practice question (corrected!)

Is this the correct set up for number 5 on the practice final exam?

(remember double click to enlarge)

Review Session

There will be a review session tomorrow afternoon 4:00-5:15ish PM in Wexler 206

where and when is the final exam

Prof. Taylor,

I just wanted to make sure when the final exam was. Your syllabus says it is May 2nd, at 7:10pm, but the ASU schedule says it will take place May 3rd, at 9:50am. I just don't want to end up showing up to the wrong exam time and day. 

Thanks in advance,

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

Glad you asked.  I have had otherwise smart people miss the final exam on this point, which was disheartening for them. You are looking at the wrong part of the ASU schedule. You need to look at the part that has the common finals, all of the mat267 sections are taking the exam at the same time. The exam will be exactly when and where the syllabus says it is. 

class/review session

do we have class tomorrow?

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

no more classes. I will be at my office hour tomorrow and I will arrange a review session, probably Tuesday afternoon. 

exam/practice#6

exam/practice#5

exam/practice#4

exam/practice#3

exam/practice problem #2

(sure would have been better if you could have done this back when this material was fresh)

exam/practice problem 1

Hi Dr. Taylor, In this E-mail I've attached pictures of worked problems from exams 1 through 3 that I did not get 100% correct. I've additionally included one or two questions from the practice final that I am not sure if I did correctly. Any feedback would be greatly appreciated. 

Thanks, 

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

this is good, and nice use of white board.  I'll be getting to the rest of these bit by bit today.  A thought for you and your classmates: these will display on the blog better if you write them so that they can be photographed in portrait rather than landscape mode.  As it is, to read this I suggest you right click (control click for mac users) and download.

13.6 confusion...

Hello Professor Taylor,

In your 9:45 lecture this past Friday I thought you mentioned you would extend the due date of WebWorK 13.6 from Friday to Sunday at the popular request of the class. I was struggling to meet deadlines for multiple courses last night, so after confirming what I believe I heard in class with another student, I opted not to prioritize the remainder of the 13.6 assignment. As of today the assignment is closed, and is labeled as being due Friday at midnight. I truly hope my classmate and I did not misinterpret your comment in class, and consequently lose our opportunity to finish the assignment. Please clarify your point of view on this situation and inform me of what the outcome will be.

*************** 

Hello Professor,

This is *********  from your calc 3 class. I was working on Webwork 13.6. and the due date is tonight April 28. This class morning you changed the date to Sunday. Thank you. 

Sincerely,

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

Well, maybe. My recollection though is that I left 13.6 alone and changed 13.7 to allow more time.  In any case, since nothing gets done until the last minute, I've changed 13.6 to be due Sunday night as well.

answers to exams

Hi Dr Taylor,

Could you post the solutions for exams 1-3 for MAT 267 on the blog.

Thanks,

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

No, because the answers won't help you if you don't do the problems. If you work the problems *again* and send photos of your answer written out on fresh paper, I will discuss your answer and give hints here on the blog. 

The last lecture notes

Lecture Notes 4/21/17

Lecture Notes 4/24/17

Lecture Notes 4/26/17 (coming, but not yet)

Lecture Notes 4/28/17

For Reals#9

Funzies #11

Estimated Grade

Score estimated as 0.75*(Average Exam Score) + 0.15*%HW + 0.10*(% Total Quiz Scores)
NOTE: extra credit not included yet.

Practice Final Exam

Practice Final (last year's final)

Office politics and numerical answers

So yah, it's true, this is an engineering class and you get to use your calculator to get the answer on the exam unless I the problem commands exact answer only.

But picture this: you're working in an engineering group meeting roughing out a device design and your boss throws out a rough model and you whip out your cell phone calculator and compute that the net voltage/force/pressure differential answer is 10^-15.  Should you report this number to the group? Or should you report that the number is zero?  Which answer would get you more respect from your cohort?  Under what conditions?  What if the true answer for the model is fairly obviously  exactly zero, even though the model itself is an inexact approximation of the device?

and 13.4 glitch

Hi Dr. Taylor,

WW 13.4 was closed early today at 11:59 am instead of pm. Was this a mistake or was it due at this time?

