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This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors' approach are to use simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original edition, there are three new chapters: Chapter 15, on infinitesimals in real and complex analysis; Chapter 16, on homology versions of Cauchy's theorem and Cauchy's residue theorem, linking back to geometric intuition; and Chapter 17, outlines some more advanced directions in which complex analysis has developed, and continues to evolve into the future. With numerous worked examples and exercises, clear and direct proofs, and a view to the future of the subject, this is an invaluable companion for any modern complex analysis course.
Prerequisite (MATH2400 or MATH2401) + (MATH1052 or MATH1072) Recommended prerequisite. MATH2000 or MATH2001.
Preliminaries The lectures will be recorded via the University's 'Lecture Capture' (podcast) system. Remember that Lecture Capture is a useful revision tool but it is not a substitute for
Complex analysis forms a basis for not only advanced mathematical topics, including differential equations, number theory, operator theory and other 3000 and higher level courses, but also for special functions of mathematical and quantum physics.
PMTH433 Complex Analysis .