Donald E. Marshall

Complex Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intuition necessary to understand this important area of mathematics.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 7. März 2019
• Englisch
• ISBN-13: 9781108651851
• Artikelnr.: 57076931

Autorenporträt

Donald E. Marshall is Professor of Mathematics at the University of Washington. He received his Ph.D. from University of California, Los Angeles in 1976. Professor Marshall is a leading complex analyst with a very strong research record that has been continuously funded throughout his career. He has given invited lectures in over a dozen countries. He is coauthor of the research-level monograph Harmonic Measure (Cambridge, 2005).

Inhaltsangabe

Preface
Prerequisites
Part I: 1. Preliminaries
2. Analytic functions
3. The maximum principle
4. Integration and approximation
5. Cauchy's theorem
6. Elementary maps
Part II: 7. Harmonic functions
8. Conformal maps and harmonic functions
9. Calculus of residues
10. Normal families
11. Series and products
Part III: 12. Conformal maps to Jordan regions
13. The Dirichlet problem
14. Riemann surfaces
15. The uniformization theorem
16. Meromorphic functions on a Riemann surface
Appendix
Bibliography
Index.