Thank you,

********

Hey,

<snip>

Was the webwork section 13.4 due sometime earlier than tonight? (Friday, 4/21 at 11:59pm)

I thought all homework was only ever due on Friday nights and even double checked earlier this week

but I could be wrong. Was it due Wednesday?

Thanks

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

My bad.  Fixed. Now due Saturday night at 11:59PM

exponentials

there are an amazing number of people who think that e^0=0 and/or cos(0)=0

It's that grade your instructor time of year...

Hi All, you now have the opportunity to grade your instructor (me).  Please go to your MyASU page, click on the Course Evaluations link and do the evaluation for MAT267

Deconstructing some practice test answers. 3.

Deconstructing some practice answers 2.

Deconstructing some practice test answers. 1.

Calculators on the exam

Hello Dr. Taylor,

I hope you’re doing well! Thank you for your help during office hours today.

I have one quick question about the test on Wednesday.  Once we set up the triple integrals for any given problem, is it ok for us to use our calculators to compute the definite integral to get our final answer? This would save a lot of time/space in the test, and given that we are being tested on mainly set-up concepts I figure it makes sense. I wanted to check with you though to make sure.

Please let me know.

Thanks!
********************
It depends in general: on whether on the way the problem is stated and also on it would even be useful.

On the one hand, if the problem states something like "Exact answers only, no calculators" then just writing down the number you compute using the calculator will get no credit.  In this case you have to compute the answer by hand without the calculator. It *could* still be useful to you to check that the answer you compute by hand matches up with the calculator answer.

And on another hand, for those inner integrals inside the iterated integral that have functions for limits of integration or for which the integrand doesnt factor as a product of functions of the different variables, your calculator doesnt even know how to compute those.

But, if you wind up with an integral with constants for limits of integration and a single variable integrand, yes please calculate away.

Practice Test 3

Professor Taylor,

I think the majority of us students greatly appreciated when you uploaded a previous year's test 2 on the blog a few weeks ago right before test 2.
Is it possible that you upload a previous year's Test 3 so that we can have more resources to study?

Thanks for your help!

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

Just emailing to remind you to post the practice test. I just checked and didn't see one! 

Thank you,

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

Here it is!

Practice Test 3

I made a boo-boo

I forgot to assign section 12.7--spherical integrals.   Now due next Friday, *BUT* you have an exam on the topic on Wednesday, so I'll give you quiz with a question on that topic on Monday

13.3#9

This problem on the 13.3 webwork is providing to be a pain. I am unable to figure out how to solve for the answers of b,c and d. I have tried taking a vector between the two points and then tried taking the magnitude of the change in x and y when going from P to Q. Is there something I am missing
when it comes to getting this problem completed and correct

*****************************
So, you're missing a basic theoretical fact about the line integrals of gradient vector fields (which is discussed in the textbook and  in the lecture notes.  You are paying a lot of money for these things, when you can't do a problem it is highly recommended to look at them. You would be likely to get an answer quicker than I'll get around to giving it to you, and since time is money you're paying extra for the wait.)  The theoretical fact you need is that the fundamental theorem of calculus applies to the line integrals of gradients: ∫_Γ ∇f∙dr = f(r_2) - f(r_1)     where r_1 and r_2 are the initial and final points of the curve Γ.  This means that your answer is the difference of the values of the function on the initial and starting contour. For example the answer to (b) is 34-38 = -4.

Lecture Notes 4/10/17 through 4/14/17 (completed)

Lecture Notes 4/10/17

Lecture Notes 4/12/17

Lecture Notes 4/14/17

FInal Exam Notice

The final exam will take place on Tuesday May 2, from 7:10-9:00PM is SCOB152

Webwork extension

Webwork due date/time is extended for 24 hours due to outage

Lecture Notes 4/3/17 through 4/7/17 (complete)

Lecture Notes 4/3/17

Lecture Notes 4/5/17

Lecture Notes 4/7/17

More on the extra credit assignment

Here's the blog post I made a couple weeks ago:

Hi, I'd like to offer an extra credit assignment. In general terms it would involve a properly formatted & properly cited, non-plagiarized 1000 word essay on what impact multivariable calculus has on your particular chosen career. Details to follow--but you could google the words in this post that you don't already understand.

