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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Partial Differential Equations 12-37
displacement but with an initial velocity given at x
by g ( x). The boundary value problem for the dis-
placement function is
22
2
22
for 0 , 0
yy
axlt
tx
∂∂
=≤≤>
∂∂
(12.126)
(
0,
)
0
(
,
)
for 0
y
t
y
lt t== >
(12.127, 12.128)
zero initial
displacement:
(,0) 0
for 0
(,0) ()
yx
xl
y
xyx
t
=
≤≤
=
prescribed
initial v
elocity: (12.129, 12.130)
By the method of separation of variables w
e set
y (x, t) = x (t) T (t) and obtain ordinary differential
equations
222
0 and 0XX TaT+= + =
′′ ′′
ll
(12.131, 12.132)
The boundar
y conditions are same as before and
hence w
e obtain eigen
v
alues
22
2
2
n
n
l
=
p
l
(12.133)
and the corresponding eigenfunctions ...
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Publisher Resources

ISBN: 9781299446557Publisher Website