Cumulative Scores and Grade Estimate

Grade estimate based on straight grade scale. The curved scale is likely different. Click on the image for enlarged view.

Scores and Estimate Grades

Note: E1 and E1Xtr amount to your exam 1 score. E2A+E2B amount to exam 2 score. Est Score is computed as (E1+E1Xtr+E2A+E2B)*0.75/2 + hw%*0.15 +Sum(Q1...q7)/4.5, and Estimated grade based on a straight scale. The curved scale would likely be different. 

13.4#3

I can't seem to setup my bounds properly for this problem. Honestly, setting up my bounds for all 
of these Green's Theorem problems has been a struggle. How should I go about setup up the bounds?



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Well, ok, you've got a piece of pie of radius 4. It's 1/8 of the whole pie. *If* you were going to actually calculate the circulation, that would be the path integral along the edge of the piece of pie. Since it has three pieces, you'd have to break up the path into three pieces: the part going outward from the origin along the x-axis, which can be parameterized as r(t) = <4t,0> for 0≤t≤1, the counterclockwise circular part of radius 4 moving from the x-axis upward and to the left to the point (2√2,2√2), which can be parameterized as r(t) = <4 cos(t), 4 sin(t)> for 0≤t≤π/4, and then the radial part moving inward that can be parameterized as r(t) = (1-t)<2√2, 2√2>. You'd have to substitute x(t) and y(t) for each part and then integrate with respect to t and add them all up.

*BUT* you're not going to do it that way, instead you're going to compute
∂F_2/∂x - ∂F_1/∂y = 5-(-4) = 9,
then use ∫∫_D ∂F_2/∂x - ∂F_1/∂y dA = 9 ∫∫_D dA = 9(Area of circle)/8 = 9(π 4^2)/8
=9*π*16/8 = 18π = 56.55

By the way, I changed the due date to tomorrow night.

12.7#11

I'm struggling with what to do for this problem. My phi bounds are pi/3 to pi/2. My theta bounds are 0 to 2pi. My rho bounds are 0 to 2. My integrand is rho^2 times sin(phi). Can you please give me a clue as to where I'm going wrong? I took this problem to the tutoring center and they couldn't figure it out either.

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 Let's see: z=3r means ρ*cos(φ)=  3ρ*sin(φ) so φ = tan^{-1}(1/3) =0.322 radians or 18.43 degrees. Your only mistake was jumping to the conclusion that webwork would default to a clean and easy lower bound.  

12.6#4

Theta can be found with the following formula, right?

arctan(y/x).   

The coordinate for this problem is (-3, 4, -1), and none of the follow are accepted:

arctan(4/-3) = -0.927295218001612 = -53.1301023542

The previous problem didn't have this issue, and the first entry for this problem accepts the following:

-3/(cos(arctan(4/-3))

Is there a way to fix this, or do I need to do something differently?

*************************************************************It requires a slightly more sophisticated notion of arctan.
The graph of the tangent function, with it's vertical asymptotes looks like this: This function doesn't satisfy the horizontal line test, so it has no inverse function. The red part of the graph is restriction of the domain of tan(x) to (-π/2, π/2), and it does satisfy the horizontal line test and the inverse function of this is what we USUALLY call arctan. These values of theta correspond to (x,y) in the first and fourth quadrants, where x>0.  The point (-3,4) is in the second quadrant though, and if you look at the angle of this point from the positive x-axis its going to have θ>π/2, corresponding to the blue curve on the right, or π-0.927295218001612 = 2.214

Lecture Notes 10/25/19 through 11/1/19

Lecture Notes 10/25/19

Lecture Notes 10/28/19

Lecture Notes 10/30/19

Lecture Notes 11/1/19

switching order of integration

....do you remember when I said *NEVER* have variables in the outside limits of integration, and that if you should find yourself with variables in the outside limits go back because you did it wrong?

sums and vectors

an amazing number of people STILL make the illogical jump equating sums and vectors: that 3+5 means the same thing <3,5>

Practice Exam 2 Answers

Professor Taylor,

<<<<<<<<<<<<<snip>>>>>>>>>>>> In class on Monday you passed out a practice exam and said that we could come ask you one question if we showed our work. Does this mean that you are not posting an answer key for us to check against? I have checked the blog and the syllabus practice exams to see if the answer key is available and I have not found it. As I have already completed the review, an answer key to check my work against would be very informative. I apologize for the late hour of this email, however I thought if I was having this problem then it is likely that I am not the only one.