To update:
1) Let's make it fewer words, say 600 words. This is not to make it easier for you to bullshit your way through the assignment, this is to force you to make it more clear and more concise.

2) This assignment is worth ten exam points.

3) Format:
   a) Double spaced.
   b) IEEE format for citations and references.
   c) Times New Roman font

4) You need to research this.  This means that you need to figure out what the engineers that graduate with your major actually do for a living.
   a) Go to the section of Noble Library with books on that topic. If it's a technical book it will probably have equations in it. Is it multivariable calc? Keep looking until you find some.   CITE THESE.
   b) Look at the professional journals in that discipline, scan a few articles in them. They will likely make no sense to you.  Keep at it until you find some multivariable calc.   CITE THESE.
   c) Citations to personal conversations with working engineers are good, provided that you provide a linked in page to document their professional status. Get references from them, and go look it up.

5) Time has been flying by. Let's make the new due date April 20.

6) I want all assignments delivered to me *ON* the due date, *BOTH* by email as an word searchable *PDF*, and as printed and bound (just stapled is fine) hard copy delivered to the front desk in the upper division math office in WXLR/PSA 216 during business hours; ask the staff at the desk to put your assignment in my mailbox.

Lecture Notes 3-27-17 through 3/31/17 (Completed)

Lecture Notes 3/27/17

Lecture Notes 3/29/17

Lecture Notes 3/31/17

Funzies Quiz#7

Scores to date and projected grades

12.3 due date changed.

Section 12.3 is due Sunday night @midnight

12.3#8 again.

Hi Dr. Taylor, I can't seem to get this one, I've tried entering   f(rcos(t),rsin(t) as well.

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

OK, you and a lot of people are making this harder than it has to be.  Still.  First of all, the only answer is doesn't like is the one about dA. It's not talking about f at all, so you don't have to worry about that.  There is a formula for dA in polar coordinates, I talk about it in my lecture notes, I talked about it about ten times in my video lecture last week that is still online, and the book talks about it in section 12.3. It is the single most important thing for you to know about polar integration. This formula DOES NOT DEPEND ON the limits of integration--that's one nice thing about it. WHAT IS THIS FORMULA?

Lecture and Lecture Notes 3/24/17

Lecture Notes Notes 3/24/17

Video Lecture For 3/24/17

Q's and Peruse

Greetings, 

You sent out a prep exam that is suppose to look like a real test. Are the answers to that anywhere? I am in dire need of another killer test grade. Also, where can I find the other tests with answers. I seem to have misplaced them. 

Is there any way to look at our current grade or will you possibly update us after the test? That would be great. Thank you for your time. 

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

1) Why yes, the answer is in your hands. Other than that, the way I roll is that you demonstrate your due diligence by telling me what you did, and why you think what you did is right or wrong. Then I will likely be motivated by your studiousness to ease any remaining confusions that you have.

2) Other practice tests are in an old blog post-what, you didn't memorize them? Diligence...

oh what the heck, look here.

3) I *will* update you after the test.

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

Professor Taylor, Sorry to bother you, I just had a quick question. I'm in your MAT 267 class and was recently working on the Test from Spring 2014 that you posted on the blog. I wanted to see if you happen to have the answer key as well that you could easily post online. If you don't already have one made then don't worry about it, I don't want it to be a hassle for you. But if you already have one made I would really appreciate it if you could post that as well. ************************** Yeah, this was an actual test that I gave in 2014, I wrote an answer key back then, but it's gone now.  And yeah, it would have been great to ask questions about this at the review session on Monday.

Practice Test Question#5 typo

Hey Dr. Taylor, I've noticed when taking the practice exam, question 5 has integral of sqrt(4+y^2) dydx, the outer bounds for x are from 2 to 0, but the inner bounds are from 2 to y?? Shouldn't the inner bounds be from 2 to x instead? I thought you had to have the opposite term in the first limits of integration. 

