Consider the transformation T: x = 24 μ-32 v₁ 40 Fill in the blanks. A. Compute the Jacobian: a(x,y) J(U₁V) = C, B. The transformation is linear, which implies that I transforms lines into lines. Thus, it transforms the square S: -40 ≤ μ≤40, -40 ≤ v ≤40 into a Square T (S) with + (40,40) = ( + (-40, 40) = ( + (-40₁-40) = ( T (40₁-40) = ( 32 Y = 40μ + 24 40 v use integral [ris) x² + y² dA +२ the transformation T to evaluate the

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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за
Consider the transformation Tix=244 24-32 v₁
Fill in the blanks
A. Compute the Jacobian:
a(x,y)
x(u, v)
=
+ (40,40) = (
+ (-40,40) = (
(-40,-40) =
т
T (40₁-40) = (
C, use
B. The transformation is linear, which implies that I
transforms lines into lines. Thus, it transforms the
Square Si
S: -40 ≤ u≤40, -40 ≤ v≤ 40 into a
Square T(S) with
32
чомт
Y = 2400M² +24
integral [[T(S) x² + y² dA
40V
-)
the transformation T to evaluate the
Sh
Transcribed Image Text:за Consider the transformation Tix=244 24-32 v₁ Fill in the blanks A. Compute the Jacobian: a(x,y) x(u, v) = + (40,40) = ( + (-40,40) = ( (-40,-40) = т T (40₁-40) = ( C, use B. The transformation is linear, which implies that I transforms lines into lines. Thus, it transforms the Square Si S: -40 ≤ u≤40, -40 ≤ v≤ 40 into a Square T(S) with 32 чомт Y = 2400M² +24 integral [[T(S) x² + y² dA 40V -) the transformation T to evaluate the Sh
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