491 reputation
414
bio website amerhesson.com
location Toronto, Canada
age
visits member for 1 year, 5 months
seen 5 hours ago

Engineering student at University of Toronto.


Mar
28
awarded  Notable Question
Feb
25
awarded  Popular Question
Feb
9
awarded  Citizen Patrol
Jan
14
asked Is the Fourier series also a Laurent series?
Dec
21
accepted Normal vector for a surface: explicit vs implicit formula
Dec
21
comment Normal vector for a surface: explicit vs implicit formula
Thanks, that makes sense, I thought the normal they used was weird because the z-component was always 1, and that's not true for a hemisphere, but if you warp it into a planar disk then it makes sense. I looked at the way they derived the formula and I understand it now because they changed the area element - thanks again!
Dec
20
comment Normal vector for a surface: explicit vs implicit formula
I posted the original problem - they get $8\pi$ using the line integral, and then they get the same answer using the surface integral. It's still beyond me why it works for the normal vector that they used if it's not a unit vector. For the surface integral, the page is cut off, but they eliminate the term with the $sin$ function and the integrand becomes $2rdrd\theta$ - the integration also gives $8\pi$. Using the other normal vector, I get the dot product to be $y + z$ and I get the integral to be $16\pi / 3$ (wolfr.am/1bUdi6R).
Dec
20
revised Normal vector for a surface: explicit vs implicit formula
added 79 characters in body
Dec
20
comment Normal vector for a surface: explicit vs implicit formula
I posted a picture from the textbook so you can see how its used. The result that the textbook gets is $8\pi$ which agrees with the result from the line integral which can be calculated easily. Using the other form of the normal vector seems to yield a different result for me for the surface integral.
Dec
20
revised Normal vector for a surface: explicit vs implicit formula
added 75 characters in body
Dec
20
comment Normal vector for a surface: explicit vs implicit formula
But as I understand Stokes' theorem which relates a surface integral to the line integral of its boundary, the normal vector of the surface to integrate must be a unit vector, but the textbook used the normal vector derived from the explicit formula which is not a unit vector. So is the textbook wrong? When I use the other normal vector to do the surface integral, I'm off by a factor from the textbook's answer.
Dec
20
asked Normal vector for a surface: explicit vs implicit formula
Dec
12
awarded  Popular Question
Dec
11
accepted Discrepancy in counting the number of poles in complex function when refactoring
Dec
11
comment Discrepancy in counting the number of poles in complex function when refactoring
Thanks, but how did you conclude from the Laurent expansion that the order is 2? Edit: I figured it out - it's because the function becomes non-zero when you differentiate it twice.
Dec
11
asked Discrepancy in counting the number of poles in complex function when refactoring
Dec
11
comment Why is this result of the Cauchy-Goursat theorem true?
@Sanchez I can grasp the idea that the closed integral of a holomorphic function is $0$ because I can see from the graph how it is possible for the values to cancel out over a closed loop. But it's beyond me why it would be different for just a simple pole, I can't see why that is true by looking at a graph.
Dec
11
asked Why is this result of the Cauchy-Goursat theorem true?
Oct
28
awarded  Yearling
Sep
1
awarded  Favorite Question