Office Hours Monday and Tuesday

I announced this in class, but here it is anyway:
M 11:30AM-12:30PM
T 12:30-1:30PM

Finals Cram and Finals Workshop

From Brian England: I have decided to hold another problem session outside of the normal time frames next week.  I get out of my own final exam <<on Tuesday>> at 2pm and will head to the engineering tutoring center and be there by 2:30.  They have agreed to keep the place open until 5pm.  As always, your students are welcome to come.

Also: There will be a MAT267 Finals workshop Tuesday May 3 at from Noon to 1:00pm in BA201.  "Finals Workshops requires the student to bring class notes, practice material and questions to the workshop. Students should be prepared to collaborate with peers and tutors. This learning environment should foster recall and understanding of information for an upcoming exam."

  See <https://tutoring.asu.edu/calendar/>, Sign up: http://bit.ly/MAT267Final

13.7no7

I don't know why its coming out wrong!

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A few reasons.  First the vector element of area dA here is what our book calls dS, and not what the book calls dA--that is dA=(r_u x r_v )dudv, or since your parameters are called  r, θ  
dA=(r_r x r_θ )drdθ.  Second,  r, θ here are just parameters, not polar coordinates: you only have drdθ for your area element in the parameter plane, not rdrdθ (in fact I guess that the whole point of this problem is to fool you into making the mistake you did make, so that you can learn not to make it).  Finally, in your integral ∫∫_S F.dA it looks like you dropped the 9 from your F and also did the dθ integral incorrectly: the answer is not 2π because the F . (r_r x r_θ ) actually not independent of θ.

13.7no2

Can you help me with Let S be the part of the plane 3x+2y+z=4 which lies in the first octant, oriented upward. Find the flux of the vector field F=1i+1j+4k across the surface S.

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OK, here's an answer in general terms, so I don't do your homework problem for you.  You can write the plane as the graph z=f(x,y) of the function f(x,y)=4-3x-2y.  You can then use the usual parameterization of the graph of a function: r(u,v)=<u,v,4-3u-4v>, and then compute that
  r_u x r_v = ai+bj+ck, 
for whatever numbers a,b,c you get from computing the cross product.  Since the orientation is upward, you have to be a little careful: c has to be positive, so if   r_u x r_v  has c negative you have to use the -(r_u x r_v) instead to get the upward orientation.  The shadow of S in the xy-plane is the triangle enclosed by the x-axis, the y-axis, and the line 4-3x-2y=0, and the same triangle is the domain D of the parameterization. Then ∫∫_S F.dS=∫∫_D ∫∫_S F.(r_u x r_v) dA

13.6 no 3

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OK, the problem here is a practical one.  The "flow outward" this problem wants is in the units kg/sec. Since the density is kg/m^3,  and since the vector field v is in m/sec, and since dS has units m^2, the product density*v.dS has units of kg/sec.  Thus the rate of flow outward will be

5∫v.dS=5x(8/3)pi

 or (40/3)Pi.

Attendance up to 4/20

(click on image to enlarge)

Exam 3 update glitch

Just at the end of my office hour (and a half) today I crashed my spreadsheet.  I was saving often, so this could only possibly affect the people who were in my office after 12:30PM.  I *think* I recovered all of the correct scores, but if you were in my office after 12:30PM today, and correcting your exam or quiz 9 scores, check the following list.  If there is a problem, bring your additional scores (the new points I gave you on your paper) to my office hour tomorrow or class on Friday and I'll fix the problem.

Course Evaluations (a.k.a. grade your instructor)

MyASU -> My Classes -> Course Evaluations

Current scores and projected final grade

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Notes:
1)"Estimated final score" is made from the current total scores combined according to the rule (Exam Scores/300)*75+Homework*15 +Quizzes*10
2) these scores do not include test corrections if you havent done them yet.

Extra credit projects

Here is your extra credit opportunity--20pts total.  The project will be three pages double spaced, 1 inch margins.  Projects will be delivered in pdf format to my inbox AND in my department mailbox (in Wexler Hall 231) before Wednesday May 4 at noon.  No credit will be given for projects that do not meet the format or deadline.  Each project will have statements clearly cited.  While I offer starting references in as Wikipedia pages, each project will require you to locate a minimum of two other published references; you may wish to speak to your engineering professors for suggestions.  Below I offer two topics, I'm open to adding other topics to the list if you can come up with one that has a compelling application of multivariable calculus.