*******************
Yes, the lower limit of integration should be x.

(BTW, this would have been a perfect question to ask the substitute instructor yesterday)

extra credit assignment

Hi, I'd like to offer an extra credit assignment. In general terms it would involve a properly formatted & properly cited, non-plagiarized 1000 word essay on what impact multivariable calculus has on your particular chosen career. Details to follow--but you could google the words in this post that you don't already understand.

Section 12.3 HW fixed

Hi, I fixed the homework section 12.3 due date on webwork.

12.3#7

I don't know if i missed this somewhere but how exactly do you know what your function is in scenarios like this? How do you know what your f(x, y) is? Would it be 1/(x^2+y^2)^13?

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

Yes, that's exactly right--the graphs mentioned are the  xy-plane and the graph of the function.  Of course what might be the interesting (or tricky) part is limits of integration.

12.2#3

Hi professor,
I believe that there is a problem with two of these Webwork answers. I may, of course, just be an idiot. In which case please let me know.

****************************************
Everybody gets to be an idiot sometimes, but I don't call anybody that except myself.  
So here's the deal: that figure is *not* a rectangle.  This means in each case your inner limit of integration that corresponds to being on the diagonal line *can't* be a constant--it has to be a function of the outer variable of integration.  The question you need to answer then is which function.

12.3#8

The region goes from pi/2 to 3pi/2 with radius' of 3 and 5 so wouldn't
those be my limits of integration? I am unsure of what to do since this
didnt work.

******************
There's nothing wrong with your limits of integration. The thing you did wrong here is putting the (rcos(t), rsin(t)) into the dA, instead of leaving it with the f where it belongs.

12.1#1

I don't know what I am doing wrong with this one.

I tried using iterated integrals, I tried doing the point thing. Neither worked. 

*********************
You do need to use iterated integrals--since the region is a rectangle the limits of integration will be constants--which makes your life easier. It would also make your life a little easier if you would do  the integral with respect to y on inside--if you remember that x is a constant for that y-integral you can use substitution. I can't tell exactly what you did wrong--your answer is only about 30% wrong though.

Tomorrow's lecture

Please watch this video in preparation for tomorrow's class.

This is my first video lecture ever, btw.  I'd heard criticisms of the usefulness of this kind of thing before--I'd appreciate your feedback.

Lecture Notes 2/27/17 through 3/17/17

Lecture Notes 2/27/17

Lecture Notes 3/1/17

Lecture Notes 3/3/17

Lecture Notes 3/13/17

Lecture Notes 3/15/17

Lecture Notes 3/17/17

12.1#8

Hi Dr. Taylor,

For this problem, does it matter if one chooses to integrate with respect to y or x first?

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

No, it only matters that you have the right limits of integration for the right variable

Another practice test 2

Some people were complaining that the practice tests online look nothing like the currents tests. Here is another practice test that you *might* think (no promises) be more closely related.

11.7#7 (to be completed)

Mr. Taylor,
I am having trouble with this problem, the values I'm finding
for the maximum and minimum values don't seem to be correct. How do you
find the absolute max and min on this region?

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

I'd be happy to tell you.  BUT, if you want me to do that work I need you to do the work of telling me what *you* did first, and preferably also how what you did relates to what's in the textbook and my lecture notes--it's a lot better pedagogy to start with what you already do know than just to repeat the lecture I gave the other day that you didn't quite get in the first place.

webwork problem & the rules

Hello Prof. Taylor, I have worked out this webwork problem and am doing everything right, but there only two parts of the problem which are refusing.

I thought the two part just required finding the Magnitude of the vector above them, but I am getting it wrong. Some people got theirs right, so I don't understand why my answer is rejected. I therefore need your help!

Below is the problem;

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

OK, 

1) first of all, lets talk about the RULES for getting my help on a webwork problem.  The rather than take a screenshot of the problem, click the "Email Instructor" button at the bottom of the problem--this will show me what you've done.  When you do this, you'll have a field to give me a message. In that field enter a brief description of what you have already done.  "Help, I don't know what to do" is NOT useful to you or to me. You have many resources, specifically the textbook, that covers the material, and each section of the webwork corresponds to a specific section of the book, which will tell you SPECIFICALLY what to do. 