Thank you for your time,

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

You heard correctly.  You do maintain the option to go to the syllabus and look at the practice test linked there, which does come with answers, as well as the review linked there.  You may also take the practice test I passed out and go to one of the review sessions hosted by the University Academic Success program and ask them how to do the problems. As I've stated several times by now,  passively getting someone else to tell you the answer fosters the delusion that you know how to do the problem, when really much of how to do the problem is learning what mistakes you're likely to make. This requires actually doing the problem and making the mistakes before you get them corrected though.  The practice test I passed out is for this purpose.

Exam 2 reviews

The University Academic Success Program will be holding some test review sessions (see table below for times/locations), in case you want to announce this to your students.  

Date	Course	Topic	Time	Location
Monday, October 21	MAT 267	Exam 2	6:00 PM	PSH 151
Tuesday, October 22	MAT 267	Exam 2	7:00 PM	PSH 153

 

LectureNotes 10/4/19 throught 10/21/19

LectureNotes 10/4/19

LectureNotes 10/9/19

LectureNotes 10/11/19

LectureNotes 10/16/19

LectureNotes 10/18/19

LectureNotes 10/21/19

permission slip

Waiver Form

scores and extrapolated grade

Here are your scores and estimated final score and grade. Please note the exam score is unusually depressed because of difficulty interpreting the exam instructions about multiple choice problems, and this number will likely come up with the extra credit report

Field Day Monday October 7

On Monday October 7 we'll meet for class at 10:55 (i.e. ten minutes late to allow for extra travel time) at the base of A Mountain, which is behind the light rail station at College and 5th Street in Tempe, about a half a block north of Tempe Main Campus. Topics to be discussed: level curves, gradients, maximum increase and decrease, critical points, absolute max and min.  We'll be doing this as we slowly hike the mountain, so this will just a little bit strenuous.

If you are unable to participate in this activity, please inform me and we'll find another activity for you.

10.9#3

This problem won't work. the integral of -25sin(5t) is 5cos(5t). But it keeps saying that is the incorrect answer, and therefore I can't get the antiderivative of that either.

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Well, you say that "the integral of -25sin(5t) is 5cos(5t)" , but this isn't true.  AN integral is 5cos(5t), but so is 5cos(5t)+K where K is any constant.  You've reflexively chosen K=0, but any other constant will also be an integral of -25sin(5t).  But this value of K gives the wrong value for v(0), as you can check for yourself.  Which is the right value?

10.9#4

I have attempted to solve this problem many times by 1) finding the velocity vector 2) finding the magnitude of the velocity vector (speed) 3) taking the derivative of the velocity vector and equaling it to zero 4) solving for t. I have gotten 3/52 seconds every time, but I am incorrect. What am I doing wrong? My original position vector is: <-5t^2,-2t,t^2-6t>



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So first a meta-analysis. solving a problem incorrectly many times is frustrating, but it's also a sign post that you missed: when you solve something incorrectly its important to figure out what you don't understand that caused your mistake. Just doing it over again usually won't help.

Secondly, you haven't told me enough of what you did that I can tell you exactly what you did wrong, but I can see that you're off by a factor of 2. Maybe this is because you're getting tangled up in the square root or maybe you incorrectly used FOIL when you multiplied out d/dt (t^2-6t). 

I guess you correctly computed that r'(t) = <-10t, -2, 2t - 6 >, did you get 
s(t) = √(100t^2 + 4 + (2t-6)^2) = √(104t^2 - 24t + 40)?

At this point you could use the chain rule, or you could recognize that s(t) and s(t)^2 are minimum at the same time; the latter is a little tidier to minimize because it's a polynomial.















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Lecture Notes 9-25-19 through .... (to be updated)

Lecture Notes 9/25/19

Lecture Notes 9/27/19

Extra credit assignment

The rules:
1) Research how vector calculus applies in your chosen discipline of engineering.
This means actually research it. This is not meant to be easy or something you can just imagine.
2) Write *about* what you discovered in your own words. Two pages double spaced,
2) Cite your references, with a number referring to the references section, in your writing. This insures that you actually did research something.
3) Document your references, page number and/or section, in a separate reference section. There should be at least four *distinct* references. At most one should be wikipedia.
4) No plagiarism. I.e. no copy-pasta, no using other peoples words or ideas without crediting them.

