final scores

the final

just in case you get lost, the following is a screen shot from the syllabus.

A practice final exam for tomorrow

Practice Final

Here's a practice final. I suggest you take an hour to work the problems before you go to class tomorow.

Current scores and estimated grades

The estimated score is based on extrapolating your final exam score as the average of your exam scores to date. The estimated flat and curved grades are determined from the estimated score using according to the grade templates described in the course syllabus.

Link to the official final exam study materials

Practice Final (Do this part first)

Practice Final Solutions 

Review

13.4#5

Hello Professor,
You asked me to email you about this question so you could explain it on the blog.
Much Appreciated,


*********************************

Ah. This is a different problem than the one I thought we were talking about.   Notice that the problem says that the path is "nonclosed"?  This means that you don't have a closed loop, just the three line segments AB+BC+CD, but you don't have DA also, so Green's theorem doesn't directly apply.  You could solve this problem directly just by integrating F=<sin(x)+3y, 2x+y> and integrating
∫ F.dr_1 + ∫ F.dr_2 + ∫ F.dr_3 where r_1(t)=t*<2,2> for 0≤t≤1, r_2(t)=(1-t)*<2,2> + t*<2,4> for 0≤t≤1, r_3(t)=(1-t)*<2,4> + t*<0,6> for 0≤t≤1. Or you *could* still use Green's theorem if you're willing to be a little sneaky: since ∂F_2/∂x = 2 and ∂F_1/∂y = 3, Green's theorem implies that
∬_D (-1)dA - ∫ F.dr_4 = ∫ F.dr_1 + ∫ F.dr_2 + ∫ F.dr_3 ,  where D is the enclosed region and where r_4(t)=(1-t)*<0,6> . This is a little bit easier approach since ∬_D (-1)dA = -Area = -8, and
r'_4(t)= -<0,6> so ∫ F.dr_4 = ∫_0^1<18(1-t), 6(1-t)>.<0, -6> dt = -36 ∫_0^1(1-t) dt.

Lecture Notes 4/19/19 through 4/24/19 (to be completed)

Lecture Notes 4/19/19

Lecture Notes 4/22/19

Lecture Notes 4/24/19

Lecture Notes 4/3/19 through 4/17/19

Lecture Notes 4/3/19

Lecture Notes 4/5/19

Lecture Notes 4/8/19

Lecture Notes 4/10/19

Lecture Notes 4/17/19

PracticeTest3 #2

Hello professor,
I was working on the Exam 3 practice ( https://math.asu.edu/sites/default/files/mat_267-post_exam3_solutions_0.pdf ) and I was confused on question #2 of the multiple choice. For the limits of integration of phi I got found them to be from 0 to pi. However, the correct answer says its from 0 to pi/2. Why is that?

Thank you

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In Cartesian (xyz) coordinates, your integration dz integration runs from z=0 to z=√(4-x^2-y^2); i.e. from the xy-plane UP to the top half of the sphere x^2+y^2+z^2=4, specifically there's nothing below the xy-plane. But the xy-plane is at 90 degrees or π/2 radians from the positive z-axis, hence π/2 has to be the upper limit.  If you went all the way to π your domain would have to include the negative z axis. 

Lecture Notes 3-27-19 through 4-1-19 (to be updated)

Lecture Notes 3/27/19

Lecture Notes 3/29/19

Lecture Notes 4/1/19

Section 12.3: Problem 8

Hi Professor,
I'm not sure why my approach is incorrect. I appreciate the direction in advance!

