Transcription of An Introduction to Complex Analysis and Geometry
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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 Geometry of addition and multiplication538. Logarithms54 Chapter 3. Complex numbers and geometry591.
) substitution from calculus. During the course several students followed up this idea and tracked down how the inde nite integral of the secant function arose in navigation. This book is more formal than was the course itself. The list of approximately two hundred eighty exercises in the book is also considerably longer than the list of
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