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Im really sad. The exam was neither fun nor friendly. :(

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Im really sad. The exam was neither fun nor friendly. :(

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Could you please possibly post a pic of the surface for question 97a in chapter 2 of the handbook

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Could you please possibly post a pic of the surface for question 97a in chapter 2 of the handbook

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would it be possible to upload the memos for 2014, 2015, 2016 second semester exams and the 2017 first semester exam?

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Hi Tracy can you please explain how to do question 11 of the 2015 june exam.

thank you

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i am really struggling to draw the surfaces for double and triple integrals, is there programme i can use to check my sketches as not all answers in the handbook have drawings

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Chapter 2 Question 97
How did the last integral  evaluate to pi/3? I  am struggling to find how it came about.

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Good Afternoon Tracy

For Chapter 3, question 29e (looking at diagram e1) the memo uses polar coordinates to solve the integral, however I didn't use polar coordinates and got a different answer. So, why did they use polar coordinates? (the integral is really simple after using Green's Theorem). And should my answer be the same as the memos even if I just integrated normally? (maybe I made a mistake?). And if you have to use polar coordinates, how would I know (I thought you only use polar coordinates if the integral will be easier to solve that way).

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The lecture went off okay, although I know many of you were affected by the shuttles not running. I went to the 3rd period tut but the venue was locked and no one seemed to be there. I left after 5 minutes. The afternoon tut will not take place in person, but Mvano will be available online. - tracy

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Hi Tracy,

can you please upload the memo for the 2014 CT2, second semester.

thank you

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Are we allowed calculators for test two?
And also please confirm for the exam.

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Hi Tracy. I'm struggling to understand how to get the limit values of the line integrals for questions 7b and 8a in chapter 3. If you could please clarify how they got these values it would be much appreciated!

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I shall be in my office all day. Feel free to pop in or to email/use padlet. If you and some friends want to come and work in the ASPECT office or in a nearby venue, that might be quite productive. The course is continuing even though face-to-face classes are suspended. - tracy

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The Lecture Video thing you'll see listed on our Vula site is supposed to allow for me to upload videos at a variety of resolutions. So far it has only allowed me to upload one video, it is refusing the second one. And I cannot see how a variety of resolutions is catered for. does it ask you when you download? #puzzled

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How can I help you during suspension of face-to-face classes? - Tracy

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How can I help you during suspension of face-to-face classes? - Tracy

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Options are to simply be in my office during office hours, or to be in a coffee shop somewhere (Wimpy?) where you could come and sit and work. If the latter, don't worry about cost; I'd buy some limited snacks and coffee etc. to stop them throwing us out. Let me know your thoughts. - Tracy

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Hi Tracy,  some of our peers in Bob's class have received an email that Test 2 is pushed to the 6th of November. Can you confirm if this is true for our class as well?

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Hi Tracy, can you perhaps upload the class test 2 of the first semester, 2017. I only see the solutions online.

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Mvano and I are online to help you if you have any questions. You can click on the padlet wall and type text, or you can paste pictures. - Tracy

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Webassign website is giving me issues. the cengage site says that the site is down.
What do I do?
I cannot complete my assignment 7

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I am throwing away old paperwork. I have some folders free to take: 2 ring binders and four lever arch files. Pop into my office and grab them if you want them. - tracy

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Hi Tracy, is our next Maths test on the 20th or the 30th of October

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Hi TRACY I'm having trouble with the first question on web assign

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Is it necessary to do the new assignments if you already done the previous ones and are satisfied with them. What if you only want to do one new assignment to replace the previous one?

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I was told the quality is rather patchy. I have adjusted some settings to make the recording higher quality. I hope it helps.

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Web Assign tool is not working on the Vula tab.

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When will we be getting our exam marks published?

BTW the June exam was alot more challenging than the past papers that i have done

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Thanks for being the best math lecturer ever ❤️ We will miss you 😢 Continue being great 😊

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Tracy, we appreciate all the work you did to help us get through this course. Thanks a million.

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i thought we could only project on the yz and xz plane...

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I don't understand how the total flux is 72pi. Won't the total flux of the two discs cancel each other since their n's are (0,1,0) and (0,-1,0

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the angle of phi is pie/3
However when i did my calculations i got pie/6

With regards to my calculations
i said my z=root(3)a and my r is a
so when i did my right angle triangle
_r_
z|   /
|/ =phi

tan-1[r/z]=tan/1[root3]=pie/6
please can you explain where am i going wrong

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question 2 part c. can you please parametrise the curve C for me from S1 and S2

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In your solutions handbook, you use equations to reach the conclusion that p = 6sin(phi)sin(theta). However in your final answer, you state that p lies between 0 and 6 sin(phi) cos(theta)? Also, how do we find out that phi lies between 0 and pi/2?

