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A First Course in Complex Analysis
These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated ``from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.
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Digital editions
Complex Analysis · Residue Theorem · Second Order Ordinary Differential Equations in the Complex Plane · The Complex Logarithm · Complex Power Series · Complex Differentiation · Residue at an Isolated Singularity · Residue Theorem · Mathematics