I need solution about exercise 6 but need Hint. Consider the Laurent decomposition at each Z k, and use Exercise 5. 5. Show that if y is a piecewise smooth closed curve in the complexplane, with trace r, and if zo ¢ T, then1dz = 0,:- zo)"n2 2. 6. Let y be a closed path in a domain D such that W(7,5) = 0 forall Ç¢ D. Suppose that f(z) is analytic on D except possibly at afinite number of isolated singularities 21,... , žm e D\T. Show that|f(e) dz = 2ri w(7, z4) Res[f, z4]-Hint. Consider the Laurent decomposition at each zk, and use Ex-ercise 5.

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6. Let y be a closed path in a domain D such that W(7, 5) = 0 for all Ç ¢ D. Suppose that f(2) is analytic on D except possibly at a finite number of isolated singularities z1,.….. , žm € D\r. Show that f(2) dz = 2ni W(%, za) Res[f, za]. Hint. Consider the Laurent decomposition at each z, and use Ex- ercise 5.

6. Let y be a closed path in a domain D such that W(7, 5) = 0 for all Ç ¢ D. Suppose that f(2) is analytic on D except possibly at a finite number of isolated singularities z1,.….. , žm € D\r. Show that f(2) dz = 2ni W(%, za) Res[f, za]. Hint. Consider the Laurent decomposition at each z, and use Ex- ercise 5.

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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