Cambridge University Press Complex Analysis 110713482X Wei Zhi

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Product details:

• ISBN 10: 110713482X
• ISBN 13: 978-1107134829
  
• Author:  Donald E. Marshall
  

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.

Table contents:

1 – Preliminaries

2 – Analytic Functions

3 – The Maximum Principle

4 – Integration and Approximation

5 – Cauchy’s Theorem

6 – Elementary Maps

7 – Harmonic Functions

8 – Conformal Maps and Harmonic Functions

9 – Calculus of Residues

10 – Normal Families

11 – Series and Products

12 – Conformal Maps to Jordan Regions

13 – The Dirichlet Problem

14 – Riemann Surfaces

15 – The Uniformization Theorem

16 – Meromorphic Functions on a Riemann Surface

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