Thanks,

**********************

Well, the positive direction in theta is counter clockwise, but limits of integration going from π/2 to -π/2 is backwards, so your your limits of integration mean that you're going backwards in the right half plane 

Lecture Notes 2/25/19 through 3/25/19

Lecture Notes 2/25/19

Lecture Notes 2/27/19

Lecture Notes 3/20/19

Lecture Notes 3/22/19

Lecture Notes 3/25/19

Scores and estimated final grade as of 3/24/19

Worksheet

(for those of you who couldn't attend today's field trip)
The link below includes a topo map of Camelback Mountain.  Get out your ruler to estimate horizontal (i.e. non vertical) distances, and your protractor to estimate angles.
1) estimate the magnitude and direction of the gradient vector at the red "x"s, direction in degrees from the right hand x-axis.
2) locate the local max's (hint: there are a lot of them) on the map, as well as the saddle points.
I'll be asking questions on the Monday after Spring Break.

Worksheet

PS: those who went on the field trip can also benefit from this work sheet.

Some thoughts for the field trip today

Hi Dr.Taylor,

I just wanted to double check with you that we should be meeting at the trail head of A mountain for todays hike correct? Which trailhead is on the corner of veterans way and and college ave ?

Thanks ,

***************************

Correct!

Here are some images you may want to save on your phone for today.

11.5#4

I am struggling with the problem question 4 in 11.5. 

The question regards the partial of w with a point.

So far I have input the variables for x,y,z 

Then I found the partial with respect to s then input the values given in the point. 

The value I calculated was 25.0855369231877 

Please help me out

*********************

Ok, it looks like you did problem 3 correctly, and there were these nice chain rule formula on the bottom of that problem:

∂z/∂s = ∂z/∂x ∂x/∂s + ∂z/∂y ∂y/∂s  and  ∂z/∂t = ∂z/∂x ∂x/∂t + ∂z/∂y ∂y/∂t

You have to do exactly what you did there using those formulas, except now you have three variables so you'd so you'd need to go just a little bit further:

∂w/∂s = ∂w/∂x ∂x/∂s + ∂w/∂y ∂y/∂s + ∂w/∂z ∂z/∂s  

and 

∂w/∂t = ∂w/∂x ∂x/∂t + ∂w/∂y ∂y/∂t + ∂w/∂z ∂z/∂t

I can't tell exactly where you went wrong because YOU DIDN'T SHOW ME YOUR CALCULATIONS, but it *looks* like you actually tried to do that, and only tangled up in the algebra--on that score you would benefit from keeping the calculation of the separate terms in those sums separated and then only combine them once you've got them all done.

11.6#12

Hello Professor,

How do you go about finding the appropriate partial derivatives to define a tangent plane given a function that is not explicitly defined as f(x,y,z)= like in this case?

I already tried defining the equation as f(y,z)=x=(z+17)/e^ycosz and finding the partial derivatives of f with respect to y and z and obtained x=17+z. I also tried defining the equation as f(x,z)=y=ln(z+17)-ln(xcosz) and obtained y=-1/17x+1/17z. What am I missing here?

**************************************
Well, as we mentioned in class today, the gradient of a two variable function is perpendicular to the tangent line of a level curve.  Similarly, the gradient of a three variable function <∂f/∂x, ∂f/∂y, ∂f/∂z> is perpendicular to the tangent plane of the level surface. specifically the level surface L_17(f) for the function xe^y cos(z) -z .  This gives you a normal vector and the problem gives you a point in the surface, which is all you need for the equation of the tangent plane. I think this is covered on page 654 of the textbook FYI, unless this version of the text has moved it around.

11.3#10

Hello professor,
I’m working on 11.3 #10 and I’m not sure as to why I’m getting the partial derivative with respect to y wrong?

**********************************

well, because when you take the derivative with respect to a variable in a limit of integration, *that* variable gets substituted into the integrand.

11.3#11

I am very certain that the answer to this problem is 1, but this is not correct. Any advice?
Problem 11 11.3

*******************************Looks like you figured it out.  Just a small request though. When you ask me a question could you please tell me *what* you did instead of just the wrong answer that you got?

