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Gil OnTop A Hill: hey mrs. brown
TiNgYbLiNgY has entered the room.
abbymath92: hi
abbymath92: sorry I'm late
Gil OnTop A Hill: -is divergence pretty much the gradient of F?
abbymath92: how's the studying going?
abbymath92: no
TiNgYbLiNgY: its ok
abbymath92: div F is the sum of the partials
Gil OnTop A Hill: oh yeah
Gil OnTop A Hill: woops
abbymath92: the sum of the x partial of the x component, the y-partial of the y-component, and teh z-partial of the z-component
CompstomperUSA: hi
CompstomperUSA: can u help me with 16.7 #17?
abbymath92: lemme look it up
abbymath92: just use dS = ||ru x rv|| dA
TiNgYbLiNgY: i think i'm going to die
Gil OnTop A Hill: is the test mostly set ups, and will it have stuff from other chapters
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abbymath92: the stuff from other chapters is the same stuff that you need to do in order to solve problems in Ch 16 homework
abbymath92: it's not "mostly set ups" but there are about three or four "only set up"
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TiNgYbLiNgY: baah
Gil OnTop A Hill: thank u
freezerburn99: so ms brown is this a pretty straightforward test
freezerburn99: theorm and setup
freezerburn99: or how would u characterize it
abbymath92: yeah...no surprises
freezerburn99: ok
CompstomperUSA: what about same section #23?
CompstomperUSA: do u convert to spherical or somethign?
CompstomperUSA: or keep it in rectangular
abbymath92: probably best to do that one in parametric...using spherical coords
abbymath92: but double check the hw assignment sheet, I may have suggested something else
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Diablo2Buu: anything happening yet?
abbymath92: there were a couple quick questions so far
abbymath92: I just got online like 10 minutes ago
Diablo2Buu: aif we arent caught up with the homework, and we dont exactly know everything yet... should we do homework problems until we understand the topic?
Diablo2Buu: oh ok
abbymath92: hw is a good way to study
Diablo2Buu: but if we dont have time to complete all of the assignments tonight, should we just go until we understand the toopic, and then when we know everything, go back and finish as much as we can for more practice?
Diablo2Buu: topic*
abbymath92: that sounds like a good plan
Diablo2Buu: ok
Diablo2Buu: :-)
abbymath92: do what you need to to cover all of the topics
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TiNgYbLiNgY: for questions about the area under a curve is it going to mainly be on the fundamental theorem of line integrals or do we have to know how to do the long way too?
abbymath92: area under a curve?
abbymath92: we didn't do problems like that in this chapter
TiNgYbLiNgY: er...
TiNgYbLiNgY: wait...lemme check
TiNgYbLiNgY: ha i'm a little confused
abbymath92: Oh! Unless you mean the 2D scalar line integrals...you won't have a question framed that way, that was just an illustration to help understand a geometric application
TiNgYbLiNgY: oh
TiNgYbLiNgY: ok
Gil OnTop A Hill: mrs. brown just wanted to know y u worte PS rabbit rabbit rabbit in the email
TiNgYbLiNgY: yea it was in the first few pages of the notes
TiNgYbLiNgY: ?
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abbymath92: ting ting
TiNgYbLiNgY: yea
abbymath92: I may have just been comparing the process of integration
TiNgYbLiNgY: oh
TiNgYbLiNgY: but i wont need to remember that
TiNgYbLiNgY: right?
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abbymath92: don't worry about it
GuardianAngelNK: i have a question on page 1103 problem number 5
GuardianAngelNK: what are we supposed to use for G?
GuardianAngelNK: and the limites
GuardianAngelNK: limits*
abbymath92: you're just integrating over the xy-plane
abbymath92: set z = blah for g(x,y)
abbymath92: and the x limits are [0,3]
abbymath92: and the y limits are [0,2]
abbymath92: it's just an odd notation
GuardianAngelNK: ok so we just take the integral of ( 1+ 2x + 3y)
GuardianAngelNK: i mean
GuardianAngelNK: gradiant
abbymath92: no: do G(x,y,z) = z - g(x,y) first
GuardianAngelNK: so z- ( 1+ 2x + 3y)
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abbymath92: yeah
GuardianAngelNK: ok thank you
freezerburn99: question, for our purposes to determine conservativde or no we just need to do del P/del y=Del Q/del x
TiNgYbLiNgY: bah i give up, i'm just going to reread the notes and sleep
GuardianAngelNK: if it's 2D
TiNgYbLiNgY: bye
GuardianAngelNK: if 3D we need curl
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freezerburn99: ya thats what i mean
x slr 600 x: will we have to solve anything step by step like the divergence theorem example in the notes?
