Stewart homework hints

Assignment for Wednesday:

• Read 12.1
• Watch the Introduction to Vectors video =====>
• Problems: (not to be turned in yet!)
  12.1/9, 11, 14, 21a, 31
  

HW from 12.1 will be discussed Wednesday, August 23

Only underlined homework is to be turned in!
This assignment is due Wednesday, Aug. 30 at the end of class.
There will also be quite a lot of HW from several more sections due then, so do this soon rather than putting it off!

Vectors 1 Video:
Introduction to Vectors

(You will need to log into your hawaii.edu account to view this. Standard youtube controls, including speed controls, should work.)

--

Slides that accompany this video (download):

Vectors 1 (Intro)

I've already put up one WebWork "assignment," for learning the WebWork system. This "Orientation" assignment will not count for your grade, and will stay open for at least a week after the semester actually begins.

This is a FREE FOR YOU online homework system. I will be giving some assignments using it over the semester. It isn't hard to use, and will even let you check correctness of your answers before submitting them.

To log in to WebWork, go to:

https://webwork.oer.hawaii.edu/webwork2/Math_253_Fall_2023_Ross/

Your login should be either your UH email address, or the part of that address before the @ sign. For example, if your UH email is myname@hawaii.edu, your login should be myname

Your initial password is your 8 digit UH ID number.

Recently (for Math 301) I created a brief video tutorial for using WebWork on our system. You might find it useful, just note it is for Math301 (and all the links are for the Math301 WebWork, not the Math253a one):

VIDEO TUTORIAL (controls to control speed)

(Note: no sound in the video.)

Class: Questions about coordinate systems and vectors. Start on dot products.

Preparation:
Read 12.2, and watch the intro to vectors video assigned on Monday

Assignment for Friday:

• Watch the Dot Product videos =====>
• Read 12.3
• Make sure you can log into WebWork.
• Do WebWork Orientation (if you haven't used it before, optional otherwise).
• Problems: (not to be turned in yet!):
  12.2/5a,d,e,7, 13, 15, 19, 23, 43, 8, 50

HW from 12.2 will be discussed Friday, August 25

Only underlined homework is to be turned in!
This assignment is due Wednesday, August 30 at the end of class.

Vectors 2: Dot Products

• Dot Product Video Part I
• Dot Product Video Part II

--

Slides accompanying these videos:

Vectors 2 (dot products)

Class: Questions about dot products. Preview cross products (12.4).

Assignment for Monday:

• Watch the Cross Product video #1 =====>
• Problems: :
  12.3/1; 3-11odd; 15, 19, 23, 25, 31, 41, 55, 63, 64
  

We will discuss this HW on Monday, Aug 28.

Underlined problems to be turned in Wednesday, August 30 at the end of class.

Vectors 3 Cross products

• Cross Product Video Part I
• (Recommend play speeded up!)

--

Slides for this videos (and the two next ones):

• Vectors 3 (cross products)

Class: Finish cross products; Start lines and planes (12.5)

Assignment for Wednesday:

• More cross product videos----->
• Problems: :
  12.4/5, 7, 13, 9, 10
  

HW from 12.4 will be discussed Wednesday, August 30, and is due Friday, Sep. 8

Vectors 3 Cross products (continued)

• Cross Product Video Part II
• Cross Product Video Part III
• (as usual, best speeded up)

Slides for Lines/Planes lectures

Class: Lines and planes concluded. Start vector functions?

Assignment for Wednesday:

• Problems: :
  
• 12.4/15, 19, 21, 24, 27, 30, 33, 37, 43, 48, 53 (important!); look at 45

HW from 12.4 will be discussed Wednesday, Sep 6, and underlined problems are due Friday, Sep. 8

NOTE: Homework from 12.1-12.3 is due TODAY.

NO CLASS TODAY! (Stanford game)

Watch the video ==========>

But there are 2 webwork assignments due today!

Class: Discuss 12.4 HW. Start Vector functions (?)

Assignment for Friday:

Problems:
12.5/3, 5, 7, 12, 13, 19, 21, 36, 37, 45, 48, 53, 61, 71, 73, 78

We will discuss 12.5 HW on Friday and Monday

Underlined problems from 12.5 will be due next Monday

Slides for Lectures on vector-valued functions:

• Slides 1: Vector functions (intro)
• Slides 2: Calculus of vector functions

Class: Continue Chapter 13

NOTE: Underlined problems from 12.4 are due TODAY.

HERE IS A PRACTICE EXAM. (We can talk about it Wednesday before the exam.)

HERE IS SOME MORE INFORMATION ABOUT THE EXAM.

