Titlebook: Complex Analysis; John M. Howie Textbook 2003 Springer-Verlag London 2003 Analysis.Complex analysis.Complex numbers.Functions of a complex

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Laurent Series and the Residue Theorem,In Section 3.5 we looked briefly at functions with isolated singularities. It is clear that a function . with an isolated singularity at a point . cannot have a Taylor series centred on .. What it does have is a . series, a generalized version of a Taylor series in which there are negative as well as positive powers of . — ..

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Applications of Contour Integration,One of the very attractive features of complex analysis is that it can provide elegant and easy proofs of results in real analysis. Let us look again at Example 8.16.

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Further Topics,In this section we examine an integral that in effect counts the number of poles and zeros of a meromorphic function .. Recall that, if . has Laurent series . at ., then ord(.) = min {.: . ≠ 0}. If ord(.) = . > 0 then .(.) = 0, and we say that c is a . . of the function .. If ord(.) = -. < 0, then . is a . ..

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John M. HowieSuitable for both pure and applied mathematicians.Takes account of readers‘ varying needs and backgrounds by presenting ideas through worked examples and informal explanations rather than through "dry

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What Do I Need to Know?,already. Ideally one would like to assume that the student has some basic knowledge of complex numbers and has experienced a fairly substantial first course in real analysis. But while the first of these requirements is realistic the second is not, for in many courses with an “applied” emphasis a co