13.7#9

I can't quite understand how to do this problem. I've tried  |(7,0) | (7,0) | (8-z^2,0) z dy dz dx

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First of all, that double integral means you need to do a double integral, but you're doing a triple integral.  That's your first clue.  The fact that you have a double integral but the three variable function f(x,y,z) contributes to the misunderstanding but, second, that little "S" down under the double integral means that you are integrating over a surface just like we've been discussing the last two lectures. So now your job becomes figuring out the parameterization of the surface.   The fact that x and z have the constraints 0≤x≤7, and 0≤z≤7 suggests that they should be equal parameters call them t,s, i.e. x=t and z=s.  Then, since  y=8-z^2 constrains y, you get the parameterization r(t,s) = < t, 8-s^2, s> .  Now have at it.

A math extra credit problem

1.  Three pages single spaced text.
2.  An #EXTRA# page with citations.
3.  Subject: "How Vector Calculus is Used in My Major."
4. At least four inline citations, not wikipedia, not random website you found on the web. Textbooks and professional periodicals are OK.
5. NO PLAGIARISM, aka no copy-paste from random online publications.   (BTW, did you know that just 7 words in sequence provide unique identifiability for more than 90% of publications?)
6. Make a reasonable effort. If you're sloppy I'll cut down your credit.
7. Worth 10 points.
8. Due the day after the final exam: 1 electronic copy in PDF format to my email,  one printed copy to my mailbox in the math department (i.e. dropped off at the main math window in Wexler 216 before it closes.

Estimated Current Grade

Estimated total is based on 0.75*(Total of Exams)/300 + 0.15*Homework + 0.1 *TotalQuiz/3

Final Exam Location

The final exam will take place at 7:10pm on Tuesday May 1st in CDC13; a map to the location is below

Review Session on Monday

There will be a mat267 final review session on Monday 4/30/18 in Wexler (PSA) 311 from 10:30 to 11:30AM.

Lecture Notes 4-20-18 through 4-25-18

Lecture Notes 4-20-18

Lecture Notes 4-23-18

Lecture Notes 4-25-18

Webwork answers

Can you open the answers Webwork 13.2 - 13.4? I want to study those sections for the exam and it opens at midnight. 

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

Done

LectureNotes 4-9-18 though 4-13-18

LectureNotes 4-9-18

LectureNotes 4-11-18

LectureNotes 4-13-18

13.4#4

I got the integral dx (x^2) +  (8x) dy= 2x + 0

(7,0) (7+y,y)  2x +0

But it doesn't seem to work

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OK, to use Green's theorem you need the formula ∬ ∂F_2/∂x - ∂F_1/∂y dA = ∫_C F_1dx + F_2dy, where the line integral is counter clockwise, while you seem to have computed ∂F_1/∂x + ∂F_2/∂y. Also, note that the line integral in question is computed clockwise, which will change the sign of the left side the above equation. 

13.4#3

I'm not sure what I got wrong.  I came out with the integral 
(3sqrt(2)/2),(0)      (sqrt(9-y^2)^2), (y)    4-2 dy dx

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Well it looks like you did two things wrong. The first and most important is that ∂F_1/∂y = -2, so you should have had 4-(-2) =6, not 4-2=2. The second might be that your integral should have been dxdy not dydx.  Also, a) the integrand is a constant and so polar integration might be easier, and b) the area of a pie wedge is (1/2)(Δθ)r^2, which is to say (9π/8) you could use that instead of doing an integral

Lecture Notes 3/19/18 through 4/6/18

Lecture Notes 3/19/18

Lecture Notes 3/23/18

Lecture Notes 3/26/18

Lecture Notes 3/28/18

Lecture Notes 3/30/18

Lecture Notes 4/2/18& 4/4/18

Lecture Notes 4/6/18

make $40?

Hi All, this is from some of my colleagues in the School of Mathematical and Statistical Sciences:
************

We are writing on behalf of our NSF-funded project, DIRACC: Designing and Assessing a Rigorous Approach to Conceptual Calculus. One task in this project was to design a Calculus 2 concept inventory (C2CI). We have done this, and we are at the stage of trying it out with calculus students.

