This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves. Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool.
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Complex analysis is an active research subject in itself, but, even more, it provides the foundation for broad areas of mathematics, and plays an important role in the applications of mathematics to engineering. This book is intended to provide a classical introduction to complex analysis for university students in the sciences and engineering. It is based on lectures for third-year students given by the author at the Tokyo Institute of Technology.
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