. Determine the domain of analyticity for the following functions, and conclude that √ f(z)dz = O where C' is the circle || = 1 with positive orientation (counter-clockwise). (a) f(z) = 2+2 1 (b) f(z) = 22+2x+2 (c) f(z) = tanz (d) f(z) = Ln(z+5) Show that f¹dz = 2πi, where C' is the square with vertices 1±i, −1±i with positive orientation. - . Show that √(4z2 — 4z + 5)¯¹dz orientation. = O where C is the unit circle |z| = 1 with positive . Find So dz for the following contours: (a) The circle |z1| = 2 with positive orientation. - - (b) The circle |z1| = ½½ with positive orientation. Find fdz for the following contours: (a) The circle || = 2 with positive orientation. (b) The cirlce || = ½½ with positive orientation. . Evaluate fc 2212dz, where C' is the "figure-eight" contour shown. The "figure eight" contour C
. Determine the domain of analyticity for the following functions, and conclude that √ f(z)dz = O where C' is the circle || = 1 with positive orientation (counter-clockwise). (a) f(z) = 2+2 1 (b) f(z) = 22+2x+2 (c) f(z) = tanz (d) f(z) = Ln(z+5) Show that f¹dz = 2πi, where C' is the square with vertices 1±i, −1±i with positive orientation. - . Show that √(4z2 — 4z + 5)¯¹dz orientation. = O where C is the unit circle |z| = 1 with positive . Find So dz for the following contours: (a) The circle |z1| = 2 with positive orientation. - - (b) The circle |z1| = ½½ with positive orientation. Find fdz for the following contours: (a) The circle || = 2 with positive orientation. (b) The cirlce || = ½½ with positive orientation. . Evaluate fc 2212dz, where C' is the "figure-eight" contour shown. The "figure eight" contour C
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:. Determine the domain of analyticity for the following functions, and conclude that √ f(z)dz =
O where C' is the circle || = 1 with positive orientation (counter-clockwise).
(a) f(z) = 2+2
1
(b) f(z) = 22+2x+2
(c) f(z) = tanz
(d) f(z) = Ln(z+5)
Show that f¹dz = 2πi, where C' is the square with vertices 1±i, −1±i with positive
orientation.
-
. Show that √(4z2 — 4z + 5)¯¹dz
orientation.
=
O where C is the unit circle |z|
=
1 with positive
. Find So dz for the following contours:
(a) The circle |z1| = 2 with positive orientation.
-
-
(b) The circle |z1| = ½½ with positive orientation.
Find fdz for the following contours:
(a) The circle || = 2 with positive orientation.
(b) The cirlce || = ½½ with positive orientation.
. Evaluate fc 2212dz, where C' is the "figure-eight" contour shown.
The "figure eight" contour C
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