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Complex analysis: An Invitation / Murali Rao.

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Chennai : World Scientifc India, 2022.Edition: 2nd edDescription: x, 414 p. : ill. ; 22 cmISBN:
  • 9781944659943
  • 1944659943
Uniform titles:
  • Complex analysis: An Invitation
Subject(s): DDC classification:
  • 23 515.9 RAO
Contents:
Preface Preface to Second Edition 1. Power Series 2. Holomorphic and Analytical Functions 3. Exponential Functions, Logarithm and Winding number 4. Basic Theory of Holomorphic Functions 5. Global Theory 6. Isolated Singularities 7. The Picard Theorems 8. Geometric Aspects and the Riemann Mapping Theorem 9. Meromorphic Functions and Runge's theorem 10. Representations of Meromorphic Functions 11. The Prime Number Theorem 12. Harmonic Functions 13. Subharmonic Functions 14. Various Applications 15. Jordan Regions 16. The District problem and Green's Function 17. Extending Riemann Maps to the Boundary 18. Caratheodory Convergence 19. Capacities 20. Loewner theory Biblography Glossary Index
Summary: “A particularly nice feature of this textbook is that throughout, the authors have sprinkled citations of expository pieces taken from the Monthly as well as from Mathematics Magazine , the Intelligencer , and even the Proceedings of the AMS . This is a great source for both students as well as their teachers. The book also is an excellent source of problems, close to 300 in total.” Mathematical Association of America "Parts of the new material in the last chapters appear here for the first time in a textbook, making this second edition even rather topical and particularly up-to-date. Each chapter contains many illustrating concrete examples and a large number of related exercises, most of which invite the ambitious reader to complement the material discussed in the text. Now as before, this unusual textbook in complex analysis has maintained its unique character, and the new material added in the second edition makes it even more special, interesting and valuable for further generations of students and teachers." Zentralblatt MATH Review of the First “… covers an unusually large amount of material in a relatively few pages, and does so in a way that provides an excellent survey of the results and techniques of function theory … the presentation often provides excellent insights into the subject.” Mathematical Reviews This volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.
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Item type Current library Collection Call number Status Date due Barcode
Text Books Text Books CUTN Central Library Sciences Non-fiction 515.9 RAO (Browse shelf(Opens below)) Available 48141

Preface
Preface to Second Edition 1. Power Series
2. Holomorphic and Analytical Functions
3. Exponential Functions, Logarithm and Winding number
4. Basic Theory of Holomorphic Functions
5. Global Theory
6. Isolated Singularities
7. The Picard Theorems
8. Geometric Aspects and the Riemann Mapping Theorem
9. Meromorphic Functions and Runge's theorem
10. Representations of Meromorphic Functions
11. The Prime Number Theorem
12. Harmonic Functions
13. Subharmonic Functions
14. Various Applications
15. Jordan Regions
16. The District problem and Green's Function
17. Extending Riemann Maps to the Boundary
18. Caratheodory Convergence
19. Capacities
20. Loewner theory
Biblography
Glossary
Index


“A particularly nice feature of this textbook is that throughout, the authors have sprinkled citations of expository pieces taken from the Monthly as well as from Mathematics Magazine , the Intelligencer , and even the Proceedings of the AMS . This is a great source for both students as well as their teachers. The book also is an excellent source of problems, close to 300 in total.” Mathematical Association of America "Parts of the new material in the last chapters appear here for the first time in a textbook, making this second edition even rather topical and particularly up-to-date. Each chapter contains many illustrating concrete examples and a large number of related exercises, most of which invite the ambitious reader to complement the material discussed in the text. Now as before, this unusual textbook in complex analysis has maintained its unique character, and the new material added in the second edition makes it even more special, interesting and valuable for further generations of students and teachers." Zentralblatt MATH Review of the First “… covers an unusually large amount of material in a relatively few pages, and does so in a way that provides an excellent survey of the results and techniques of function theory … the presentation often provides excellent insights into the subject.” Mathematical Reviews This volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.

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