2) The gradient 

∇f = <-160*2x/(x^2+y^2+2)^2, -160*2y/(x^2+y^2+2)^2>

   = -320/(x^2+y^2+2)^2 <x, y>

so ∇f(2,2) = -3.2 <2, 2> = <-6.4, -6.4>.  This means that the direction of maximal change, AS A UNIT VECTOR is u = <-1/√2, -1/√2> .  The answer to part c) that you have is NOT A UNIT VECTOR AND NOT THE GRADIENT, but it does point in the right direction. I don't know at all why you want that vector--but I guess you are trying to normalize incorrectly.  The norm of that vector is the answer you give. What you needed, though, is the directional derivative in that direction is
D_u = u . ∇f  = <-1/√2, -1/√2> . <-6.4, -6.4> = 6.4*2/√2 = √2*6.4
which is also equal to |∇f(2,2) |.  All in all I *guess* that the mistake you made was multiplying by
1/√2 while *not* taking the dot product 

Webwork Section 11.6 reopened

Due to the mass of requests, I've re-opened the section 11.6 webwork until Sunday night.

11.5#5

Hello Prof.Taylor,

This problem really needs your intervention:

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

While non-interventionism has some attraction on a Friday night, OK.  This problem is really all about the chain rule (discussed in the book and in the lecture notes), for example 

∂W/∂s = ∂F/∂u ∂u/∂s + ∂F/∂v ∂v/∂s, 

and you are given all of the required components above for the values s=1 and t=0.

the most common mistake

The most common mistake people make when working a math problem is not that they don't know how to do the math, it's that they don't know what math to use and they don't know how to find out what math to use.  The reason that they don't know what math to use is because the don't know what the words mean (and so they stare at it and ponder and nothing gets done).  The reason that they don't know what the words mean is because they didn't read the textbook, or at least they didn't read the right part of the textbook.  Now anyone could be forgiven that last, because the textbook is so thick and heavy you could use it to kill poisonous snakes just by dropping it on them, so actually reading it might be fatal.

Except. It's so easy to find the right part of the textbook. Because. Each problem set refers to just one little section in the textbook, which is by itself quite light and slender. That means that the words that you don't understand are in that one little section.  And those words will have some equations that come right after that describe what those words mean, and those equations will be the math that you need to use to solve the problem.

problem

Hi Dr. Taylor,

 I need help answering this question. I dont know how to answer without an equation. Thank you.

***************************
OK, first of all: at the bottom of every webwork page is a little button that says "Email Instructor".  If are having trouble with a problem you push that button and it will send me all of the info from the work you have been doing.
The equation you need here is the definition of directional derivative:
D_u f = ∇f . u = <∂f/∂x, ∂f/∂y>. u  for a unit vector u.  You are given a vector <4,6> which has unit vector <4/√52, 6/√52> and a vector <3,7> that has unit vector <3/√58,7/√58>.  This means that the directional derivatives given in the problem satisfy
6/√52 =  ∇f . <4/√52, 6/√52> or 6 =  ∇f . <4, 6> and
6/√58 =  ∇f . <3/√58, 7/√58> or 6 =  ∇f . <3, 7>.
These amount to the two equations
4 ∂f/∂x + 6 ∂f/∂y = 6
3 ∂f/∂x + 7 ∂f/∂y = 6
which you can solve for the two unknowns  ∂f/∂x, ∂f/∂y

11.5#1

Dear Professor Taylor,

I am struggling with this problem. For finding
dw/dt I am using the following for my partial derivative:
((y*(dx/dt)-x(dy/dt))/y^2)+((z*(dy/dt)-y*(dz/dt))/z^2). For each derivative
with respect to t I am taking the derivative of the expressions given for
each x,y,z.

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

You wrote y/x^2 when you meant y/z^2.

11.6#5

I am also stuck on part 2 of this one

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

You're almost right: you just made one little sign error.  You correctly realize that the maximum rate of change is the same as the magnitude of the gradient, and I *think* you correctly realize that the direction of the maximum increase is the unit vector in the direction of the gradient, but it looks like you incorrectly compute that the partial derivative ∂(y/z)/∂z = y/z^2 to get the gradient as
i + j + 5 k instead of the correct ∂(y/z)/∂z = - y/z^2 to get the correct gradient i + j - 5 k

10.3#8

Hi Dr. Taylor,

Will you remind me again what the notation means for E and F?

