OK. About your answers.

I know I told you that it didn't matter to me, if you wrote down a mathematical answer like sin(1) versus the numerical answer like 0.84147, and it doesn't.   BUT it is becoming clearly that I can't trust *everybody* to know to use radians vs degrees, and that is something I should probably reinforce your awareness about.  The problem is that if I follow the policy about not caring I wind up sanctioning the people who actually try to compute a numerical answer and use degrees, and the people that would have got it wrong and the people who don't bother to evaluate numerically but would have gotten the wrong answer get away free.

SO from *now* on numerical answers are required for all evaluations (e.g. those questions where I say "Evaluate" something. 

PracticeTest3#3

Hello Dr. Taylor,
I am going over the exam 3 review posted on the ASU calc 3 site, and cannot figure out how the solution for the upper bound of the dy integral is sqrt(1-x^2) as opposed to just 1-x^2. I have included a pdf with the original question and the given solution. Thanks in advance.

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Yeah, that's a mistake, as you correctly note it should be 1-x^2.

Practice Test Problem

The answers key says all of these are zero and I don't understand why


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a) because along lines parallel to the y-axis all of the vectors are contant and all pointing in the positive x-direction. Each dot product on upper half of the circle will have the negative of dot product on the other half of the circle because the x-direction of dr is pointing the opposite direction.

b) all of the arrows of the vector field are pointing perpendicular to the circle, hence dot product is zero at each point. 

c) this vector field is the gradient of x^2-y^2 (check it out). but the path integral along a closed path of any gradient is zero .

An extra credit assignment

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 November 29: 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.)

Lecture Notes 10/19/18 through 11/2/18

Lecture Notes 10/19/18

Lecture Notes 10/22/18

Lecture Notes 10/24/18

Lecture Notes 10/26/18

Lecture Notes 10/29/18

Lecture Notes 10/31/18

Lecture Notes 11/2/18

exam scores and your current estimated grade

I have been informed that I'm not allowed to send your graded exam by email, sorry. Here are your updated scores and current estimated grade

just a little fact about polar coordinates

The radial coordinate is a distance from the origin. Since a distance can never be negative, when you're doing an integral in polar coordinates the lower limit of integration can NEVER be less than zero.