:// xydrdy Am = A00 %3D 0 0 3= The value of Am0 is, 1 1 Amo = 2 ху cos mлxdxady 0 0 cos mл — 1 , -ydy = 2 m² n² (-1)" –1 %3D m² n²

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I don't understand the value of A00 and Amo.Can you please explain it to me. Thank you.

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00
u (x, y, t) = A00 +
E Amo e
-km² n²t
E Aone
e-kn²n²t
cos nny
cos MTX +
%3D
n=1
n=1
(13)
00 00
cos MTX cos nty
m=1 n=1
At boundary conditions = 0, - = 0,
ди
ди
ди
ди
= 0,
—D 0 and u (х, у, 0) — ху,
dx Ix=0
dy ly=0
dy ly=1
The value of A00 is,
1
1
!!
4
A00
хуахdy
72
0 0
The value of Am0 is,
Amo
ху сos mлxdxdy
= 2
0 0
1
1
-ydy
cos MT
= 2
m2 n2
(-1)" –1
m2 n2
The value of Aon is,
1
1
!!
Aon = 2
ху сos плуdxdy
0 0
(-1)"–1
n² n2
Th.
X GET 10 FREE QUESTIONS
Amn = 4
ху сos mлx sin плуdхdy
Transcribed Image Text:6:25 PM Sun Apr 25 80% AA bartleby.com G Patterns Loop-it Puff... Patterns fro... G jaya amitabh... Problems 1 a... Facebook - L... = bartleby Q Search for textbooks, step-by-step explanatio... Ask an Expert Math / Bundle: Differential Equations with Boundary-Value Proble... / In Problems 1 and 2 solve the heat equation (1) subj... : In Problems 1 and 2 solve the heat equation (1) subject to the given conditions. 2. d u... Get live help whenever you need from online tutors! Try bartleby tutor today > 00 00 u (x, y, t) = A00 + E Amo e -km² n²t E Aone e-kn²n²t cos nny cos MTX + %3D n=1 n=1 (13) 00 00 cos MTX cos nty m=1 n=1 At boundary conditions = 0, - = 0, ди ди ди ди = 0, —D 0 and u (х, у, 0) — ху, dx Ix=0 dy ly=0 dy ly=1 The value of A00 is, 1 1 !! 4 A00 хуахdy 72 0 0 The value of Am0 is, Amo ху сos mлxdxdy = 2 0 0 1 1 -ydy cos MT = 2 m2 n2 (-1)" –1 m2 n2 The value of Aon is, 1 1 !! Aon = 2 ху сos плуdxdy 0 0 (-1)"–1 n² n2 Th. X GET 10 FREE QUESTIONS Amn = 4 ху сos mлx sin плуdхdy
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