Topics:

1) The use of divergence, curl and gradient in electrodynamics.
Some starting references:

A) https://en.wikipedia.org/wiki/Electromagnetism
B) https://en.wikipedia.org/wiki/Classical_electromagnetism
C) https://en.wikipedia.org/wiki/Maxwell's_equations

Specific questions to answer:  What does the divergence of an electric field tell you?  What does the curl of an electric field tell you?  What does the divergence of a magnetic field tell you?  What does the curl of a magnetic field tell you?  What does the gradient of an electric potential tell you? Suppose that there is an electron sitting at the origin. What is flux integral over the sphere of radius 1?


2) The use of divergence, curl and gradient in fluid dynamics.
Some starting references:

A) https://en.wikipedia.org/wiki/Fluid_mechanics
B) https://en.wikipedia.org/wiki/Fluid_dynamics
C) https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

Specific questions to answer with regard to a velocity field of a fluid in motion: What does the divergence  tell you?  What does the curl tell you?  How are these related to pressure?  What are the properties of a potential flow?

Lecture Notes 4/18/16 through 4/22/16

Lecture Notes 4/18/16

Lecture Notes 4/20/16

Lecture Notes 4/22/16

13.5 number 2

I'm not sure what I am doing wrong? why do i keep getting it wrong, i've
reworked it a few times already.

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Well, what are you trying?  Let's see....you've done the divergences correctly, so that's not the problem.   Uh...wiki has this formula for the curl:

which is the same as ours...which for part A) gives curl(F)=-xi + (2y-(-y))j+(-2z)k, so it looks like you made an sign error leading to an arithmetic error in the j component.  In part B) you've done the curl correctly, so there was only the one error

13.5 number 9 (updated)

I do not know how to approach this at all.  Please give me some insight!  I
work the majority of the weekend, so an extension until Sunday would be
heaven-sent too.  If not, I'll do what I can before midnight.  Just
throwing that in there! ;-)

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First of all, the book talks about this in some detail. I recommend that everybody read it.  The *general* notion is that the curl measures both the amount and direction of circulation around an axis--for which counter-clockwise is positive--as well as the direction of the axis as a vector.  The important examples to keep in mind are the ones we worked in class last Friday: the vector fields

F=xi+yj+zk for which curl(F)=0

and the vector field F=yi-xj+0k, which looks like this:

for which curl(F)=-2k (and the negative is because the vector field is circulating clockwise around the z-axis).

The Final Exam

TUESDAY, May 3: 7:10-9:00pm in COOR 184

Homework Due This Friday

Hello Professor Taylor, 

I was hoping that we could extend the 13.6 homework to Wednesday or Friday next week considering we finished the notes today. Also it would be extremely hard for me to make it into the tutoring center before Friday and spend a decent amount of time on it, so any extension into next week would help. Thank you!

Regards,

AND

Hello Dr. Taylor,

I was planning to begin HW for section 13.6 this evening
(since I'm fairly certain it was open since Friday), but after walking away
from my computer for a bit and refreshing my browser I no longer have
access to 13.6.  Were we supposed to have access to it originally?  Or was
this recent change an error?

Thank you for your time.

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

Oops, right you are.  OK, 13.6 is now due on the 29th along with 13.7. (which is the last day of classes, mind you.)  It's still open though, so you can work on it, even though it's not due until next week.

Lecture Notes 4/15/16

Lecture Notes 4/15/16

About negative volumes...

There aren't any.  If you get a negative answer for a volume you did something (very) wrong.  You should figure out what it is.  Then fix it.
(Of course, you could hope that you just made a sign mistake at the last minute and that the true answer is just the negative of your negative answer.  From what I've seen on a lot of exams, though, odds are that you made a *much* bigger mistake than that)

RE: taking notes

Article on NPR

<<Not that it's easy to take laptop notes in math class.>>

13.4 no 5

Don't know what's wrong on this one either...

did green's theorem for the
entire figure as if it was closed, then subtracted the AD portion with a
simple line intergral and got 18 for the area of the trapezoid, and got
81/2 for the AD integral.

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As you didn't say but I suppose you know ∂Q/∂x-∂P/∂y=9-8=1, so the integral counterclockwise around the closed path is equal to the area. This means, as you know, that the integral ABCD plus the integral DA is equal to the area.  In other words it's the area minus the integral DA is equal to the integral of ABCD, which is the same as the area PLUS the integral AD:  the correct answer is
 18+(81/2).

13.4 no 4

I'm trying to answer 13.4 #4 but its saying its wrong.