11.4#1

Hello Thomas,
I'm having difficulties in figuring out what I'm doing wrong in this problem. I followed the equation that is given in the book for finding the equation of a tangent plane to a surface and it keeps telling me it's wrong. I've tried a few different responses but they don't either.
Thanks

*******************************************************

Well, that because you haven't quite followed the equation as in the book.  For another approach, another way of writing the equation of the tangent plane is z=L(x,y), where L(x,y) is the linear approximation of f at the point (a,b)  given by that nice formula in the lecture notes for last Monday (the 18th):  z=L(x,y) = f(a,b) + (∂f/∂x)(a,b)(x-a) + (∂f/∂y)(a,b)(y-b).  If you had given me your calculation I could have told you more, but in your calculation you've dropped some minus signs on (∂f/∂x) and/or (∂f/∂y) and, I'm not sure how, miscalculated the right side of the equation.  

************

Lecture Notes 2/18/19 through 2/22/19

Lecture Notes 2/18/19

Lecture Notes 2/20/19

Lecture Notes 2/22/19

Lecture Notes 1/30/19 through 2/15/19

Lecture Notes 1/30/19

Lecture Notes 2/1/19

Lecture Notes 2/4/19

Lecture Notes 2/8/19

Lecture Notes 2/11/19

Lecture Notes 2/13/19

Lecture Notes 2/15/19

Scores as of 2/13/19

Please note that 1) the grader has dropped the laptop that had your quiz 1 scores on it and is not sure if those scores can be recovered, and 2) that most people got a very good score on that quiz. Please tell me 

For discussion later (Tempe Butte)

10.7#16

Hi Professor,
I'm not really sure how to go about beginning this problem. I was hoping for some direction on where to start and how to execute problems like these.
Thank you

**********************

It's easier than you're making it.  So you did part a) correctly. Here's your hint: if you replaced the 't' in part a) by some other linear function a*t + b to get r(a*t + b), for which t would r(a*t + b)=P and for which r(a*t + b) = Q?  Now in case (b) choose a,b to make the first time be 7 and the second time be 10.  Similarly 0, -4 for part c).

Practice exam complaint

Good afternoon Professor,

You said 10.9 would not be on the exam, but #3 asks about the velocity vector in part a as well asking for the acceleration vector which are both in 10.9. I remember in class you said #7 wouldn’t be on the exam, should we still be able to complete #3?
************************************

Well, ok, you're right about that. It's kind of awkward, and the reason I didn't notice is, because that's the kind of problem I always put it because it's dead easy, but I'll have to replace it with something else.

hyperboloid of two sheets

x^2 + y^2 - z^2 = -1  OR  -x^2 - y^2 + z^2  = 1

hyperboloid of one sheet

x^2+y^2-z^2 = 1

hyperbolic paraboloid

z = x^2 - 2y^2

Elliptic Paraboloid

z=x^2 + 2y^2

Generic ellipsoid

4x^2 + y^2 + (1/4)z^2 = 1

Football (subtype of ellipsoid)

x^2+y^2+(1/2)z^2 = 1

Pillow (subtype of ellipsoid)

x^2+y^2 + 2z^2 = 1

Sphere

x^2+y^2+z^2 = R^2 (a subtype of ellipsoid)

10.5#10

Hi Professor,

Number 10 on 10.5 asks 

Determine whether the lines

L1:x=24+7t,y=21+6t,z=22+7t and L2:x=−13+8ty=−13+8tz=−19+10t

intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty.

I attached my work so you can see what I did so far. I came to the conclusion that those lines are skew and fail to see how they intersect even though ww says they do. 

Thank you for your help,

*****************************************************

It was just a simple arithmetic error. In fact going through your calculation it fooled me too at first.