The value to you: UP TO 66% of the points you lost on Exam 1. You will have to earn your points, though.

Due Date: October 25 at 11:59 PM. 

Firefox browser is giving trouble

As has been pointed out to me, and I've verified for myself: The latest update of Firefox shows a File Not Found error when trying to load the syllabus or the blog.  I recommend that you view the syllabus or blog using Chrome, which still seems to function as normal.

Lecture Notes 9-16-19 through 9-23-19

Lecture Notes 9/16/19

Lecture Notes 9/20/19

Lecture Notes 9/23/19

The test...

It looks like some people don't bother to read the instructions. It looks like some of them are smart in other ways, but since they didn't show their work I can't really tell whether they might have just copied from their neighbors. I bet they'll be unhappy with their scores.

The exam today

Prof. Taylor,

I had a question regarding the topics on our first MAT267 Exam tomorrow. Should we only expect the subjects covered on the practice exam? Are there any topics that we should prepare for that weren't on the practice exam?

Thank you for your time,

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

1) Anything in sections 10.1-10.7 is fair game, and anything that we've covered in the lectures is fair game.

2) Of course. We've covered many topics, but only have about ten questions on any practice exam.

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

Hello,

I’ve looked for info about the exam but I’m not sure where to find it. Will it be in class tomorrow or another time and location? 

Thanks, 

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

All of the midterms will be in the classroom.  The final exam may be somewhere else.

10.7#1

I know the domain for sqrt(t-2) should be 2-> infinity but the value seems so be broken. Plugging this into a graphing calculator with the other functions shows this. What is wrong?

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uh, it looks like you figured it out. Maybe the part about the interval notation and open and closed endpoints is what confused you?

10.5#17

Hi Dr. Taylor. I am having trouble with getting the correct answer on this problem. I took the dot product of the two normal vectors and got -6. I took the magnitude of the two vectors and got the square root of 21 and the square root of 26. I then took the inverse cosine of -6 divided by the magnitudes. I checked my answer with multiple people and said that my calculations were correct. I am not sure what I am doing wrong. Let me know if you can help! Thank you!

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

yes, that's a confusing and frustrating situation, and you're doing the right calculation--almost!
Let's imaging you're looking at the two planes edge on. You should see two lines, something like this:

and note that there are two angles between these two lines, one acute labeled as 𝛂 and the other one obtuse, and labeled as 𝛃.  They satisfy 𝛂+𝛃=π radians or 180 degrees. By convention, the angle between the two planes is take to be the acute angle 𝛂.  Similarly, let's look at the normal vectors for these planes. I've drawn the two normal vectors you've used in black, but for every normal vector n the vector -n is also a normal vector, which I've drawn in red.  The angles 𝛂 and 𝛃 show up between these normal vectors again, and you've computed 𝛃. What you need though is 𝛂, which you can compute as cos^(-1)(6/(√21√26)).

A worry about the homework

On Fri, Sep 13, 2019 at 5:15 PM ***************** wrote:

Hello Professor Taylor,

The 10.6 homework is set to close today at 11:59, but we have not covered all of the material in class yet. Could you please extend this homework?

Thank you for your time,

##########################################
Oh, yes.  Fixed.

Lecture Notes 9/9/19 through 9/13/19 (UPDATED 9/15/19)

Lecture Notes 9/9/19

Lecture Notes 9/11/19

Lecture Notes 9/13/19

Lecture Notes 9/4/19 through 9/6/19

Lecture Notes 9/4/19

Lecture Notes 9/6/19

LectureNotes 2-26-19 through 2-30-19

Lecture Notes 2/26/19

Lecture Notes 2/28/19

Lecture Notes 2/30/19

Office Hours Announcement

M 9:30-10:30, W 12:00-1:00, F 3:00-4:00

Worried about your grade?

(Here's one approach. Or maybe not.)

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, 10.2, and 10.3 which due on Friday September 6 at 11:59 PM.