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when D=0
how do i choose my cross section strategically ??

please can you give me a detailed explanation

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why do we equate the partial derivatives to 0 when determining stationery points

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How can I identify when I am supposed to use polar coordinates?

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Could you please upload solutions to 2013 (semester 1) exam. many thanks :)

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in one of your solutions there is a sqrt(2) of which i dont really get how did you get it. please kindly explain that one for me.

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Does it matter if you use the unit tangent vector as your normal vector when  finding a normal plane, instead of using r'(t)?

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how were the max and min values of t on each side of the triangle chosen?

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Is there going to  be bonus marks in exam ?

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Is there going to  be bonus marks in exam ?

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Section 3.1, Question 5
number 5.a) i) Why are the limits of integration from -pi/2 to 0 and not from 0 to pi/2?

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the memo has k=-0.5
please can you explain how we got k=0.5
and in general how do i approach such a question cause i am not understanding the method behind it

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Section 3.2, Question 30 in the handbook, when it is stated that the Unit circle is oriented positively does it mean it is only in the first quadrant? That was my first assumption but my calculations prove otherwise.

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how did the square root of 9(sint)^2cost)^4 + 9(sint)^4(cost)^2 go to 3(sint)^2(cost)^2

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we were never tested on chain rule
Do we need to learn it for the exam??

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where does the pi disappear to in the second last line of the first flux calculation?

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am I correct in thinking that the volume density is given? p(x,y,z).
Because then how can we use the volume density in the mass equation for a surface integral? Why would we not have to use it in the mass equation for a triplle integral?

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Tracy would it be possible for you to please post a photo to the comments of how to parametrise the curve of intersection of the two surfaces as no matter what I do I cannot get the right answer

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How do you get  (x/2y)^0.5 + (y/2x)^0.5 from [1+ (x/2y) + (y/2x) ^0.5 ?

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The weather website windguru (https://www.windguru.cz/91) which I find very accurate, is predicting another storm for next week Wednesday. If that prediction remains in place then I'll be available for online, not office, consultation. - Tracy

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Can you please explain how you parametrised C1? (the points on the line are (1,0) and (e,0) so i got r(t)=(1,0)+t<e-1,0> tE[0,1] but your method seems simpler)

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if i may ask about the conditions that we were given for a point to be a minima or maxima  what if the d>0 and fxx is 0?

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considering the region in the 1st quadrant, should the limits not be from 0 to pi/2 instead of the -pi/2 to 0 used in the handbook solutions

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In Q17, how did they get the values for z in the cylindrical coordinates?

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Were there only 7 tut-tests?

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What was the pass rate and highest mark?

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Tracy
Thank you for the great maths lectures. With that said, I really hope I don't see you in a classroom next semester   :)

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why does the integrand become 3x^3 + 3y^3 ? and not just 3x^3

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Thank you so so much for being one of the best maths teachers/lecturers I have ever had. I really enjoyed this course; all thanks to you. Thank you for really putting in extra effort for all of us and making 8am maths so enjoyable! We will all miss you next semester. Have a happy holiday and thank you for being the best!

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when  i calculated D(x,y) where (x,y) are the stationary points  (0,0) (3,0) (0,3)
when i calculated these, all D(x,y) were negative, which is why i assumed they where saddle points, however the memo does not state that......is my answer incorrect?

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Would we ever be given a function where its local and absolute max cannot be classified
because I have just done 18b and I have been trying so many functions to get a possible answer, however when i looked at the memo it showed more information is required

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How would i know how to draw such a curve. I tried using the let z= k method , however that got me nowhere,
Please can you explain to me how would i go about approaching this

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How would i be able to explain such an answer , there is no way that i would know the rate at which these 2 values are changing hence i would not know when it increases and when it decreases

Please help me

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We have conditions where fxx<0 and fxx>0 , what is the interpretation for fxx=0
??

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Why do I just assume that the expansion up to the third degree is the function  f(x,y)??

What is the explanation of it

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when calculating the flux through the plate that you've added do we always assume that z=0?
The flux should always be outwards, right?

also, how (by just looking at the vector equation

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Are we going to get a formula sheet in exams? Is it like the one found at the beginning of the handbook?