Please and thank you.

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

for example f_{xy} means ∂/∂x ∂f/∂y or the derivative with respect to x of the derivative with respect to y of f(x,y). In other words, first take the derivative of f with respect to y, then take the derivative of that with respect to x.

Lecture Notes 2/20/17 through 2/24/17 (complete)

Lecture Notes 2/20/17

Lecture Notes 2/22/17

Lecture Notes 2/24/17

11.2 #3

Hey Dr. Taylor, 

I did ok on WW 11.2 but I was wondering if you have any resources like khan academy videos that I could view to ensure I really know the material. I had a hard time with when y=mx or y=x with the limits and I am not sure what to look up to clarify it.

I'll insert a screenshot of one of the problems for reference. 

Thank you,

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

I don't know of a specific Khan Academy or other online video that deals with this, but if anyone comes up with it I'll post the link.  This specific problem is actually not that bad though, once you apply the idea of substitution: for example if y=mx, then you replace y by mx in the above limit to get rid of the y-variable, from which you get:

11.2#6

Hello professor Taylor, 

I am sending you the picture of my work for problem 6 of 11.2 webwork.  I have simpliefed the expression after using polar coordinates but I don't know what next after there!  Need your help!

Thanks, 

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

What you do after is think this way:  

"Well, now I am taking the limit of a function that is the product of two factors, r and some junk that depends on θ.  The r factor is interesting because it just measures how far (x,y) is from (0,0), and since (x,y)-->(0,0) that means that the limit of r is just zero.  At the same time, the junk involving θ, although it doesn't really have a limit, it is staying bounded above and below: since -1 ≤ cos(θ) ≤ 1 and -1 ≤ sin(θ) ≤ 1 we get   

-10 ≤ cos^3(θ) + 9 sin^3(θ) ≤ 10.

This means that  -10 r ≤ r(cos^3(θ) + 9 sin^3(θ) )≤ 10 r.   Since both 10 r and -10 r have zero as a limit, the limit of my function must be zero too!"

President's day

On Fri, Feb 17, 2017 at 5:28 PM,  ********* wrote:

Hello Mr. Taylor,

I have noticed that Monday is President's Day and wondering if there is still class or not. The syllabus says there is, but I just want to make sure.

Sincerely,

*********

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

Yes, class the same as always on Monday

Lecture Notes 2/10/17 through 2/17/17 completed)

Lecture Notes 2/10/17

Lecture Notes 2/13/17

Lecture Notes 2/15/17

Lecture Notes 2/17/17

Projected Grade

Section 11.1 resched

Is it correct that the homework for section 11.1 is due today? I ask
because we have not yet lectured on it.

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

Good point. I pushed it back a week.

Attendance Record to Date

Lecture Notes 1/30/17 through 2/3/17

Lecture Notes 1/30/17

Lecture Notes 2/1/17

Lecture Notes 2/3/17

Quiz on Monday, practice tests, extra pretest problem session

1) You should notice that there is material we covered this week that will be incorporated in the final exam next week--even though the homework on the subject isn't due until next Friday.  To encourage you to engage with this material, I am announcing that there will be a 10 minute quiz on Monday on topics that we covered this week, namely vector functions and things that can be done with them.

2) Practice exams and review questions can be accessed at this link.  After the quiz we will be having a review session, so work the practice exams and come with your questions.

3) One of the mat267 instructors will be running a problem session on Monday afternoon:

MAT267 Instructors,

Apparently there is no class scheduled in the same room prior to my Monday Wednesday class in WXLR A118.  Therefore, I chose to switch 2 hours of office hours for 2 hours of problem session work immediately before their class from 3:30 to 4:30, (our class starts at 4:35).

Feel free to let your students know.  I will be there simply to work problems on the board.  Usually these problem sessions only consist of a few students and thus fire code issues due to occupancy are minimal.  If it becomes excessive we can take action at that point.

...and 10.5#18

I am having trouble with this problem as well. I must be doing something
wrong in the way I am calculating angles but I don't know what.

