Problem 1 Find formulae for gradients of functions f of x and y in terms of coordinates u and v given by Х (и, v) — Зи — 40, Y(и, 0) — 4u + З0. - Find A and B so that ▼ƒ fe Te dx dy A · e + B · e, with the orthonormal basis vectors eu and ev: %3D 1 ax əy] 1 [ax əy e e : du' du dv' dv dv

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 1 Find formulae for gradients of functions f of x and y in terms of coordinates u and v given by
X(и, v) —
Зи - 40,
Y (u,
Ү(и, v) — 4u + 30.
Find A and B so that Vf = , o
af af
A · e! + B · e, with the orthonormal basis vectors eu
and ev:
[ax əy"
ди ди
1
1
e :
:=
ƏY
Jv' dv
du ' du
dv ' dv
Transcribed Image Text:Problem 1 Find formulae for gradients of functions f of x and y in terms of coordinates u and v given by X(и, v) — Зи - 40, Y (u, Ү(и, v) — 4u + 30. Find A and B so that Vf = , o af af A · e! + B · e, with the orthonormal basis vectors eu and ev: [ax əy" ди ди 1 1 e : := ƏY Jv' dv du ' du dv ' dv
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