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Complex analysis

By: Marshall, Donald E.
Material type: materialTypeLabelBookSeries: Cambridge mathematical textbooks. Publisher: New Delhi Cambridge University Press 2019Description: 272 p. Includes index.ISBN: 9781107134829.Subject(s): Mathematical analysis | Functions - complex variables | Complex analysis | Zipper algorithmDDC classification: 515.9 Summary: 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. Includes over 200 exercises, set at varying levels of difficulty to engage and motivate the reader Illustrates analytical functions with color figures to grant a high level of detail and accessibility Provides complete and detailed proofs and ties the subject with several other areas to give readers a comprehensive understanding of complex analysis and its applications https://www.cambridge.org/gb/academic/subjects/mathematics/real-and-complex-analysis/complex-analysis-4?format=HB
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Slot 1382 (0 Floor, East Wing) Non-fiction 515.9 M2C6 (Browse shelf) Available 200148

Table of Contents
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.

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.

Includes over 200 exercises, set at varying levels of difficulty to engage and motivate the reader
Illustrates analytical functions with color figures to grant a high level of detail and accessibility
Provides complete and detailed proofs and ties the subject with several other areas to give readers a comprehensive understanding of complex analysis and its applications

https://www.cambridge.org/gb/academic/subjects/mathematics/real-and-complex-analysis/complex-analysis-4?format=HB

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