We are seeking volunteers from Calculus 2 and Calculus 3 students at ASU to help us validate the C2CI. We will make a cash payment of $40 to each student taking it. Students scoring in the top 50% will receive a bonus of $20.

Test dates are April 16 and 17, with arrival times staggered at 4:30, 5:30, 6:30.

Go to http://bit.ly/RecruitC2CI to register. You will pick a date and time when registering.

Thank you in advance,

Pat Thompson, PI
Fabio Milner, co-PI
Mark Ashbrook, co-PI

Estimate Grades so far

(Double click on the image to enlarge)

12.3#15

I don't understand this problem. I've tried multiplying the base and hieght and tried to do this:
I (pi 0) I (8 0 )(x=rcosA - r^2)r dr dz dA

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well, its hard to figure out what you mean but I guess maybe you mean A=θ, and I guess you're doing a triple integral, which could work but is excessive for a homework problem dealing with polar integrals (and wrong as you've implemented here).

From the way the plane z=x cuts the xy-plane at the y-axis,  and from the fact that the region is above the xy-plane, you have a base that's a semidisk in the x≥0 part of the xy-plane and a height (z) that's equal to x above that, which gives the integrals

∫_{-π/2}^{π/2} ∫_0^8 r cos(θ) r dr dθ,

so you kind of have the integrand except for that -r^2) part.  The limits of integration in r are fine, but the limits of integration in θ would be for the plane z=y instead of z=x.

12.3#9

I'm unsure what a and b are equal to. I'm pretty sure they should be a = -pi/2 and b = pi/2



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Well no, but you could think that if you didn't understand the geometry.  Did you follow the instructions and graph those curves?  Because that would have been very instructive, since r=1/(3 cos(θ)), which is the same as  r cos(θ)=1/3,  which is the same as x=1/3, which is a vertical straight line at x=1/3.  The constraint  -π/2≤θ≤π/2 means that you've got the whole line from y = -∞ to y = ∞.  You only get the part of the line inside the curve r=1,  which is the unit circle,  which has the equation x^2 + y^2 = 1, and when you substitute x=1/3,  you can get y^2 = 2/3 or y = ± √2/√3, which are a long way from ±∞.  Now that you have an x and a y, you should be able to use them to find your limits in θ.

12.3#10

The problem asks for a function for the integral and it is not f(r,t)*r and wondering why I'm incorrect.

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Well, because you are given f(x,y), and you x≠r and y≠θ; you need to substitute the actual formulas for x and y in terms of r and θ.

mat267 review sessions at math tutoring center

Lecture Notes 2/21/18 through 3/2/18

Lecture Notes 2-21-18 through 3-2-18

11.6#5

I do not understand why this is wrong

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

 

I don't know what you did since you didn't tell me, and it's hard to tell, but I guess you
computed ∂f/∂y incorrectly and/or then you did the algebra incorrectly when you tried
to normalize the gradient to get the direction vector.

Lecture Notes 2/12/18 through 2/19/18

Lecture Notes 2/12/18

Lecture Notes 2/14/18

Lecture Notes 2/16/18

Lecture Notes 2/19/18

exam#1

ASA DataFest 2018 registration now open! March 23-25, 2018

The dates have been set — March 23-25, 2018. Register now for the inaugural ASA DataFest competition at ASU, sponsored by Discover®.

Undergraduate students from any major are invited to participate in this 48-hour data hackathon. Put your team of 2 to 5 students together and register today!

Lecture Notes 1/31/18

Lecture Notes 1-31-18

Section 10.9 due date changed to next Friday

I just changed the section 10.9 due date to Friday 2/9/18

Due dates and answers available dates

Good afternoon, wanted to ask about this sections due date since its closed
but not due until tonight.
Thanks for your help.

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No one has every asked me that before but it's a natural confusion.  The due date was on Friday. *Your* answers were due then. The *correct* answers for all of the problems for that section will be available later tonight.

10.7#11

***** The feedback message: *****

I do not understand how to solve this problem. I tried taking the
derivative of each x,y, and z and then solving for t.