********************
I prefer to be in the business of getting you unstuck rather than doing the problem for you.  If you get back to me and tell me what you're did do, maybe I can help out.

10.5#17

I used the formula cos(theta)=n1(dot)n2/|n1|*|n2|

where n1=(5,-2,3) and n2=(2,-5-5)

in the end I did theta=arccos(5/sqrt(2052))

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

everything you did is just fine...except the problem was meant to fool you. Notice the second equation is written 2y - 5x -5z=2.  In order to get the normal vector you should rearrange it so it looks like -5x+2y-5z=2.  The correct normal vector is <-5,2,-5>.

The webwork was slightly broken

I'd be surprised if another student hasn't brought this up already, but our webwork shows 12.4 and 12.8 due Next Monday, with 13.8 and 13.9 due on Wednesday. This seems to be a different order than the syllabus suggests, so I'm guessing it is an error?

If not, I'd better get on it soon.

Thanks for your consideration!

******

Yes, that's an error. You should be surprised, though, because you are the first one to bring that particular error to my attention.  Thanks!   I think it's fixed now.

Quadrics Pics

ellipsoid#1 x^2/4+y^2+z^2=1

ellipsoid#2 x^2+y^2/4+z^2/4=1

ellipsoid#3 x^2/4+y^2/9+z^2=1

circular paraboloid z=x^2+y^2

elliptical paraboloid z=2x^2+y^2 

hyperbolic paraboloid or saddle z=x^2 - y^2

hyperboloid of one sheet x^2+y^2-z^2=1

hyperboloid of two sheets x^2+y^2-z^2= -1

Lecture Notes 1/23/17 through 1/27/17 (complete)

Lecture Notes 1/23/17

Lecture Notes 1/25/17

Lecture Notes 1/27/17

Lecture Notes 1/18/17-1/20/17 (complete)

Lecture Notes 1/18/17

Lecture Notes 1/20/17

A slight office hours change

I changed my Thursday office hours. They are now 2:30-3:30PM

10.2#11

Professor Taylor,
This problem has me stumped.
1/2 * 12 = 6
arctan(3/6) = 26.6 <-- should be using radians instead of degrees

1*9.8=2Tsin(26.6) <-- good 



9.8/2sin(26.6)<-- = T

1/2 (9.8)/sin(26.6)=10.943

I might be applying the wrong formula. But even so, I would
appreciate it if you could help me.
Sincerely,

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You had all the pieces and did most of the calculations correctly. It looks like you just got distracted at the end and lost track of your goal--you needed T and not θ.

First of all, use radians instead of degrees--there's a button on your calculator for this.
Second, always draw a picture--insufficient understanding of the geometry is one of the biggest problems that people have in this course and making a picture is the best solution. This one should look like this:

The force of gravity vector is pointing straight down and has magnitude 9.8m/sec^2 x 1kg=9.8N.  The tension on each half of the line is pointing from the tip of the pole to kink in the line. They make an angle of θ with respect to the horizontal, so as you already understand tan(θ)=3/6=1/2, so
sin(θ)/cos(θ)=1/2 so 2 sin(θ)=cos(θ), and cos^2(θ)+sin^2(θ)=1 so 4 sin^2(θ)+sin^2(θ)=1 so
5sin^2(θ)=1 so sin(θ)=1/√5 so cos(θ)=2/√5---and of course yes θ = 26.6 degrees or 0.464 radians of them, but you only need sin(θ) anyway and you already have that.

Got a cool project? (apply for the OZY genius award)

Ozy Genius Award

Lecture Notes 1/11/17 through 1/13/17 (finished)

Lecture Notes 1/11/17

Lecture Notes 1/13/17

10.1#7 (First student question and answer of the semester!)

Dear Professor Taylor,

I was working on the webworks assigned  problems
and the answer wasn't correct (answer is below). I was hoping to see what
is wrong because I'm pretty sure the answer is correct.

(x-2)^2+(y-7)^2+(x-3)^2-62

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You were thinking the right thing, but you didn't write what you were thinking: the (x-3)^2 should be (z-3)^2.  (this is a innocent example of how mistakes are made, for example how little-bitty bugs get in software that cause million dollar software failures)