From Real to Complex Analysis

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Calculus
Cover of the book From Real to Complex Analysis by R. H. Dyer, D. E. Edmunds, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: R. H. Dyer, D. E. Edmunds ISBN: 9783319062099
Publisher: Springer International Publishing Publication: May 14, 2014
Imprint: Springer Language: English
Author: R. H. Dyer, D. E. Edmunds
ISBN: 9783319062099
Publisher: Springer International Publishing
Publication: May 14, 2014
Imprint: Springer
Language: English

The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology.

Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon.

Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology.

Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon.

Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.

More books from Springer International Publishing

Cover of the book Strategic Thinking in a Hospital Setting by R. H. Dyer, D. E. Edmunds
Cover of the book Intelligent Tools for Building a Scientific Information Platform: From Research to Implementation by R. H. Dyer, D. E. Edmunds
Cover of the book Nanobiotechnology Applications in Plant Protection by R. H. Dyer, D. E. Edmunds
Cover of the book Dark Energy and the Formation of the Large Scale Structure of the Universe by R. H. Dyer, D. E. Edmunds
Cover of the book Exciton Transport Phenomena in GaAs Coupled Quantum Wells by R. H. Dyer, D. E. Edmunds
Cover of the book Developments in Environmental Regulation by R. H. Dyer, D. E. Edmunds
Cover of the book Patterns and Mechanisms of Climate, Paleoclimate and Paleoenvironmental Changes from Low-Latitude Regions by R. H. Dyer, D. E. Edmunds
Cover of the book Peripheral Ulcerative Keratitis by R. H. Dyer, D. E. Edmunds
Cover of the book Cloud Computing and Security by R. H. Dyer, D. E. Edmunds
Cover of the book Bank Funding, Financial Instruments and Decision-Making in the Banking Industry by R. H. Dyer, D. E. Edmunds
Cover of the book The Black Sea by R. H. Dyer, D. E. Edmunds
Cover of the book Multifunctional Land-Use Systems for Managing the Nexus of Environmental Resources by R. H. Dyer, D. E. Edmunds
Cover of the book Surface Flute Waves in Plasmas by R. H. Dyer, D. E. Edmunds
Cover of the book Counter-terrorism and the Prospects of Human Rights by R. H. Dyer, D. E. Edmunds
Cover of the book Artificial Life and Evolutionary Computation by R. H. Dyer, D. E. Edmunds
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy