Use Stoke's theorem to evaluate ?

C

CalleighMay

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Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help!

I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P

Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help?

We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book.

The problem is on pg 1133 in chapter 15.8 in the text, number 14. It reads:

Use Stoke's theorem to evaluate Integral (with C at bottom) of F (with a dot) dr
It states that in each case, C is oriented counterclockwise as viewed from above.
For this specific problem is gives,
F(x,y,z)=4xzi + yj + 4xyk
and
S: z= 9-x^2-y^2
and z>=0

Again, i literally haven't a clue where to go with these =/ I looked at the soln's to the other problems in this set but still haven't a clue where to go! =/
Any help at all would be greatly appreciated. Thanks guys ;)
 
CalleighMay said:
Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help!

I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P

Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help?

We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book.

The problem is on pg 1133 in chapter 15.8 in the text, number 14. It reads:

Use Stoke's theorem to evaluate Integral (with C at bottom) of F (with a dot) dr
It states that in each case, C is oriented counterclockwise as viewed from above.
For this specific problem is gives,
F(x,y,z)=4xzi + yj + 4xyk
and
S: z= 9-x^2-y^2
and z>=0

Again, i literally haven't a clue where to go with these =/ I looked at the soln's to the other problems in this set but still haven't a clue where to go! =/
Any help at all would be greatly appreciated. Thanks guys ;)
Click to expand...

What section have you finished now - (so that this section can be helped properly)?

First thing to know - what is Stoke's theorem?

Please tell us from your book how they describe (and look at the proof) Stoke's theorem.

There are several useful examples worked out in the book - how is this problem different from those?

These are all vector equations - you need to figure out curl of a vector.

Finally, If you are planning to take engineering (specially electrical or mechanical) - think about why/where it would be important to calculate F.dR.
 
What section have you finished now - (so that this section can be helped properly)?
-The last section of the book we had before our final exam (what he taught to us) was chapter 12. He said next semester we will start off in section 13 so all these random problems he's giving us to look at are from 13 to the end of the book... I really don't know this stuff at all. He doesn't "expect" us to know how to do it, he just wants us to talk about them amongst each other and see what we can do with them having been taught NOTHING. I don't think it's fair, and to be honest all it's doing is making me go crazyyyy that's why i joined this forum, for some help. I really want to understand these problems to show my professor i am trying really hard. I may not be able to figure all of them out by myself but at least i'm putting in the effort to understand them. All i want is to learn them and know how to do them in the future before all this crap is piled on top of me in the fall.

First thing to know - what is Stoke's theorem?
-I read the theorem in the book and still have no idea what it's talking about =/ Is F force? I remember that from physics in High School but never used it in calculus, all i know is that it's F=MA. And i don't know what a "curl" is or what C means... One of the examples gives this strange symbol which obv has some effect on the answers but i don't know it's value or what it does.

Please tell us from your book how they describe (and look at the proof) Stoke's theorem.
-"Let S be an oriented surface with unit normal vector N, bounded by a piecewise smooth simple closed curve C with a positive orientation. If F is a vector field whose component functions have continuous partial derivatives on an open region containing S and C, then," (it gives the formula).

There are several useful examples worked out in the book - how is this problem different from those?
-I have found several problems just like it, on pg 1129 after the theorem and in the review exercises, but i cannot follow the work. He's given us a lot more problems from these future sections that i've been able to figure out looking at solutions of similar problems, this just being one of them that i cannot follow =/

These are all vector equations - you need to figure out curl of a vector.
-that's the thing, i don't understand where the book is calculating this. There's some strange symbol in the matrix that is giving me trouble.

Finally, If you are planning to take engineering (specially electrical or mechanical) - think about why/where it would be important to calculate F.dR.
I'm actually going to college to teach math (i want to teach middle school math (gotta be k-12 GRR), god only knows why i need up to Calc III) so i'm trying to get the hard math over with as soon as i can. I took Calc I AP and Physics 1, and II AP in high school and am taking this class, calc II now this summer at my college to get ahead. Maybe i'll find out this isn't for me- which i'm leading to the conclusion of... My dad's into bio and my mom hasn't taken simple algebra, nevermind calc, in her life so i'm basically on my own.

Thanks
 
Hey guys, can someone give me the full solution please? We had class last night and he didn't really explain them but i would like to know the answers.

Thanks!
 
You have to show us that you are at least trying - and are capable of attending these classes that teach at this level.

The copy of the book that I have (2 nd edition) has very good example problems - almost exactly like the problem posted - I would assume 8 th edition will have similar/same example problems.

Read through those - copy one of those problems onto these pages to show that you are at least looking at those - then I would work with you....
 
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