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A concise course in complex analysis and Riemann surfaces

A concise course in complexanalysis and Riemann surfacesWilhelm SchlagContentsPrefacevChapter 1. Fromitoz: the basics of complex analysis11. The field of complex numbers12. Differentiability and conformality33. M obius transforms74. Integration125. Harmonic functions196. The winding number217. Problems24 Chapter 2. Fromzto the Riemann mapping theorem : some finer points of basiccomplex analysis271. The winding number version of cauchy s theorem272. Isolated singularities and residues293. Analytic continuation334. Convergence and normal families365. The Mittag-Leffler and Weierstrass theorems376. The Riemann mapping theorem417. Runge s theorem448.

4. Integration 12 5. Harmonic functions 19 6. The winding number 21 7. Problems 24 Chapter 2. From zto the Riemann mapping theorem: some finer points of basic complex analysis 27 1. The winding number version of Cauchy’s theorem 27 2. Isolated singularities and residues 29 3. Analytic continuation 33 4. Convergence and normal families 36 5.

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