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Math 656 Complex Variables I - Information Services and ...

Math 656 Complex Variables IProf Cummings February 2, 2010 Contents1 Introduction to the Complex numbers .. Exponential representation of Complex numbers .. Algebra of Complex numbers .. Complex conjugates and inequalities .. Solving simple Complex equations ..92 Subsets of the Complex Introduction: Simple subsets of the Complex plane .. Elementary definitions .. Stereographic projection .. Paths in the Complex plane .. Paths and connectedness ..203 Analytic functions: The Complex sequences, series, and functions .. Limits and continuity of functions .. Differentiability of Complex functions .. The Cauchy-Riemann theorem .. Harmonic functions .. Multivalued functions .. General non-integer powers ..41 Department of Mathematical Sciences, Logarithms .. Contours and multivaluedness .. Branch cuts to ensure single-valuedness .. Composite multifunctions.

Math 656 Complex Variables I ... Book: M.J. Ablowitz & A.S. Fokas. Complex variables: Introduction and Applications (2nd edition). Cambridge University Press (2003). 1 Introduction to the course ... Two complex numbers are equal if and only if both their real and imaginary

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  Applications, Variable, Complex, And applications, Complex variables

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