Stewart homework hints

Assignment for Wednesday:

• Read 12.1, 12.2
• Watch the Introduction to Vectors video =====>
• Problems: (not to be turned in!)
  12.1/9, 11, 14, 21a, 31
  

HW from 12.1 will be discussed Wednesday, August 27

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)

Assignment for Friday:

• Watch the Dot Product Part II video =====>
• Read 12.3
• Try logging into webwork (let me know if you have problems)
• Problems: :12.2/5a,d,e,7, 13, 15, 19, 23, 43, 8, 50:
  12.3/1; 3-11odd; 15, 19, 23, 25, 31, 41, 55, 63, 64
  

HW from 12.2-3 will be discussed Wednesday, September 3 (maybe Friday, Aug 29 for 2.2)
Quiz on 12.2-3 (and maybe 12.1) September 5

Vectors 2: Dot Products

• Dot Products Part II

--

Slides accompanying today's class and the video above:

Vectors 2 (dot products)

I've 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_2025_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.

I've 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 CANCELED DUE TO ILLNESS. WATCH THE VIDEOS TO THE RIGHT BEFORE WEDNESDAY.  HAVE A GOOD LONG WEEKEND!

Class: Finish dot products. Answer any pressing questions from 12.2. Preview cross products (12.4).

Assignment for Wednesday:

• Watch the Cross Product video #1 =====>
• (I won't assume you've watched 2&3 before Wednesday, but you might want to get ahead of the class and watch the other two ASAP) =====>

Vectors 3 Cross products

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

--

Slides for these videos

• Vectors 3 (cross products)

Class: Continue cross products. Questions on 12.2 and 12.3

Easy problems on cross products: :
12.4/5, 7, 9, 10, 13

HW from 12.4 will be discussed Wednesday Sep. 10, and there will be a quiz on the section Friday, Sep. 12

Class: Finish cross products. Start lines and planes?

Harder problems on cross products: :
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. 10, and there will be a quiz on the section Friday, Sep. 12

QUIZ TODAY on 12.2 and 12.3

Slides for Lines/Planes lecture

Class: Lines and planes continued.

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 Wednesday, September 10 and Friday September 12. Quiz on 12.5 HW on Monday

Short video: Another way of getting the distance from a point to a line (text formula)

Class: Lines and planes concluded. Start vector-valued functions (13.1)

Slides for Lectures on vector-valued functions:

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

Class: Continue vector-valued functions (13.1). Answer HW questions from 12.5

QUIZ TODAY on 12.4 and 12.5

WebWork assignment on cross products is due tonight.

Class: Continue vector-valued functions

QUIZ TODAY on 12.5

WebWork assignment on lines and planes is due tonight.

Class: Continue vector-valued functions. Review for Midterm I

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

HERE IS SOME MORE INFORMATION ABOUT THE EXAM

Solutions to problems 2 and 6 from the practice exam

Class: Discuss exam; continue Chapter 13

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

Discuss Wednesday; quiz on Friday

Class: Continue Chapter 13 (Arc Length and Curvature)

Arc length: class. Curvature: videos===>

13.3/1, 3, 4, 11, 14 (Arc length)
13.3/17, 18, 22, 23, 28, 47, 50, 53, 62 (curvature)

• 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.

Class: Quiz on 13.1,2. Start moving frames and osculating planes (13.4)

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.

13.4/5, 9, 19, 22, 37, 39, 42, 45 (draw a picture for 45!)

Discuss October 8; quiz October 10.

Homework: watch video on surface sketching over the next few days----->
This covers 14.1, but also 12.6

Problems: :
14.1/13, 15, 25, 32, 36, 41, 49, 54
14.2/8, 9, 11, 15, 17, 19, 20, 37, 41

Discuss Wednesday, October 8. Sketches don't have to be beautiful!

Quiz on these sections October 10.

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

Watch the first video by Monday, the others by Wednesday

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

(This is covered by the 1st video.) Discuss Wednesday, October 8, quiz on Friday October 10 (along with the sections above).

• 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)

Problems: :
14.6/9, 13, 14, 21, 28, 33, 37
(These are on directional derivatives; see video above, also through p993 in text)
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)

Discuss these October 15
Quiz on these October 17

14.6/43, 45, 49, 57, 58 (these last 3 are easier than they look!)
(These are tangent plane problems, but use the "gradient=normal vector" approach ====>)

Class: Finish tangent planes. Chain rule in several variables.

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

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 next exam!)

Discuss Monday and Wednesday, Oct. 20 and 22

Video: optimization of functions of n variables (14.7) on closed domain.

(Watch ASAP!)

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 next exam.

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

Lagrange multipliers (14.8) will be covered by video======>
and discussed after the exam

(We will discuss this after the exam.)

Class: Start multiple integrals (15.1)

HERE IS SOME MORE INFORMATION ABOUT THE EXAM

HERE IS A PRACTICE EXAM

(no sound)

Class: Comments on Lagrange multipliers; Start multiple integrals (15.1)

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

Discuss Wednesday
No quiz on these

Class: Continue multiple integrals (15.2)

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. 5

Quiz on these (and more sections) November 7

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 soon):

• 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)

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

Discuss Nov. 5; Quiz November 7

Finding the area of a surface

Some more examples

15.4/3, 17, 5, 9, 11 and 12, 6 and 18 (mass and moments problems)
15.5/3, 5, 8, 10, 11, 23 (Surface Area problems)
15.6/3, 7, 11, 14, 20, 33, 39, 47; look at 55a

Discuss: Nov 12
Quiz Nov. 14

There is also a WW assignment due today!

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

Discuss: Nov. 19
No quiz on these, but they will be covered on the exam!

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

SOLUTION TO QUIZ
(Oops, this has a mistake. Will correct tomorrow.)
(Corrected!)

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

Watch this soon.

Note on the audio: I apparently had the gain on my microphone set far too high when I did the voice-over, and I've not been able to fix the resulting clipping. Sorry for the distortion.

There's WW due today.

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.

This will not be covered on the midterm, but please try to get them watched by Nov. 26

No quiz today.

Chapter 16 homework

16.1/11-14, 29-32

Discuss these Nov. 26

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 these December 3

Quiz on these 3 sections: December 5

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

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 3
Quiz on these 3 sections: December 5 (this will be a big quiz, covering 16.1-16.5

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

No quiz on 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 (16.6), 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

No quiz on 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

• Video on Theorems of Pappus

• Problems on Pappus

• This is due at the beginning of the final exam at the very latest (you can also turn it in any class period). I will not accept electronic or late submissions under any circumstances.

Final Exam!

Friday, December 19, 12-2

Keller 404 (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 (though maybe I will post a few as requests arise)

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