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(5.3) Why is it not possible to apply Cauchy's integral formula to calculate fo f(z) dz, directly? (5.4) Calculate fc f(z) dz, by appropriately splitting fc f(z) dz into two integrals and applying Cauchy's integral formula to each of these (it needs to be clear from your solution that you are using Cauchy's integral formula and not Cauchy's residue theorem).

(5.3) Why is it not possible to apply Cauchy's integral formula to calculate fo f(z) dz, directly? (5.4) Calculate fc f(z) dz, by appropriately splitting fc f(z) dz into two integrals and applying Cauchy's integral formula to each of these (it needs to be clear from your solution that you are using Cauchy's integral formula and not Cauchy's residue theorem).

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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Please answer 5.3 and 5.4

Let f(z): = e2z+3 22-z-6 26 and let C be the positively oriented contour C = {z € C : |z − 1| = 5}. (5.1) Find and classify the isolated singular points of f and calculate the residues at these points. (5.2) Use Cauchy's residue theorem to calculate fo f(z) dz. (5.3) Why is it not possible to apply Cauchy's integral formula to calculate fo f(z) dz, directly? (5.4) Calculate fc f(z) dz, by appropriately splitting fc f(z) dz into two integrals and applying Cauchy's integral formula to each of these (it needs to be clear from your solution that you are using Cauchy's integral formula and not Cauchy's residue theorem).
Transcribed Image Text:Let f(z): = e2z+3 22-z-6 26 and let C be the positively oriented contour C = {z € C : |z − 1| = 5}. (5.1) Find and classify the isolated singular points of f and calculate the residues at these points. (5.2) Use Cauchy's residue theorem to calculate fo f(z) dz. (5.3) Why is it not possible to apply Cauchy's integral formula to calculate fo f(z) dz, directly? (5.4) Calculate fc f(z) dz, by appropriately splitting fc f(z) dz into two integrals and applying Cauchy's integral formula to each of these (it needs to be clear from your solution that you are using Cauchy's integral formula and not Cauchy's residue theorem).
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