freezerburn99: i was just wondering if we needed to fo the vector F= gradient of potential function
freezerburn99: for*
abbymath92: well, the divergence thm stuff is different than the F = del f stuff
abbymath92: but either is fair game
GuardianAngelNK: i think what she means is when you do it the long way
GuardianAngelNK: like on page 23 of the notes
freezerburn99: uhuh
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freezerburn99: i thpought for buidling the potential function you found what was common between the two functions
GuardianAngelNK: you do
freezerburn99: and added a + c
GuardianAngelNK: mhm
abbymath92: the +C depends on what you're looking for
abbymath92: if you are asked for the potential function, put +C
freezerburn99: but on pg4 it uises waht is common and adds the parts that arent
freezerburn99: then slaps the c
abbymath92: but we don't bother with the +C if we're doing the fundamental thm
abbymath92: since when we subtract the +C's would just cancel out
freezerburn99: is no one here?
freezerburn99: heh
abbymath92: just quiet tonight
freezerburn99: to say the least
Gil OnTop A Hill: in which situations does it matter if g-z or z-g
GuardianAngelNK: for number 13 on page 1103 what does G equal?
tutwabee: it depends on what terms you put G in... x,y or y,z or x,z
abbymath92: z = Sqrt[4 - x^2 - y^2]
GuardianAngelNK: ok
Gil OnTop A Hill: j?
GuardianAngelNK: so x^2 +y^3 +z^2 - Sqrt[4 - x^2 - y^2]
GuardianAngelNK: and gradiant of that?
tutwabee: no
GuardianAngelNK: oh
GuardianAngelNK: what is it then?
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tutwabee: i think it's Sqrt[4 - x^2 - y^2] - z
GuardianAngelNK: not z- that?
tutwabee: it might be z - that
GuardianAngelNK: which one lol
tutwabee: i didn't check that just a sec.
tutwabee: ah it's z - that
tutwabee: you're right
GuardianAngelNK: ok thanks
Gil OnTop A Hill: in which situations does it matter if g-z or z-g
tutwabee: all?
GuardianAngelNK: haha
tutwabee: you need to make sure that the terms that need to be positive will be positive
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tutwabee: same with negative
abbymath92: sorry...
abbymath92: I'm kinda distracted...
abbymath92: the G(x.y,z) = z - Sqrt[4-x^2-y^2]
abbymath92: then you need the gradient of that
GuardianAngelNK: ya
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abbymath92: it looks ugly, but when you take the magnitude it simplifies some
GuardianAngelNK: that's good
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abbymath92: and then when you plug in for z in the integral it cancels with the ||delG||
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iamgodot1187: h/o
Gil OnTop A Hill: mrs brown/
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abbymath92: yes?
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Gil OnTop A Hill: n which situations does it matter if g-z or z-g
yangchazz: wheres brown
abbymath92: most of the time it is z - g so that the vector points up
yangchazz: oh
abbymath92: if you want the vector to point down, use g - z
abbymath92: up = positive orientation
abbymath92: unless it is a closed surface and you are working with one of the lower surfaces
abbymath92: positive orientation = outward
abbymath92: in that case
Diablo2Buu: hey
Diablo2Buu: oops
Diablo2Buu: nvm
Gil OnTop A Hill: so if we want the inward flux it negative orientation
Gil OnTop A Hill: ?
abbymath92: that's one way to look at it, but when we measure flux, we consider outward (or upward) to be positive
Gil OnTop A Hill: ok
Gil OnTop A Hill: i think i kind off get now
Gil OnTop A Hill: wiht the inward and out ward, it helped me
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GuardianAngelNK: can you help me with number 14 on page 1104
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abbymath92: where are you stuck?
GuardianAngelNK: how to interpret how to use the surface and the z=
GuardianAngelNK: like which parts refer to which parts in teh problem
Gil OnTop A Hill: thank u mrs. brown, now i finally got the problems, YYYYYYYEEESS!
GuardianAngelNK: specifically in G, and in substituting back in for xyz
abbymath92: G comes from the surface
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GuardianAngelNK: ok
abbymath92: in this case G = z - g
abbymath92: where z = g(x,y) .... the cone in this problem
GuardianAngelNK: oh
abbymath92: oops!!!
abbymath92: no!!