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Green's Thm where F(P,Q) is not defined at a certain point

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Green's Thm where F(P,Q) is not defined at a certain point

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So far all the all the questions have P and Q that have the same denominator. I noticed that for Q40, 41 and 42 you chose the equation of the function/curve you to be equal to the denominator (of P & Q). is it wise to do that all the time. if not what is the trick to finding this equation.
Also, are P and Q always going to be fractions where dQ/dx == dP/dy such that when you apply Green's thm the answer is zero??
Thank you in advance

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From my knowledge , if a function is conservative and closed , work=0
When i looked at quest 26b i assumed the work =0 because t is between 0 and 2pie, and it is a closed surface, why is this not true, because the answer is a non zero value

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We are now 3 lectures behind due to unforeseen circumstances,(the storm), The plan according to the work book is to finish the syllabus by the 15/06, some of us have already planned on how we are going to prepare for the exams, thus if maths lectures fall behind that puts alot of pressure on your dear 2085 student. :(

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For question 44 a) in chapter 4, shouldn't the respective equations be x^2 + y^2 - 5  and 4x - y^2 instead of x^2 + y^2 - 6 and 3x - y^2 ,
as it is in the memo?

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i have a query  on the limits of the double integral.
i don't get how the conversion factor was implemented in the question

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Good day, may you please upload the memo for the above mentioned exam.

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Why is the upper limit for theta pi/2 and not pi?

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Could you please upload the memo for 2013 end of semester exam please

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What is the difference in approach when the fluid is moving in the upward direction as opposed to outward?

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Why is the mass of the sphere multiplied by 2

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Are we expected to know such flux questions because the memo shows that the answer was calculated using Divergence therom??

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apparently mainstream was told that grad (direction derivatives was in the test on mon, is this correct

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how did
sin^4t+cos^4t=1-2cos^2sin^2

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Hi Tracy :) in the solution to 117, line number 6, it seems as though you have integrated sin^2(theta) to 1/3 sin^3(theta). Is it possible to maybe show how you got to that step? Because I thought that you need to use the identity sin^2(theta) = 1/2(1-cos(2theta))

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how do you integrate
cost(1-sin^2(t))?

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Are there any more past papers for the class test

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what is the radius of the sphere?
we are given z =sqrt(x^2 + y^2 + z^2) what is this z?
thanks in advance

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Why is phi between 0 to pie/2
The region R is only in the first octant. Would that not restrict phi to 0 to pie/4

And for quest 115 c
Why would i change to cylinderical coordinates
I already have my intergral in spherical co ordinates in b when i calculated the mass, so the only thing different between b and c is that b has a density and C will not have a density
Please can you help me

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Ma'am in your flux notes you said diversional therom will not be tested. Did we do diversion therom?

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Do we start studying from double intergrals or Directional derivatives?
because in class test 1 grad f was not included so do we need to know grad f as well or start learning from double intergrals
??

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For the square root part of the integral, why does the memo say that the partial derivative under the square root is (4t^3)^2 and not ((4t^3)^2+(1)^2)

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For the curve C1, the z part of the integral, you say that it is (-t)^2(-1)dt. But why is the -1 not the square root of (-1)^2 (which would make it +1)? Because I thought that the formula uses the modulus of r'(t) because it is the length

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I understand that it is a circle in the first quad, and since it is in the first quad i would assume it goes from 0 to pi/2
However the memo has the intergral from 0 tp -pi/2
why is this so ?
by using 0 to pi/2 I get an answer of 8pi+16
but if i where to use 0 tp -pi/2 i get 8pi-16

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Hi Tracy , Could ma'am please upload the rest of the solutions for chapter 2? from 97 on wards

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why do i break down the integral of 0 to pi to 0 to pi/2 + pi/2 to pi
???

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They say calculate the mass of the parabolid. Why does the memo have a ds in the integral. They are not asking for surface area so why would we need to use ds for the calculation??

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the memo has the integral for pie/2 to pie/4  for r is 0 to sec(teta)
However I dont see how this is possible because when i draw my triangle I get 1/r = sin(teta), which means my r is cosec(teta)
Is the memo wrong am I wrong?

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they have sqrt(x^2+y^2) as the density and they some how get this to equal to r^2 and with the co ordinate change it is r^3

my answer for sqrt(x^2+y^2)=r

please can u help me