SOLUTIONS TO EXAM I

Class: Discuss exam; continue Chapter 13 (arc length)

Problems: :
13.1/3, 5, 6, 9, 15, 19, 21-26, 49, 50, 53b, c
13.2/17, 19, 23, 26, 37, 39, 57 (hint: what is the cross product of a vector with itself?)
13.3/1, 3, 4, 11, 14 (Arc length)

Discuss Wednesday; turn in underlined problems on Friday

• Video 1
• Video 2
• Video 3

This is the second part of 13.3; it is pretty technical, and examples take a while, so it is probably better in video form.

You should watch these as soon as possible so that you can do the second set of 13.3 problems.

NOTE: we will only cover 13.4 in class through page 915. The Kepler's Laws material will be extra credit, and done by video.

Problems: :
13.3/17, 18, 22, 23, 28, 47, 50, 53, 62 (curvature)
13.4/5, 9, 19, 22, 37, 39, 42, 45 (draw a picture for 45!)

Discuss: 13.3, 13.4 problems Monday, Sep 25
Turn in underlined problems Friday, Sep. 29
(There will be Ch. 15 problems due thn as well!)

HW on 13.1-3 due today

Weekend homework: watch video on surface sketching ----->
This covers 14.1, but also 12.6

Kepler's laws (pp876-7) will be an extra credit video

14.1/13, 15, 25, 32, 36, 41, 49, 54

Discuss Wednesday, Sep. 27. Sketches don't have to be beautiful!

14.2/8, 9, 11, 15, 17, 19, 20, 37, 41

Discuss Monday, October 2

Underlined problems from 14.1 due Friday, Sep. 29
Underlined problems from 14.2 due Friday, Oct. 6

Video(s) on differentiation of functions of n variables. (14.3,6) =====>

Watch the first video by Friday, the others over the weekend

• General definition, and partial derivative
• Gradient, and the relationship between the g' and ∇g
• Directional derivatives (Note this is 14.6 in the text! We'll do 14.4 and 14.5 afterwards.)

(Slides I used in the first video)

HW on 13.3, 13.4, 14.1 due today

Class: Differentiation - general and partial derivatives. (14.3, but also some ideas from later sections.) Watch (first) video on definitions and partial derivatives before coming today!)

HW:

14.3/15, 25, 29, 33, 39, 49, 55, 61, 65, 71 (important!), 46, 72, 74, 77, 103

Discuss: October 4
Underlined problems due: October 6

Discuss HW from 14.2

HW: 14.6/9, 13, 14, 21, 28, 33, 37
(These are on directional derivatives)

Discuss: October 6
Underlined Due: October 13

Class: Finish theory. Increment of a function (14.4)

Discuss HW from 14.3

Class: Finish increments; Start chain rule?

Discuss HW from 14.6

HW from 14.2,3 due today!

14.4/3, 4, 13, 15, 21, 33, 34
(Note: some problems ask you to "use differentials", but OK to just use the fact that the linearization is a good approximation near x0)

14.6/43, 45, 49, 57, 58 (these last 3 are easier than they look!)

Discuss Wednesday, Oct 11
Underlined Due: October 13

(There will also be problems from 14.5 due Oct. 13 Oct 16)

Watch the video for Wednesday======>

14.5/(chain rule and implicit differentiation)7, 10, 13, 15, 17, 21, 22, 25, 31, 38, 43, 45

Discuss Friday, Oct 13
Underlined Due: Monday, October 16

Video: optimization of functions of n variables

Discuss HW from 14.4, 14.6

Discuss: HW from 14.5

HW from 14.4, 14.6 due today

HW on 14.7 is in two parts:
14.7(a)/(min-max, closed region) 31, 33, 36, 37

(These will be covered on the exam!)

Discuss Monday and Wednesday

Underlined problem will be due after the exam:
Underlined Due: Friday, October 27

Class: Finish 14.7; discuss HW from 14.7(a)

HW: 14.7(b)/(more min-max problems) 9, 12, 17, 21, 43, 46, 49, 55; Look at 39, 40;

These will not be covered on the exam.

Discuss: Monday, Oct 23
Underlined Due: Friday, October 27

(We will discuss this after the exam.)

HERE IS A PRACTICE EXAM. (We can talk about it Wednesday before the exam.)

HERE IS SOME MORE INFORMATION ABOUT THE EXAM.

(Sorry about the sound issues.)

HW from Lagrange Multipliers:
14.8/ 6, 18, 19, 21, 29 36, 43, 44

Discuss Wednesday
Underlined Due: Friday, October 27

(Updated 10/23/23)

HW:

Watch Video 3 ASAP =====>

15.1/3a, 9, 11, 15, 20, 21, 29, 31, 32, 35, 41, 42,, 43, 49

Discuss October 30

15.2/7, 9, 16, 17, 23, 25, 39, 52, 61, 65

Discuss Nov. 1

Underlined (from both sections) due November 3 (but do them sooner!)