A complaint, reviews, and how to prepare for the exam

Professor,

I’m having a hard time understanding how you set up the homework assignments for the week (I thought homework was due the next week after we covered it). A few days ago you said 10.5 would be due on Friday, and there were some other miscellaneous chapters that needed to be removed. Today I log on to start 10.5 to finish it before the due date tomorrow, and now there are not only 3 assignments due tomorrow night, but two more assignments due 2 days later on the 3^rd, and our exam is on the 6^th. I feel like I’m doing my due diligence to keep up with what needs to be completed, but it’s not fair that you added these assignments out of nowhere. I’m only frustrated because I thought 10.5 was due this week, and I planned for it, now there are 3 total assignments to complete which will take anywhere from 6-8 hours, and two more assignments due on Sunday, another 4-6 hours, and we’re expected to study for the exam three days later.

The other part that is frustrating is that the due dates aren’t located anywhere else other than webwork (and since the dates have been wrong, I just look at what’s active and what makes sense to what you’ve been teaching in class), I tried to use the syllabus to see what will be due this week because of the webwork errors but could not find anything.

This also happened the other week for me, I logged on to see what would be due and there was 1 assignment from what webwork showed, but when I went to complete it Friday night, you had added another assignment ( which I’m okay with you adding homework but there was no sort of notification to let us know). It’s very frustrating because I’m trying to succeed in the class since I dropped this class last semester in session A, then failed session B.

I feel like the only way to track what assignments are due is to log on to webwork every day to ensure you didn’t make any changes to it. I also read over the syllabus and couldn’t find anything to answer my questions which is why I’m emailing you now.

Syllabus
“Homework: Homework will be performed using the (free!) WebWork online homework system (NOT the WebAssign system that accompanies the textbook).   Assignments will be due every Friday at 11:59PM.  No late homework will be accepted.  Homework assignment will reflect the material covered up to the *previous* Friday.  Assignments will be announced in class, here on this website and on your mat267 blog. “

Well, you raise some good points.
So, yes, we've fallen behind, due to my being out sick Wednesday (last week I think), and also my being sick but not out the Monday of that week.  And as you point out there is an exam to be taken next Wednesday.  And while I have some ability to shift the exam material, I think you will understand that it's also not ideal to add very much extra material in addition to that scheduled to the second exam.

Tomorrow I'd like to get input from the class (briefly!) on whether you would prefer to have sections 10.8 and 10.9 on the first test or the second test.

Allow me to bring the very first line of the syllabus to your attention:

Note: All items on this syllabus are subject to change. The instructor reserves the right to modify any of the following (including the dates of the tests) to meet the needs of the class or university policy.  Any in-class announcement, verbal or written, constitutes an official addendum/modification to this syllabus. It is the student responsibility to attend class regularly and to make note of any change. 

I said the very first day of class that we may push up the due dates before the exam, which constitutes an "in class announcement".

Some considerations:

• I  hadn't changed the due dates other than 10.5, because they were about where they needed to be for the exam.  I changed 10.5 because someone in the class requested it and it was reasonable. 
•  I understand the frustration though, so in response I've changed the due dates slightly. Perhaps I'll change them again depending on what I decide, based on class feedback, about material to be covered on the exam.
• I could announce the due dates and their changes on the blog, and I used to do that in the past. What seems to happen is that people wind up looking only at the webwork anyway, so I've fallen out of the habit.  
• The syllabus also about the studying you must do "continuously throughout the semester,"  which means that it's really a fine idea for you to be looking at the webwork every day.     
• It looks like I'll only get in one review day for exam one, sorry about that.  My preferred teaching strategy, in response to student feedback over the years, has become is to push a little harder on covering the course material early and then have a couple of review days before the exam.  The university has no policy at all about review, and is fine with teaching new material up the last minute of the last day before the exam, and I did that for years. 
• Likewise, people usually do better on the exam problems if they've done the homework problems first. I really don't mind having the homework due on Friday after the exam, and I'm happy to go with the class consensus on this. 

RE: Section 12.8

Section 12.8 - Closes 01/28/2019 at 12:06pm MST

This section seems out of place with regards to its due date. The other sections due this week are all from Chapter 10 and the other Chapter 12 sections are not due until February/March. The other concern I have is the questions assigned to this Section seem far out from the pace we have been going in class and from reading through the book. Is the deadline on this section due to an error?

