- #1
JustAChemist
- 5
- 0
I appologise in the lack of distinction between curly d's and infinitesimals! All derivatives are partial and anything outside of brackets is an infinitesimal.
also, I sincerely apologise for any dodgy terminology, but I am for the most part self taught (regarding calculus) :/
(also, 0 is my poor attempt to represent theta :P)
More my obsessive compulsiveness when it's really something I'm just supposed to remember, but here goes...
Express (dz/dx) in polar coordinates for some arbitrary z = z(r, 0)
the answer given by my book (Steiner - The Chemistry Maths Book):
(dz/dx) = (dz/dr)cos(0) - sin(theta)(1/r)(dz/d0)
dz = (dz/dr)dr + (dz/d0)d0
(dz/dx) = (dz/dr)(dr/dx) + (dz/d0)(d0/dx)
essentially, my problem is in evaluating (dr/dx) and (d0/dx) (0 is theta)
ATTEMPT AT EVALUATING (dr/dx)
x = r cos(0) => r = x/cos(0)
=> (dr/dx) = 1/cos(0)
which is... wrong :/. I've also tried so much more silly sh*t like implicit differentiation, and inverting dx/dr, always arriving at the same answer ):
ATTEMPT AT EVAUATING (d0/dx)
x = r cos(0) => 0 = arccos(x/r)
and I have no idea how to start evaluating that...
Any help anyone could give would be greatly appreciated! (:
EDIT:
I am an idiot... after 3 days of ploughing through with this and 10 minutes typing the problem to physicsforums, I just worked out that r can be represented in terms of x and y as sqrt(x^2 + y^2) and theta as arctan(y/x)... the rest writes itself lol :P
I hate my life. :P
also, I sincerely apologise for any dodgy terminology, but I am for the most part self taught (regarding calculus) :/
(also, 0 is my poor attempt to represent theta :P)
Homework Statement
More my obsessive compulsiveness when it's really something I'm just supposed to remember, but here goes...
Express (dz/dx) in polar coordinates for some arbitrary z = z(r, 0)
Homework Equations
the answer given by my book (Steiner - The Chemistry Maths Book):
(dz/dx) = (dz/dr)cos(0) - sin(theta)(1/r)(dz/d0)
The Attempt at a Solution
dz = (dz/dr)dr + (dz/d0)d0
(dz/dx) = (dz/dr)(dr/dx) + (dz/d0)(d0/dx)
essentially, my problem is in evaluating (dr/dx) and (d0/dx) (0 is theta)
ATTEMPT AT EVALUATING (dr/dx)
x = r cos(0) => r = x/cos(0)
=> (dr/dx) = 1/cos(0)
which is... wrong :/. I've also tried so much more silly sh*t like implicit differentiation, and inverting dx/dr, always arriving at the same answer ):
ATTEMPT AT EVAUATING (d0/dx)
x = r cos(0) => 0 = arccos(x/r)
and I have no idea how to start evaluating that...
Any help anyone could give would be greatly appreciated! (:
EDIT:
I am an idiot... after 3 days of ploughing through with this and 10 minutes typing the problem to physicsforums, I just worked out that r can be represented in terms of x and y as sqrt(x^2 + y^2) and theta as arctan(y/x)... the rest writes itself lol :P
I hate my life. :P
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