, 5(*), 6, 11(*), 13, 15(*), 17, 19(*), 33(*), 34, 42, 45(*) (I will go over 14.4 again on Tuesday--so if you want to save 14.4 problems until the next assignments, that's okay.)

READ 14.4, 14.5 (For Tuesday)

READ 14.6 (For Thursday)

Lecture 4: Sept 9, 2025

Lecture 5: Sept 11, 2025

Week Four: Due Week of Sept 22nd

Section 14.4: 1(*), 3, 5(*), 6, 11(*), 13, 15(*), 17, 19(*), 33(*), 34, 42, 45(*) (also listed in previous assignment)

Section 14.5: 1(*), 3, 5(*), 6, 7(*), 9, 10, 11(*), 12, 13(*), 14, 15(*), 21(*), 22, 23(*), 27, 29(*), 31, 34, 45(*), 47(*), 49(*), 51(*)

Section 14.6: 4, 5(*), 6, 7(*), 8, 9, 11(*), 13(*), 20, 21(*), 22, 23(*), 24, 27(*), 28, 29(*), 35(*), 37, 39(*), 40, 41(*), 43(*), 47(*), 49(*), 50, 52, 53(*), 55(*), 56, 57(*))

Lecture 6: Sept 16, 2025

Lecture 7: Sept 18, 2025

READ 14.7 For Tuesday

READ 14.8 For Thursday (and the following Tuesday)

Week Five: Due Week of Sept 29th ---

Section 14.7: 1(*), 2, 5(*), 7, 9(*), 11(*), 13(*), 15, 19(*), 29(*), 31(*), 33, 35,(*) 39, 41(*), 43(*), 45(*), 51(*), 53(*)

Study for the midterm.

Read Section 14.8 for class on Tuesday, Oct. 1

Lecture 8: Sept 23, 2025
Lecture 9: Sept 25, 2025

(powerpoint) Lecture 9: Sept 25, 2025

Week Six: Due Week of Oct 6th

Section 14.8: 3, 5, 9, 11, 13, 15, 17, 19, 21, 40, 41, 45

Lecture 10: Sept. 30, 2025

Week Seven: Due Week of Oct 13th

Please read 15.1 through 15.3

Section 14.8: 3(*), 5, 9(*), 11(*), 13, 15(*), 17, 19(*), 21(*), 40, 41, 45(*) (yes, I forgot to star section 14.8, so I am giving you an extra week.

Section 15.1: 1(*), 3(*), 11, 13, 17(*)

Section 15.2: 1, 3(*), 5, 7(*), 8, 9(*), 11, 13, 15(*), 17, 19(*), 25, 27(*)

Conceptual Problems: Chapter 14: 61,62,63. Chapter 14 Review: 6, 19 [concept check problem]; all the true-false questions, problem 50. In Problems Plus: 5, 7(*), 8.

Read 15.3, 15.4 for the following Tuesday

Lecture 11: Oct. 7, 2025

Lecture 12: Oct. 9, 2025

Week Eight: Due Week of Oct 20st

ANNOUNCEMENT

Just to be clear, the section numbers below refer to Edition 8 of Stewart.
Section 15.3: Double Integrals in Polar Coordinates: 1, 3(*), 5, 7, 9(*), 11, 13(*), 15, 19(*), 21(*), 23(*), 25, 31(*), 39(*)
Section 15.4: Applications of Double Integals: 3(*), 5(*)
Section 15.5: Surface Area: 3, 4, 5(*), 6, 7(*), 9, 10(*), 11(*), 12, 13(*), 15, 17(*), 23

Section 15.6: Triple Integals: 3(*), 5(*), 7, 9(*), 11, 13(*), 17, 19(*), 20, 21, 22(*) (and for those of you that want to get a head start, the problems below are what will be due on Oct 28th)
Section 15.7: Cylindrical Coordinates: 1, 3,(*) 9(*), 15(*), 16, 17(*), 19(*), 21(*), 22
Read 15.9

Lecture 13: Oct. 14, 2025 Lecture 14: Oct. 16, 2025

PLEASE READ the section on change of variables before class on Tuesday, Oct. 21

Week Nine: Due Week of Oct 27----

Section 15.8: Spherical Coordinates: 1, 3(*), 5, 7(*), 17, 19(*), 21(*), 23(*), 27, 29, 35

Section 15.9: Change of Variable: 2, 3(*), 4(*), 5(*), 6(*), 7(*), 10(*), 11(*), 12(*), 13(*), 15(*), 17(*), 19(*), 21, 23(*), 24

Problems from Review Section for Chapter 15: I think you should do the following, but it is up to you: [1,3,4,5,7,9,11,13,14,15,17,18]

Lecture 15: Oct. 21, 2025

Lecture 16: Oct. 23, 2025

Read 16.1 through 16.2 (I should have put this up before today's lecture: "my bad'')
Read 16.3 and 16.4 for next week

I suggest you to do the following to prepare for the midterm:

You don't have to! But I suggest it.

