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6. The Joukowski map is defined by w = f(x) = (²+²) Show that J maps the circle S = {|z| = ro} (ro > 0, ro #1) onto an ellipse+ the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z. = 1 and

6. The Joukowski map is defined by w = f(x) = (²+²) Show that J maps the circle S = {|z| = ro} (ro > 0, ro #1) onto an ellipse+ the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z. = 1 and

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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6. The Joukowski map is defined by w = f(2) = (2+ Show that J maps the circle S = {[2] = ro} (ro> 0, ro #1) onto an ellipse+ = 1 and the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z.
Transcribed Image Text:6. The Joukowski map is defined by w = f(2) = (2+ Show that J maps the circle S = {[2] = ro} (ro> 0, ro #1) onto an ellipse+ = 1 and the unit circle S = {|z| = 1} onto the real interval [-1,1]. Hint: use polar form of z.
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