380_checklist_1_Sp10[1] - & su cient conditions for f (...

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Math 380 Spring 2010 Midterm Exam Checklist Date of Exam: Friday, March 12, 2010 What to bring: Pencil, eraser, calculuator (not really needed). The exam will be closed book and closed notes. Complex Arithmetic mulitplication, addition, division, complex conjugation real and imaginary parts, modulus, and polar form of a complex number geometric view of complex addition, subtraction, multiplication, and division ±nding nth roots of a complex number De±nitions for planar sets: interior point, boundary point, path-connected set, open set, closed set, domain the complex derivative f 0 ( z ) f is analytic at z 0 f is di/erentiable in the complex sense at z 0 harmonic function harmonic conjugate of a harmonic function a zero or pole of order m of a rational function e z ; sin z , cos z , arg ( z ) ; Arg ( z ) , log ( z ) , Log ( z ) Be able to state precisely: general necessary conditions for f 0 ( z 0 ) to exist
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Unformatted text preview: & su cient conditions for f ( z ) to exist & su cient conditions for f to be constant & the Fundamental Theorem of Algebra & For a given function f = u + iv , be able to & determine where f ( z ) exists and where f is analytic & compute f ( z ) in terms of the partial derivatives of u and v & For a real valued function u on a domain be able to & determine if u is harmonic & nd a harmonic conjugate for u in the case that u is harmonic & For the basic analytic functions built from e z , sin z , cos z , Log ( z ) ; z n (where n is an integer) & evaluate at specic values of z & di/erentiate & nd the image of a simple set under the specied function & determine if the function is one-to-one on a given domain & Find all values of arg z; log z , z a for a given value of z: 1...
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This note was uploaded on 09/16/2011 for the course MATH 380 taught by Professor Staff during the Spring '11 term at S.F. State.

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