Two Essays:

Essay #1: Write an essay structuring the material in Chapter 14, explaining how to get to Lagrange multipliers. (1) What do I mean by this? I mean explain how all the material in Chapter 14 fits together. The essay should not be all words---please use equations, etc. (2) What I am *not* looking for is a collection of definitions and theorems. (3) So, here is a structure: "Lagrange multipliers are a way of solving (XXX,YYY). As an example, consider AAA,BBB, with the goal of solving AAA subect to BBB. Lagrange multipliers say that CCC and DDD, must point in the same direction. In order to make sense of that we need to define CCC and DDD, as well as the idea of "same direction". When we say CCC, we mean that EEE, which relies on the use of FFF and GGG, which themselves require...." I hope you get the idea. In order to do so, you will end up explaining partial derivatives, gradients, level sets, optimization problems, the "D" test, tangent lines and planes, orthogonality conditions, etc. (4) How long should it be? Long enough so that one could actually learn from it--and so that when you find it two years from now, you will read it, and it will make sense, and long enough that you can hand it to a friend taking the course next year.

Essay #2: Write an essay structuring the material in Chapter 15, explaining how to get to the change of variables section (15.9). (1) What do I mean by this? I mean explain how all the material in Chapter 15 fits together. The essay should not be all words---please use equations, etc. (2) What I am *not* looking for is a collection of definitions and theorems. (3) So, here is a structure: "Change of variables allows you to transform a double (or triple) integral in one coordinate system into another..In order to make sense of that we need to define ...
Read 16.1 through 16.3

Week Ten: Due Week of Nov 3rd

Study for Midterm: Don't forget Lagrange multipliers.

Section 16.1: (Vector Fields) 1, 5(*), 7, 9(*), 11, 12, 13(*), [14], 21, 24,

Section 16.2: (Line Integrals) 1, 3, 5(*), 7, 9(*), 11, 12(*), 13, 15(*), 19, 21(*), 29(a), 33(*)

Section 16.3: (Fundamental Theorem for Line Integrals) 1, 3(*), 5, 7(*), 9, 11(*), 13, 15(*), 17(*), 19, 21(*), 23, 25(*), 29

(This depends on how far I get on Tuesday and Thursday) Section 16.4: (Green's theorem) 1, 2, 3(*), 5(*), 6, 7(*), 8, 9(*), 10, 11(*), 12, 13(*), 14, 19(*), 22, 29(*)
Lecture 17: Oct. 28, 2025 and (powerpoint version) Lecture 17: Oct. 28, 2025

Lecture 18: Oct. 30, 2025

Week Eleven: Due Week of Nov 10th

(yes, this is from last week) Section 16.4: (Green's theorem) 1, 2, 3(*), 5(*), 6, 7(*), 8, 9(*), 10, 11(*), 12, 13(*), 14, 19(*), 22, 29(*)

Section 16.5: (Curl and Divergence) 1, 2, 3(*), 4, 5(*), 6, 7, 8, 9(*), 11, 12 (really, really understand this one), 13(*), 14, 15(*), 16, 17(*), 19(*), 20, 21(*),

Read 16.5, 16.6 and 16.7

Lecture 19: Nov. 4, 2025

Week Twelve: Due Week of Nov 17th

Section 16.6 (Parameterized Surfaces): 1, 3(*), 5(*), 13(*), 14, 19(*), 20, 21(*), 23(*), 33(*), 35(*), 39(*), 45(*)

(We almost finished 16.6 on Thursday--it would be great if you got them done by Monday, but it's okay if you hand them on Monday Nov 24th. ) Section 16.7 (Integration of Vector Fields over Surfaces): 1, 3(*), 4, 5(*), 6, 7(*), 9(*), 10(*), 11(*), 13(*), 15(*), 17(*), 19(*), 20, 21(*), 23(*), 25(*), 27(*), 29(*), 40

Lecture 20 and Lecture 21: Nov. 13, 2025

Week Thirteen: Due Week of Nov 24th
(note: This is due on Monday of Thanksgiving week. There is *no* homework that you are supposed to do during Thanksgiving week. I believe in taking the time to give thanks, however you choose. But if you want, you can hand this homework in on Dec. 1st.

Section 16.8:(Stokes Theorem) 1, 2, 3(*), 4, 5(*), 7(*), 8, 9(*), 10, 13(*), 14, 16(*)

Section 16.9:(Divergence Theorem) 1, 3(*), 4, 5(*), 6, 7(*), 8, 9(*), 10, 11(*), 12, 13(*), 14, 17(*), 18, 19(*), 24
Lecture 22: Nov. 18, 2025

Lecture 23: Nov. 20, 2025

Lecture 24: Dec. 2, 2025