Int (dQ/dx-dP/dy) dA

Qx=4
Py=0

Int (4) * dA = 4A(Area of paralellogram) which is Area*Base

x0=6, y0=6, therefore A = 6*6 =36

=4*36 = 144

Is there anything I'm doing
wrong?

***********************
Your contour is clockwise, instead of counter clockwise, i.e. the opposite of the direction that Green's theorem is about.  The result is that true answer is -144.

final exam quibbles

I read the syllabus and it says the final is May 3rd a Tuesday at 7:10 pm to 9:00 pm. According to the ASU finals schedule it says our final is Monday May 2nd at 9:00 am. Which day and time is the final at?
*********************

I wish. To be fair, I've been fooled a few times too, and I should know better.  However, MAT267 has a common final, and is listed here in the Common Finals on May 3rd in the evening.

Lecture Videos MAT267

<https://math.la.asu.edu/~surgent/video/mat267_exp.html>

13.2no5

Professor,

We got value 9031 and have no idea where the sqrt(5) came from???? 

The other image attached is the work we have done for this problem please steer us in the right direction.

Thanks, 

Team Night TRAIN

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

you multiplied by ||<1,2>||^2=5 instead of multiplying by ||<1,2>||=√5.

mat267 reviews

T/TH - COOR L1-88    6:00pm - 8:00pm

M/W - CPCOM 213  6:00pm - 8:00pm

review 12.6 no4

Having trouble setting up the bounds for theta in this situation z is bounded by 0 to 1 an r is bounded 0 to sqrt(2) but we realized that because the of the bounded region it is not a simple 0 to 2pi. Theta is also cut down because of the Z being only from 0 to 1 which cuts off part of the radius. We know it is something less the pi/2 but do not know what, so what do we do to find the region in which theta is bounded? 

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

I guess you mean this problem?

Between y=0 and y=sqrt(2-x^2) is the half circle in the upper half plane of radius sqrt(2)--that makes theta run from 0 to pi. z between 0 and 1 has nothing to do with it.

webwork typo

Hello Professor,
I am confused about the notation used to describe the gradient vector fields.

I see that there is a problem which has the function f(x,y,z)=4x+4y+2z and we are told to take the gradient of the function  <grad>f(x,y)=_i+_j+_k

The answer that was considered correct was based on a gradient which created a R^3 vector field.

Please help me understand, I don't know what I just did.

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

I see what you are saying:  problem D has a function f(x,y,z) of three variables but <grad>f(x,y) has just two variables.  That's a typo in the code, and I think I fixed it. Reload the webwork and let me know if it changed.

BTW, thanks for getting started on this early.

Lecture Notes 4/4/16-4/8/16

Lecture Notes 4/4/16

Lecture Notes 4/6/16

Lecture Notes 4/8/16

12.6 number 6

Do i have the boundaries of z correct?  Also how exactly do i calculate boundaries for x and y?  Replace something w zero or set it equal to zero or..?

Thank You,

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

Yes.  To calculate the boundaries for x&y you have to understand what is the shadow of the figure on the xy-plane.  Since E is part of three dimensional space below z=4-4(x^2+y^2)  and above the xy plane, and since the xy plane is give by the equation z=0, the intersection is given by the equation 0=4-4(x^2+y^2) or x^2+y^2=1--this is the unit circle of course. Depending on the order of your integration you have to use this formula to get the limits above and below in the middle integration, while the outside integration has the limits which allow the full extent of the circle. 

12.6 Number 4

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

Why am I not getting theta correct?  I used inverse tan(-3/5) and got
-.5404 and it is saying it is incorrect.

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Well, tan^{-1}(-3/5) is indeed -0.5404 as you suggest, which is the same as 2.601 as you wrote. *BUT* (-5,3) is in the second quadrant, while the formula θ=tan^{-1}(y/x) only works for (x,y) in the 1st and 4th quadrants.  The correct formula for the second and third quadrants is instead
θ=π + tan^{-1}(y/x).

Lecture Notes 3/28/16-4/1/16

Lecture Notes 3/28/16

Lecture Notes 3/30/16

Lecture Notes 4/1/16

HW section 12.5 reopened.

Hello professor, i am here at work half panicking and trying to do my homework without getting in-trouble. Can you please extend the homework until tomorrow please. I won't get out of here until 11pm. Thank you so much! 

I'm getting frustrated with how to set up 12.5.  Is there any way you can extend the assignment until Monday when I can get some face to face time with you to figure it out?  Or with a tutor since I'm sure you'll be busy with extra credit people?

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How about Sunday night?  It has been reopened.