FinalTopicsGuide

# FinalTopicsGuide - (a Taylor series = Holomorphic...

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Math 375 Final Topics Guide Chapters 1-4: see Midterm Topics Guide; about 30% Chapter 5: Cauchy’s Formula (a) Cauchy’s Integral Formula for derivatives (b) FTCs (c) Morera’s Theorem Chapter 6: Harmonic Functions (a) deﬁnition (b) relation to holomorphic (c) Mean-Value Theorem (d) Maximum/Minimum Principle Chapter 7: Power Series (a) Sequences, series, power series (b) Convergence: pointwise vs. uniform; absolute; tests (root, ratio, etc) (c) regions of convergence/radii of convergence for power series Chapter 8: Taylor Series
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Unformatted text preview: (a) Taylor series = Holomorphic function (uniquely) (b) coeﬃcients in terms of an integral (c) Classiﬁcation of Zeros (d) Identity Principle and Max-Modulus Theorem (e) harmonic series; exp, sin, cos, geometric power series Chapter 9: (and some of Ch. 8) Laurent Series and Singularities (a) double series (b) Singularities: isolated; classiﬁcation into removable, pole, essential (c) singluarities in terms of power series (d) Residues (e) the Argument Principle (f) Rouche’s Theorem 1...
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