There will also be some WebWork

• Video 1 (sketch of proof that continuous functions are integrable)

• Video 2 (sketch of proof of fact that you can switch the order of integration in the iterated integral)

• Video 3 (some properties of the double integral)

Here's a review of Polar Coordinates, for those of you who either haven't seen them or are rusty on them. You might also need this before doing the extra credit on Kepler's Laws (posted above):

• Link to first Polar Coordinates video - review of polar coordinates
• (Slides from first video - download these first to take notes)
• Link to second Polar Coordinates video - graphs and area in polar coordinates
• (Slides from second video - download these first to take notes)

Class: Finish integration in polar coordinates

15.3/1, 4, 9, 13, 15, 16, 19, 24, 28 (harder!), 38, 39

Discuss: Nov. 6
Due: Nov. 10 Nov. 13

Finding the area of a surface

Some more examples

15.5/3, 5, 8, 10, 11, 23 (Surface Area problems)
15.4/3, 17, 5, 9, 11 and 12, 6 and 18 (mass and moments problems)

Discuss: Nov. 8
Due: Nov. 10 Nov. 13

15.6/3, 7, 11, 14, 20, 33, 39, 47; look at 55a

Discuss: Nov. 13
Due: Nov. 17

15.7/3, 13, 15, 17, 22, 27, 29
15.8/7, 23, 28, 32, 43

Discuss: Nov. 15
Due: Nov. 20

• Video on Theorems of Pappus

• Problem set (extra credit).

• This is due on the last day of class (before the review period and before exam week).Dec 11

HW on 15.9:
15.9/11, 13, 16, 17, 21a, 23, 24, 25, 28

Discuss: Nov. 17
Due: Nov. 20

I apologize for the absolutely terrible sound quality, I apparently had the gain on my microphone set far too high, and while I should re-record the audio it doesn't seem like a great use of time.

Some more examples of COM, MOI

Another example. There were technical difficulties, so it starts without sound.

Also (depending on time) more examples of COV, maybe start Chapter 16

HW from 15.7-9 due today!

Will cover 14.7, 14.8, all of Ch. 15

Here is some more information about the exam.

Practice exam, including the formulas that I will give you on the exam.

Full solution to Practice Exam #10 (by request)

Solutions to the exam:

Part I

Part II

We've already talked about 16.1 (and to some extent 16.3). 16.2-3 are mainly covered in the videos to the right. Make sure you've watched at least the first 2 by class on Monday.

16.1/11-14, 29-32 (I'm not collecting any of these, but there will be some webwork)
16.2/3, 7, 8, 13, 15, 14, 19, 21, 22, 36, 48
16.3/ 11, 13, 14, 17, 19, 25, 26, 31-34

Discuss: Nov. 29
Due: December 1

1. Line integrals of vector fields
   
2. Line integrals for scalar fields
   
3. Line integrals of conservative fields
   
4. Why the fundamental theorem of line integrals is true.

Note: Conservative field=gradient of someth.ing. We've touched on conservative fields already in class.

16.5 is mainly notation, and will be covered by video=====>

16.4/5, 6, 9, 13, 19, 18, 27, 29
16.5/12, 13, 15, 16, 19, 20, 27

Discuss Dec 6

Video on div, grad, curl notation

(Here are the slides I used in the video.)

Again, mainly done by videos, since they are more efficient for this material. ============>

HW:

16.6/Warm up: 3, 5 (see also 48), 21, 13, 15, 17; Do these: 41, 48, 49

16.7/5, 7, 13, 21, 23

I will NOT be collecting these, but they are covered on the exam!

1. Surface integrals of scalar fields
2. Surface integrals of vector fields

The first video covers parametrized surfaces (6.6), surface area ( a different way than we've already done it), and surface integrals of scalar fields (a slight generalization of surface area). The second covers surface integrals of vector fields.

(The first video is a little rough, I haven't editied it to remove pauses and corrections, so it ended up at 36 minutes. Sorry!)

HW:

16.8/7, 9

16.9/5, 9, 17

I will NOT be collecting these, but they are covered on the exam!

1. Stokes Theorem
2. Divergence Theorem

I tried to keep these short. However, the Stokes video got edited/sped up too much, sorry.

The divergence theorem video is a little longer (20 minutes) than the others, but partly that is because I included some calculations of surface integrals without using the divergence theorem

Discuss HW from 16.4-5

2:30-??

Zoom redentials - check your email, also on Laulima

Final Exam!

Friday, December 15, 12-2

Keller 403 (usual room)

Some useful information for the exam

Practice Final Exam 1
Practice Final Exam 2
Practice Final Exam 3
Practice Final Exam 4

I will NOT be posting solutions to these.

Here are some formulas I will give you on the exam. (I might give you more.)

Some solutions, by request:

Practice Final Exam 1/2, 6
Practice Final Exam 3/2, 4

(more to come?)

The finals are now graded.

LOOK UP YOUR FINAL EXAM SCORES HERE.

(Please also check your midterm grades here. Exam 3 was split into 2 parts, there is also a column for any extra points you might have received when I regraded Problem 2 from the second part of midterm 3.)