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

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Chapter2: Second-order Linear Odes
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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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