Cartesian and polar coordinates in the plane are related by: x = r cos 0, y = r sin 0 i) Let T(x, y) be the temperature at a point (x, y). Use the chain rule to ƏT express dr in terms of ƏT dx and ii) Now suppose that T(x, y) = f(x' + y') for a given function f of one variable. Show that: = &' + y°)f'(x³ + y³) ar ƏT Vx2 + y2 for some number k, which you should find.
Cartesian and polar coordinates in the plane are related by: x = r cos 0, y = r sin 0 i) Let T(x, y) be the temperature at a point (x, y). Use the chain rule to ƏT express dr in terms of ƏT dx and ii) Now suppose that T(x, y) = f(x' + y') for a given function f of one variable. Show that: = &' + y°)f'(x³ + y³) ar ƏT Vx2 + y2 for some number k, which you should find.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Cartesian and polar coordinates in the plane are related by:
x = r cos 0, y =r sin 0
i) Let T(x, y) be the temperature at a point (x, y).
Use the chain rule to express
ƏT
ar
ƏT
дх
T
in terms of
and
ду
ii) Now suppose that T(x, y) = f(x' + y') for a given function f of one variable.
Show that:
(x³ + y³)f'(x³ + y³)
= k-
ar
ƏT
|3D
Vx2 + y²
for some number k, which you should find.
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