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# Functions of a Complex Variable I MATH 5320

TTU

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This 2 page Class Notes was uploaded by Ms. Ally Koelpin on Thursday October 22, 2015. The Class Notes belongs to MATH 5320 at Texas Tech University taught by Kent Pearce in Fall. Since its upload, it has received 14 views. For similar materials see /class/226460/math-5320-texas-tech-university in Mathematics (M) at Texas Tech University.

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Date Created: 10/22/15

Final Exam Formulation Math 5320 The nal exam will consist of problems of the following types 1 Problems andor direct calculations illustrating the operationsarithmetic of C Similar to problem 1 or 2 on Exam 1 2 Veri cation of a topological property of a metric space a setA is open if condition XXX 7 a setA is closed if condition YYY 7 a point x is a limit point of a setA if condition ZZZ 7 a setK is compact if condition WWW etc Similar to problem 3 4 5 or 6 on Exam 1 3 Classi cation Problem which of the following sets are open closed bounded connected compact etc Similar to problem 8 on Exam 1 4 Find the radius of convergence of a power series Similar to problem 1 on Exam II 5 Construct a conformal map from one region G to anotherH Similar to problem 4 or 6 on Exam II TakeHome 6 Determine the image of a speci c region under a speci c Mobius transformation Similar to problem 5 on Exam II 7 Use the CauchyRiemann equations to 1 Verify a function is or is not analytic on a region 2 Verify a function is constant on a region Similar to problem 2 on Exam II 3 Construct a harmonic conjugate of a given harmonic function on a region Similar to problem 7 on Exam II TakeHome 8 Verify a complex functional identity Similar to problem 3 on Exam II 9 Evaluate line integrals 1 2 3 4 Using Theorem 19 for piecewise smooth paths of integration Using the Fundamental Theorem of Calculus for Line Integrals Using Cauchy s Integral Formula 0 and its corollaries Using Cauchy s Theorem 0 10 Apply Louisville s Theorem 11 Apply the Identity Theorem 12 Apply Cauchy s Estimate 13 Apply the corollaries to Theorem 28 14 State and prove certain theorems Problems representing Question Types 1 8 will constitute 40 of the exam Problems representing Question Types 9 14 will constitute 60 of the exam

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