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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 12-5
2
2
,,
or
where
zz z
pfg qfg sfg
xyxy
pq fg fg fg fg sz pq sz
z
s
xy
∂∂∂
== == ==
′′ ′′
∂∂∂∂
=⋅= ⋅= =
′′′′
=
∂∂
(12.21)
(c)
Formation of PDE b
y elimination of arbitrary
function of the form F ( u, v) = 0
Consider a relation between x, y and z of the type
F ( u, v) = 0 (12.22)
where u and v are known functions of x, y and z;
and F is an arbitrary function of u and v. Also, z is a
function of x and y.
Differentiating (12.22) by chain rule, with
respect to x and y we obtain
0
Fu u Fv v
pp
ux z vx z
∂∂∂ ∂∂∂
⎛⎞⎛⎞
++ +=
⎜⎟⎜⎟
⎝⎠⎝⎠
∂∂ ∂∂∂
(12.23)
0
Fu u Fv v
qq
uy z vy z
⎛⎞⎛⎞
∂∂∂ ∂∂∂
++ +=
⎜⎟⎜⎟
∂∂
∂∂
(12.24)
Eliminating F between (12.23) and ...
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Publisher Resources

ISBN: 9781299446557Publisher Website