2. Let's think a bit about symmetry. We've seen even and odd symmetry in our first discussion-what about some others? (a) Consider the square of side length 2 with the center fixed above the origin (0,0) E R2 and with sides parallel to the axes. (i) Write a double integral that computes the area using rectangular coordinates. (ii) Write a double integral that computes the area using polar coordinates. Would you rather calculate this one, or the rectangular one? (iii) What symmetries does the square have?
2. Let's think a bit about symmetry. We've seen even and odd symmetry in our first discussion-what about some others? (a) Consider the square of side length 2 with the center fixed above the origin (0,0) E R2 and with sides parallel to the axes. (i) Write a double integral that computes the area using rectangular coordinates. (ii) Write a double integral that computes the area using polar coordinates. Would you rather calculate this one, or the rectangular one? (iii) What symmetries does the square have?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Let's think a bit about symmetry. We've seen even and odd symmetry in our first discussion-what about
some others?
(a) Consider the square of side length 2 with the center fixed above the origin (0,0) E R² and with sides
parallel to the axes.
(i) Write a double integral that computes the area using rectangular coordinates.
(ii) Write a double integral that computes the area using polar coordinates. Would you rather
calculate this one, or the rectangular one?
(iii) What symmetries does the square have?
(iv) Suppose we had a function z = f(x, y) with the property f(x, y) = f(y, x) (as an example: the
function f(x, y) = sin|x – yl). What symmetry does this function have, and does the square
also have this symmetry?
(v) Using question (iv) and the below integral, compute the integral of f over the square:
f(z, y) dydz = "
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