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An Introduction to Complex Analysis and Geometry

An Introduction to Complex Analysis and GeometryJohn P. D AngeloDept. of Mathematics, Univ. of Illinois, 1409 W. Green St., Urbana IL 2009 by John P. D AngeloContentsChapter 1. From the real numbers to the Complex numbers111. Introduction112. Number systems113. Inequalities and ordered fields164. The Complex numbers245. Alternative definitions ofC266. A glimpse at metric spaces30 Chapter 2. Complex numbers351. Complex conjugation352. Existence of square roots373. Limits394. Convergent infinite series415. Uniform convergence and consequences446. The unit circle and trigonometry507.

the complex exponential function to simplify trigonometry is a compelling aspect of elementary complex analysis and geometry. Students in my courses seemed to appreciate this material to a great extent. One of the most appealing combinations of the geometric series and the expo-nential series appears in Chapter 4.

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