Prove that is a function f is harmonic =0, then - dx -Ldy =0.
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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Question
![a). Prove that is a function f is harmonic-
= 0, then
Ldy =0.
af
b). Using Green's Theorem, evaluate the line integral feh -y dx+ e°% +y ]dy where C =C; +C;
is the boundary of the region R that is inside the circle x= 5cos0, y= 5sin0 and outside the eclipse
x= 2cos0, y=sin0.
c). Find
the
surface
area
in
the
accompanying
of
the
helicoid
r(r,0)=(rcos0)i+(rsin0) j + Ok, 0sos2a, Osrsl.
(1, 0, 2m)
(1, 0, 0),](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2d6f60d-e8d2-442d-bf9b-b55e3c7e22c8%2Fbff8c6bc-16b8-4c7c-bf7f-4f239d3cc91e%2Fyl115yn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a). Prove that is a function f is harmonic-
= 0, then
Ldy =0.
af
b). Using Green's Theorem, evaluate the line integral feh -y dx+ e°% +y ]dy where C =C; +C;
is the boundary of the region R that is inside the circle x= 5cos0, y= 5sin0 and outside the eclipse
x= 2cos0, y=sin0.
c). Find
the
surface
area
in
the
accompanying
of
the
helicoid
r(r,0)=(rcos0)i+(rsin0) j + Ok, 0sos2a, Osrsl.
(1, 0, 2m)
(1, 0, 0),
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