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Complex integration of holomorphic functions along arbitrary continuous paths. Homotopy version of Cauchy's theorem.

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Elements of homology and homological version of Cauchy's theorem. Cauchy-Green's Formula and relation to Cauchy's Integral formula. Power series expansion of holomoprhic functions.

Cauchy-Hadamard formula. Theorem of Morera. Cauchy's estimates.

## An Introduction to Complex Analysis: Classical and Modern Approaches

Liouville's theorem. Application to the Fundamental Theorem of Algebra.

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Compact convergence and Weierstrass theorem. Order of zeroes.

The identity principle. Laurent series expansion in a ring.

Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

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## A Complex Analysis Problem Book - Daniel Alpay - Google книги

He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer Telecom Paris, graduated and mathematician PhD, Weizmann Institute, His research includes operator theory, stochastic analysis, and the theory of linear systems.

Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University.