coordinates, x, y, z, such that /(x, y, z.) = 0. Taking x as a function of y and z, the exact differential, dx, in terms of partial derivatives with respect to y and z is given by dv = dz. (a) In a similar fashion, write down the exact differential, dy in terms of partial derivatives with respect to x and z. (b) By making use of the answer in (a) and the expression of dr given above, show that (島) dr = dr+ (c) Argue how you would obtain the relation 1 based on the eouation shoun in (b)
coordinates, x, y, z, such that /(x, y, z.) = 0. Taking x as a function of y and z, the exact differential, dx, in terms of partial derivatives with respect to y and z is given by dv = dz. (a) In a similar fashion, write down the exact differential, dy in terms of partial derivatives with respect to x and z. (b) By making use of the answer in (a) and the expression of dr given above, show that (島) dr = dr+ (c) Argue how you would obtain the relation 1 based on the eouation shoun in (b)
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Transcribed Image Text:5. Suppose there exists a functional relationship among three independent
coordinates, x, y, z, such that f(x, y, z.) = 0. Taking x as a function of y and z, the
exact differential, dr, in terms of partial derivatives with respect to y and z
is given by de =|
dy +
de.
(a)
In a similar fashion, write down the exact differential, dy in terms of
partial derivatives with respect to x and z.
(b)
By making use of the answer in (a) and the expression of dr given above,
show that
dr =
dr+
(c)
Argue how you would obtain the relation
1
based on the
equation shown in (b).
(d)
Argue how you would obtain the relation
= 0 based
on the equation shown in (b).
(e)
Based on the relations in (a) to (d) above, show
=-1.
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