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i. Let Cr be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo + r exp(it) where r > 0. Explain why ii. Show that f(z) f(z) | 1(2), dz = √ (²) dz. 2-20 2-20 - 20 dz - 2πif (zo) = √[ƒ(²) - ƒ (20) 20 dz.

i. Let Cr be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo + r exp(it) where r > 0. Explain why ii. Show that f(z) f(z) | 1(2), dz = √ (²) dz. 2-20 2-20 - 20 dz - 2πif (zo) = √[ƒ(²) - ƒ (20) 20 dz.

Advanced Engineering Mathematics
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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= i. Let CÃ be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo + r exp(it) where r > 0. Explain why ii. Show that f(z) C 2 - 20 So ƒ(z) Set - 20 dz f(z) Jaz - dz - 2πif (zo) = Sci Cr 20 dz. ƒ(z) — ƒ(zo) 2- 20 dz.
Transcribed Image Text:= i. Let CÃ be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo + r exp(it) where r > 0. Explain why ii. Show that f(z) C 2 - 20 So ƒ(z) Set - 20 dz f(z) Jaz - dz - 2πif (zo) = Sci Cr 20 dz. ƒ(z) — ƒ(zo) 2- 20 dz.
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