Attendance Totals to Date

(Click on table to enlarge)

Lecture Notes 2/19/16 through 2/26/16 (Updated!)

Lecture Notes 2/19/16

Lecture Notes 2/22/16

Lecture Notes 2/24/16

Lecture Notes 2/26/16

the numbers are in...

Just for funzies...for all of my MAT267 classes for the last couple of years, over 200 students,  I plotted everybody's total homework score vs their final grade.  The data look like this:


Clearly there is a strong trend that relates performance on the homework to overall performance in the course.  The red line is the linear least squares fit; hopefully you've heard of it in one of your lab classes, it's an important tool for data analysis--Engineers use it a lot, so you should feel comfortable with its use.   The precise linear least squares description is this:

%Final Score=8.90 + 0.80 %HW + "Noise"

In this model "Noise" indicates a random effect with a Standard Deviation of 10 points in the final score and an average of zero--this is to say that homework scores don't absolutely determine the final score in this model, but they nevertheless have a strong effect on the outcome.  Of course by "random" we mean really mean all the effects that I don't have data on, for instance how much of the homework was actually done by each students in question.

Note however, that the homework is only 15% of the final, while the exams are 75% of the final score. If the only effect of the homework on the final score was from the homework itself, we would expect a slope of the least squares line to be at most 0.15.  This is to say that the homework has an effect on your grade much larger than just the numerical contribution from the homework scores.

This course has an average homework score of 73% with a standard deviation of 25%.  Clearly there is a lot of room for a lot of people to do a lot better.

Moral of the story: work hard on your homework, it will help you do better in this course.

section 11.1#10

For problem 10 i do not understand how to complete it. I plugged (0,0) into
the equation and I got the first answer 140. after that I attempted to plug
in (1,1) which did not work, (.4,0) with the same result, and then trying
to subtract 10 from 140 since it said it was spaced by 10 but still no
answer.

**************
This is interesting....I spoke to another student about this problem earlier gave the wrong answer.  OK,  on the line at y=0, the function f(x,0)=140e^x which is increasing with x so since they are equally spaced multiples of 10,  f(.4,0)=140e^.4=140*1.49 which is approximately 210--which should be =B. The gap between the contours thus should be 70, so that C=280 and D=350

on the unit normal vector....

“When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

’The question is,’ said Alice, ‘whether you can make words mean so many different things.’ Through the Looking Glass, by Lewis Carroll, page 367

So let me try to correct the record.  It is true that for a parametric curve r(t), the velocity vector v(t)=r'(t) is simply related to the unit tangent vector T(t)=r'(t)/||r'(t)||=v(t)/||v(t)||.  And it's also true that the acceleration vector is a(t)=v'(t)=r"(t).  While grading the exam I saw about fifty wishful but incorrect statements to the effect that there is a simple relationship between the unit normal vector and the acceleration:  N(t)=a(t)/||a(t)|| BUT THIS IS INCORRECT.

Like Humpty Dumpty, we can define things to mean whatever we want, and a(t)/||a(t)|| is a perfectly good unit vector. The people who thought of the unit normal vector as something useful were looking for more. They wanted N(t) to point in the direction that v(t) is turning toward AND to be orthogonal to v(t).  Unfortunately for the sake of simplicity a(t) can't do this job.  This is easy to see: sometimes a(t) points in the same direction that v does, for instance when v is increasing in magnitude but doesn't change direction.  In order to get what we need, we need to define a different unit vector N(t)=T'(t)/||T'(t)||, which is always perpendicular to the direction of motion.

Your scores and extrapolated final grade

These are your scores as of Wednesday 2/17/16.  The extrapolated score is based on the course syllabus, which gives 10% weight to quizzes, 15% weight to homework, 50% weight to midterms and 25% weight to the final exam.  Since we haven't hit the final exam, I gave 75% weight to the midterm, 10% to quizzes and 15% to homework.  The extrapolated score represents what you might get if you continue to proceed as you have been--you could go up or down depending on how hard you work of course.  As of this time, everyone is capable of pulling their grade up to a passing or better grade.



(Click on the image to enlarge)

11.1 Problem 6

Could we go over contour plots in class? They were not in the notes and it
came up in the homework which confused me greatly.

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

Sure, you only need to ask me in class.  But since the deadline on the HW is creeping up, let's address it a little bit now.  First of all, I recommend that you consult the textbook on this subject, you paid a lot of money for it and it covers this subject pretty well.    Second, we have used contour plots in class, though usually written on the whiteboard and as you point out not in the lecture notes.  Thirdly, this link takes you to a topo map of the downtown Tempe and ASU area, including Tempe Butte.  I recommend that you print the map and go climb A-Mountain and compare the features of the map to the topography of the butte.

The general notion is that each contour represents a trace of the graph of a function z=f(x,y) for some value of z, and the contour map is a whole family of contours for a variety of different values of z.  Usually the z-values are chosen to be evenly spaced, for example it looks like the contours in the topo map of Tempe are spaced every 20 feet in height.  Sometimes the contours are closer together,  this happens when the graph of the function steeper, and sometimes they are further apart, which happens when the graph is less steep.  In some regions where you don't see any contours at all the graph of the function is so flat that the height doesn't change enough to take you to the next contour. As a specific example, let's look at your contour plot b)

Notice that the contour lines are all straight lines and all parallel to the line y=x--this means that f(x,y)  depends only on the value of y-x.  The graph is pretty flat around the line y=x but on both sides the contours are getting closer and closer as you move away from y=x, hence the graph of the function is getting larger and steeper.  If you look at what function could do this, you focus in on b) (x-y)^2 which has the requisite properties.

