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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.

1. Complex-valued functions 107 2. Line integrals 109 3. Goursat’s proof 116 4. The Cauchy integral formula 119 5. A return to the de nition of complex analytic function 124 Chapter 7. Applications of complex integration 127 1. Singularities and residues 127 2. Evaluating real integrals using complex variables methods 129 3. Fourier ...

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