Complex analysis : the hitchhiker's guide to the plane

By: Stewart,IanContributor(s): Tall, DavidMaterial type: TextTextPublication details: New York : Cambridge University Press, 1983Edition: 1stDescription: viii, 290 pages : illustrationsISBN: 9780521287630 ; 0521287634 ; 9781108436793 ; 110843679XSubject(s): Functions of complex variablesDDC classification: 515.9
Contents:
Preface; Acknowledgement; 1. The origins of complex analysis and a modern viewpoint; 2. Algebra of the complex plane; 3. Topology of the complex plane; 4. Power series; 5. Differentiation; 6. The exponential function; 7. Integration; 8. Angles, logarithms and the winding number; 9. Cauchy's theorem; 10. Homotopy versions of Cauchy's theorem; 11. Taylor series; 12. Laurent series; 13. Residues; 14. Conformal transformations; 15. Analytic continuation; Index.
Summary: This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.
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Index

Preface; Acknowledgement; 1. The origins of complex analysis and a modern viewpoint; 2. Algebra of the complex plane; 3. Topology of the complex plane; 4. Power series; 5. Differentiation; 6. The exponential function; 7. Integration; 8. Angles, logarithms and the winding number; 9. Cauchy's theorem; 10. Homotopy versions of Cauchy's theorem; 11. Taylor series; 12. Laurent series; 13. Residues; 14. Conformal transformations; 15. Analytic continuation; Index.

This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.

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