Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
APM346-2016F
»
APM346--Lectures
»
Chapter 8
»
HA9, Problem6
« previous
next »
Print
Pages: [
1
]
Author
Topic: HA9, Problem6 (Read 1856 times)
Shentao YANG
Full Member
Posts: 24
Karma: 0
HA9, Problem6
«
on:
November 13, 2016, 01:20:23 PM »
Can any explain in detail the reason behind the hint "solution must be a harmonic polynomial of degree $3$ and it should depend only on $x^2+y^2+z^2$ and $z$"?
Concretely, there are $3$ question need to be addressed:
$(1)$ Why the solution need to be a harmonic polynomial?
$(2)$ Why it should have degree $3$?
$(3)$ Why it should depend only on $x^2+y^2+z^2$ and $z$ but not the other terms?
The solution from the previous year basically made no reasonable explanation and just copied words from the textbook
http://forum.math.toronto.edu/index.php?topic=731.0
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
Re: HA9, Problem6
«
Reply #1 on:
November 15, 2016, 07:06:04 AM »
Consider it as a Hint. We have not finished harmonic polynomials on the lecture.
Also, since problem depends only on $x^2+y^2$ and $z$ (is invariant with respect to rotations around $z$ axis), so does the solution
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
APM346-2016F
»
APM346--Lectures
»
Chapter 8
»
HA9, Problem6