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Question

f{xy), x = X(s, t), y = Y(s, t), then u is a function of s, t, call it

(a) Write ᎧF

/Ꭷs and ᎧF /ot in terms of of / oa, ò f / òy, ᏭX / os, OX / Ꭷt, ᎧY / Os, and

_ᎧY ] ᎾᎿ

(b) Suppose that ƒ/(əxəy) = 0²ƒ/(Əyər), show that

7. (1pt) Let u

u = F ( 85 k ) .

ᎧᎵ - fᎧ · (

=

.

Ꮎx ds2

4 ( Ꭹ ) .

Os

ᎧX Ꭷ Ꭷ f

of Ꮽ-Y

0s Ꮽs oroy " òy ( ) *

+

- f ( ᎧY

0s , dy? მა

+2-

Fig: 1