*******************************

Very out of place, since section 12.8 isn't even on the syllabus.  I fixed it.

10.4#5 (Edited)

I still have a question about number 5. It asks:
Find two unit vectors orthogonal to a=⟨−4,1,4⟩ and b=<5, -4, 3>

Enter your answer so that the first non-zero coordinate of the first vector is positive.
I attached my work below so you can see my thought process; however, I keep getting the k coordinates incorrect and I'm not sure where I'm going wrong.
Thank you for you time,

****************************************************

It looks to me like you've done it correctly.  BUT, if you click the "Email Instructor" button down at the bottom of the web page of your problem it will give me what you've done and what your numbers are so I can see exactly how and why it's misbehaving.

(Edit)
OK, you did that. Playing around with the webwork, it looks like all it wants is four decimal points instead of three.

Lecture Notes through 1/28/19

Lecture Notes 1/11/19

Lecture Notes 1/14/19

Lecture Notes 1/18/19

Lecture Notes 1/23/19

Lecture Notes 1/25/19

Lecture Notes 1/28/19

Video Lecture To Replace Wednesday 1/16/19

Lecture Notes Page 1

Video Lecture Page 1

Lecture Notes Page 2

Video Lecture Page 2

Lecture Notes Page 3

Video Lecture Page 3

Lecture Notes Page 4

Video Lecture Page 4

Lecture Notes Page 5

Video Lecture Page 5

Office Hours

Monday 4:00-5:00 PM
Wednesday 12:00-1:00 PM
Friday 2:00 PM-3:00 PM

10.3 #14, first pass

Hello Tom!

I am having problems with finding what components of F are perpendicular and parallel to v. My initial answer was that the component -16j is perpendicular to v but the system is telling me I am wrong because "the first and second coordinates are wrong". I rephrased my answer to 0i-16j and to <0, 16> without success. I had similar issues with the parallel components; I started with the answer 0i and the system rejected it, as well as 0i-0j and <0, 0>, with the same message. Am I missing something or is the system being weird?

Thanks!
*********************************************

******************************************************

OK, you're trying to do something, which experimenting, and that's is a good start. On the other hand you're trying anything you can think of, except maybe a strategy to figure out how to understand what you should do here.


Let me say, I see this a lot. Let me point out though, that your boss is expecting to pay you to figure out the answers to the problems she/he has, and is most definitely not expecting to pay to say "I don't know what to do". In fact you'll be expected to develop information sources on your own, and use them.


So my hint to you is this: Where do you think you could find the information you'll need to understand this problem? In fact here's another hint: what do you suppose those numbers up at the top of the problem could tell you about where to look?


Tell me what you come up with and get back to me, and we'll have another go-round on this.

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Welcome to MAT267

Hi All, welcome to your MAT267 blog. You can look here to find assignments, posted scores & estimated grades, questions and answers. I SUGGEST THAT YOU BOOKMARK THIS PAGE, and also subscribe to email updates to this blog in the subscription field to the right.

1) Your Posting ID. Your Posting ID will be used to identify your scores. You should not share your Posting ID or do anything to compromise it's security. To quote from this link:

Posting ID
Your Posting ID is a seven-digit number composed of the last four digits of your ASU ID number plus the last three digits of your Campus ID number, separated by a hyphen. Your Posting ID is printed on the class rosters and grade rosters your professors work with. You can also view your Posting ID on the My Profile tab in My ASU.

2) For that matter, especially don't do anything to compromise the security of your ASU or Campus ID numbers--they can be used to for identity theft or invade your privacy. For instance, DO NOT SEND ME YOUR ID'S BY EMAIL--I don't need them to interact with you and email is an inherently insecure form of communication.

3) The first homework assignment is sections 10.1 and 10.2, which due on Friday January 18 at 11:59 PM.