Lecture Notes 2/5/16 through 2/17/16

Lecture Notes 2/17/2016

Lecture Notes 2/15/2016

Lecture Notes 2/12/2016

Lecture Notes 2/8/2016

Lecture Notes 2/5/2016

and the classics should not be neglected either...

the ever hopeful insistently tell me this on exams:

√(a+b)=√a + √b, 

for instance as in √(1+4t^2)= 1+2t

IT'S NOT TRUE!

another thing not to do...

Suppose you are given two planes, say:

5x-2y+z-3=0  and -x+y+2z-1=0

and you want the intersection of these two planes, which is a line, and 0=0 so you should set these equations equal each other

5x-2y+z-3=-x+y+2z-1, 

which gives you 

6x-3y-z-2=0,

right?  

DO NOT DO THIS.

Do not do this because your are trying to find the points <x,y,z> that make both equations true. Yeah, both equations are equal to zero and so 5x-2y+z-3=-x+y+2z-1 when x,y,z satisfy both equations, but 5x-2y+z-3=-x+y+2z-1 for a lot of triples  <x,y,z> that don't make either equation true.  You need to figure out how to solve both equations at once and this won't help you do this.

New Course Policy

From now on:  ONLY your writing on the actual exam paper in the actual space provided for the problem will be considered in assessing your score.  What you wrote on scratch paper will not be considered.

something not to do....

Here's a logic I'm seeing on the test, in fact I've seen it on a lot of tests for a lot of years:

r(t)=<t,t^2,t^3/3>

so

r'(t)=<1,2t,t^2>   evaluated at t=0 gives

1+0+0 so

r'(0)=1,

right?

WRONG!

<strong emphasis>DO NOT DO THIS</strong emphasis>

evaluating a vector function at a given time does NOT mean that you get to add all the components. The correct answer is r'(0)=<1,0,0>.  You have to substitute t=0 in every component, the fact that evaluating the component gives that the component is equal to 0 does not mean that the component disappears.  It is still there being zero.

homework extension

Hello Dr. Taylor,
   I don't seem to get these 2 sections at all and am getting so frustrated with them.   Is there any possible way I can get an extension on these two sections? Maybe until I can talk to someone and go through my issues with them or at least another day so I can research more online on how to do it... Sorry for the inconvenience, but I just don't seem to get it.

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

OK, given that you just took the exam, you all can have until Sunday night

webwork 10.9

Hi Dr Taylor,

I'm stuck on calculating the speed in this problem from 10.9 homework, I feel like I am close but not quite there. I'm unsure what I am doing wrong will appreciate any help.

Thank you

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

OK, you're going to need to compute the root sum of squares of the components of v; it looks like instead you've used the components of a., or maybe you forgot the t multiplying the trig functions.  The right answer should be made from

 √((7sin(t)+7tcos(t))^2+(7cos(t)-7tsin(t))^2+14^2t^2)

which you can and should simplify considerably, but you need at least another t^2 in there somewhere.

Problem 10.8#4

Hey Prof. Taylor,

I don't understand why I'm getting the wrong answer for

Tanget Unit Vector. I was able to get the Normal Unit Vector fine which

requires TUV in the first place. To find it, I did r' / |r'|.

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

ehr...it looks like you've computed |r'|=17...but r'=4sin(-4t)i-4cos(-4t)j -4k, so  |r'|=√(16sin^2(-4t)+16cos^2(-4t)+16)=√32=5.66.

MAT267 Review Questions

 I'm having troubles finding the calc 3 review from the math dept site... do you happen to have a link for it?  I know one of the fellow classmates mentioned they had a review posted on that site.  If not, do I just study webwork and the book?  And which sections is it up to again?

**************************************
The test tomorrow is on everything we covered from Chapter 10.  The webwork and book are useful indications too, especially study the questions you didn't get right the first time, if any. There's a link to the review question on the syllabus, but here's the link again.

ASU Online MAT267 Lectures

at this link.

Pretest Review Session Tomorrow Night!

There will be a review session on Tuesday night for MAT 267. It will be at Wexler 116 at 8:15pm. 

Service Announcement from a fellow student

U of A is coming to Swim Asu on Saturday the 6th at 1:00 PM.  During the breaks Michael Phelps and the other professionals will be giving an olympic preview (exhibition swims) and after the met there will be a meet and great with the same.  The meet will be held at the Mono Plummer aquatic center.

Biweekly Review Session

There will be a biweekly problem review session in WXLR A 107 on Mondays and Wednesdays from 2:30 - 4:00 pm.

attendance to 2-4-16 (&your posting ID)

Your Posting ID. To quote

"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. Many faculty use Posting IDs to post incremental grades like mid-term exam scores, lab results, etc., in public places such as the departmental bulletin board, or the wall in the classroom. The Posting ID is used to permit your professors to get your incremental grades out to you quickly and efficiently while at the same time protecting your privacy."

Lecture Notes 2/1/16-2/5/16(to be updated)

Lecture Notes 2/1/16

Lecture Notes 2/3/16

Lecture Notes 2/5/16