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

Hmmm, you might be trying to represent the tangent line p using the symmetric equations. You could make that work but the parametric form r(t)=u+tv is better for this. And solving for t that way won't work because you are confusing the t that would be the parameter in the parametric equations for the line--that you solve for to get the symmetric equations--for the t that's a variable in the curve. THOSE ARE PARAMETERS FOR DIFFERENT CURVES. You can get the t for the curve from knowing that the point (7, 9, 32) is on the curve, like for example from the equation t^3-1=7 (hence t=2). From the definition of tangent line on the top of page 585 (in my book anyway) you know it has to pass through the point (7,9,32) and be parallel to r'(2)=<12,12,80>,

Some Homework Due Dates Changed

I changed the homework due date for section 10.7 to Sunday Feb 4, and the 10.8 due date to Monday Feb 5. 

New Office Hours

(also posted on the syllabus)

M2:40-3:30PM
W12:00-12:50PM,
Fr 1:10-2:00PM

Limits (just for funzies)

Lecture Notes 1/22/18 through 1/29/18

Lecture Notes

10.5#12 and #14 (The Rules)

I don't know how to approach the problem.

and

I keep on getting this problem wrong. I don't know where I am making a
mistake.

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Well, it looks like you figured it out after awhile, and that's all to the good. In a lot of these situations people were just making an arithmetic mistake and fixed it on their own after a few minutes, which is good practice for the exam.

There is an issue I want to bring to your attention though, which is documenting your own due diligence when you asl for my help on a problem. I will have a much easier time helping you if I know what your already tried--and if I know that you did the basics like READ THE TEXTBOOK SECTION. I am often surprised how many people didn't pick that basic notion in the course of their education before now, and I don't want you to go through my class without the same misunderstanding. Moreover the ability and willingness to undertake the effort to gather the basic foundational skills is an important sign of professional maturity, and the profession will often be impatient or unkind if it judges you lacking in this regard.

10.3#5

I have no idea how to format the response for #5 on 10.3, i understand the
process but first vector value is throwing me off.

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It looks like you figured it out ok after all.  But look, finding a vector v orthogonal to some other vectors,  <3,-1,0> and <0,-1,-3>  in this case, only depends on the direction of v. Specifying the particular value of some entry, the first in this case,  is a way of specifying a particular vector in that direction--because it makes it easier for the webwork software to check that the answer is correct

A nag

You told us in class that you would move the due date of 10.5 to Saturday. It is 4 hours until the due date closes and I am, in your words, nagging you :)

Thank you for your time

Dr. Taylor,

Earlier today in the 10:45 class we were told that 10.5 would be extended one day. I just wanted to confirm that this would happen since I checked online and 10.5 said it was still due 1/25 at midnight. I was hoping to get some clarification on whether that assignment would be due today or tomorrow.

Thank you so much!

Sincerely,

Good Afternoon Dr. Taylor,

I apologize to email you the day of but I wanted to see what the possibility was of having Webwork chapter 10.5 extended. I have had a rough time staying on pace with the course load thus far. I appreciate your consideration in advance.

Thank you

Hey Prof. Taylor,

I'm just here to nag you about pushing the homework due date to the 27th. 

Thanks,

Hello Dr. Taylor,

Just a reminder to change for you 10.5 homework to be due tomorrow 1/27 instead of tonight 1/26.

Thank you very much,

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

Yes, thanks, did so.

Section 10.5

Dr.Taylor,

       I am really struggling with all of 10.5 webwork and I have been using all the resources available to me. I do not think you taught this section in class and I was wondering if you could move the deadline back? Or how can I get help from you?
Thank you,

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

It's all really about r(t)=u+tv , i.e. parametric lines, and v.(<x,y,z>-u)=0,  so we did cover it.  Sure, I'd be happy to help.  And how about if we push the deadline for this section back to Saturday night?

Lecture Notes 1/17/18 through 1/19/18

Lecture Notes 

10.2#9

I got the answer but I don't know how to format it. It says that "Operands for '+' must be of the same type"

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That's because -6i+3j is a vector and you're trying to add 6z to it which is a scalar variable.  I think you meant to have +6k. Also, you do have the right direction but that vector has length √((-6)^2 + 3^2+6^2)=√(36+9+36)=√81=9, which is three times long as you want.

Lecture Notes 1-10/12-18

Lecture Notes January 10 and 12

I am worried about my grade

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3) The first homework assignment is sections 10.1 and 10.2, which due on Friday January 19 at 11:59 PM.