GuardianAngelNK: ya
abbymath92: I was reading it wrong....sorry
GuardianAngelNK: it's the part of the sphere
GuardianAngelNK: right?
abbymath92: the sphere is the surface
GuardianAngelNK: ok and find what z=
abbymath92: yes...this one is easiest in parametric form
GuardianAngelNK: then do z minues that
abbymath92: the cone just helps us find the limits
GuardianAngelNK: oh
GuardianAngelNK: ok so how do we use the cone to find limits?
abbymath92: use x = rho*sin phi * cos theta
abbymath92: etc
abbymath92: but use rho = 1 since that's the radius of the sphere
GuardianAngelNK: hmm
abbymath92: and then call phi = u and theta = v
abbymath92: and then do the ru x rv stuff
GuardianAngelNK: uh i'm not sure how to do that
GuardianAngelNK: can i see the work for this on the white board?
abbymath92: I don't have the whiteboard set up tonight
abbymath92: I can do it w/ type
GuardianAngelNK: ok
abbymath92: x = 1 sin u cos v
abbymath92: y = 1 sin u sin v
abbymath92: z = 1 cos u
abbymath92: do you see where those come from?
GuardianAngelNK: no
abbymath92: it's from the conversion to spherical coordinates
abbymath92: x = p (sin phi)(cos theta)
GuardianAngelNK: ah ok
abbymath92: (I can't do the greek letters)
GuardianAngelNK: ya
GuardianAngelNK: and what about for z?
abbymath92: since we're on the surface of the sphere, rho ("p") is always = 1
GuardianAngelNK: mhm
abbymath92: so then I just set up u to act like phi (the angle measured from the z-axis) and v to act like theta
GuardianAngelNK: mhm
GuardianAngelNK: what about for z=
abbymath92: since we're going all the way around the v limits will be (the theta limits will be) 0 to 2 Pi
abbymath92: I'll get to that
GuardianAngelNK: ok
abbymath92: for the v limits (the phi limits) you have to figure out what the angle is for the where the cone and the sphere intersect
abbymath92: like we did in chapter 15
abbymath92: it's a "snowcone" problem
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GuardianAngelNK: and how do we do that?
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abbymath92: the sphere is z = Sqrt[1-x^2-y^2] and the cone is z = Sqrt[x^2+y^2]
abbymath92: set them equal to each other and simplify
GuardianAngelNK: ok
GuardianAngelNK: and solve for each variable
abbymath92: you'll get x^2 + y^2 = something that will tell you the radius of the circle of intersection
GuardianAngelNK: oh ok
abbymath92: then you can set up a triangle
GuardianAngelNK: which leg will this be?
abbymath92: the hypotenuse is 1 (the radius of the sphere) and the legs are the radius of that circle and z (the height where they intersect...but you don't even need to find that)
GuardianAngelNK: oh
GuardianAngelNK: well ya two sides will be ok
abbymath92: to get phi, you'll do arcsin of the radius over the hypotenuse
GuardianAngelNK: mm
abbymath92: draw the triangle with one leg along the y-axis, the hyp extending into the yz-plane and then the radius for that circle of intersection coming out of the z-axis parallel to the y-axis
GuardianAngelNK: i seriously doubt i could follow all of this for the test tomorow
GuardianAngelNK: i understand the basic process
GuardianAngelNK: but it seems complications like this catch me up
abbymath92: that's part of the challenge of this chapter
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abbymath92: you have to be able to apply skills from earlier work
freezerburn99: ya i undestand iut all but i lose formulas sometimes heh
abbymath92: okay...now that we know what the surface is
abbymath92: we have to set up for converting dS to dA
abbymath92: this one is easier in parametric form
GuardianAngelNK: ok
abbymath92: so r(u,v) = < 1 sin u cos v, 1 sin u sin v, 1 cos u > from before
yangchazz: wheres the answers for larson ws
abbymath92: brb ...phone
freezerburn99: so to clerify ds is line integrals and dS is surfaces
freezerburn99: whats ds
freezerburn99: imean dr
yangchazz: line integrals
GuardianAngelNK: depends if it is vector or scalar
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yangchazz: how do u know what limits of integration to use for stokes thm?
GuardianAngelNK: same for any double integral
yangchazz: ugh
GuardianAngelNK: exactly
yangchazz: wanna fight?
GuardianAngelNK: lol
GuardianAngelNK: gluck
GuardianAngelNK: don't make miss brown have to edit this again charles
GuardianAngelNK: lol
yangchazz: rofflecopter!!!!!!!!
yangchazz: lollerskates!!!!!!!!
yangchazz: lmaonade!!!!!!!!111111one.
yangchazz: you are quite the comedian short!!!
GuardianAngelNK: sanks!
abbymath92: I'm sorry
abbymath92: I have to go now
abbymath92: I will try to get to school super early tomorrow (like 6:30)
GuardianAngelNK: tahnk you for the help
GuardianAngelNK: thank*
abbymath92: sure
Diablo2Buu: oooooooh
Diablo2Buu: i might be there if i can get up -_-