This book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. Its aim is to provide a gentle yet rigorous first course on complex analysis. Metric space aspects of the complex plane are discussed in detail, making this text an excellent introduction to metric space theory. The complex exponential and trigonometric functions are defined from first principles and great care is taken to derive their familiar properties. In particular, the appearance of π, in this context, is carefully explained. The central results of the subject, such as Cauchy's Theorem and its immediate corollaries, as well as the theory of singularities and the Residue Theorem are carefully treated while avoiding overly complicated generality. Throughout, the theory is illustrated by examples. A number of relevant results from real analysis are collected, complete with proofs, in an appendix. The approach in this book attempts to soften the impact for the student who may feel less than completely comfortable with the logical but often overly concise presentation of mathematical analysis elsewhere.
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"Good bibliography; adequate index."Choice
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This review is from: Lecture Notes on Complex Analysis (Paperback)
This is a great book on complex analysis . It is mathematically wellmotivated. So every step is taken for a given reason. The steps do not drop from thin air. It covers a lot of material in a compact and understandable form and yet is is only 238 pages long. The book has some surprises I have never seen anywhere. For instance on page page 11 the author after saying " now watch closely", proceeds to show , without no obvious flaws that 1=-1 ! This is carefully explained latter on page 103 immediately after showing an example were [(z.w) ^1/2] is not equal to [(z)^1/2 . (w)^1/2]. As you can see complex powers are thoroughly explained and so are the other topics treated in this book
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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isolated essential singularity, punctured disc, modulus principle, integral formulae, punctured plane, power series converges, harmonic conjugate, negative real axis, finite subcover Key Phrases - Capitalized Phrases (CAPs): (learn more)
Identity Theorem, Cauchy's Theorem, Maximum Modulus Principle, Cauchy's Integral Formula, Deformation Lemma, Liouville's Theorem, Intermediate Value Theorem, Argument Principle, Mean Value Theorem, Comparison Test, Fundamental Theorem of Algebra New!
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isolated essential singularity, punctured disc, modulus principle, integral formulae, punctured plane, power series converges, harmonic conjugate, negative real axis, finite subcover Key Phrases - Capitalized Phrases (CAPs): (learn more)
Identity Theorem, Cauchy's Theorem, Maximum Modulus Principle, Cauchy's Integral Formula, Deformation Lemma, Liouville's Theorem, Intermediate Value Theorem, Argument Principle, Mean Value Theorem, Comparison Test, Fundamental Theorem of Algebra New!
Books on Related Topics | Concordance Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 12
books:
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- Elements of Complex Analysis by John Duncan in Back Matter
- Complex Analysis by Ian Stewart in Back Matter
- Basic Complex Analysis by Jerrold E. Marsden in Back Matter
- Mathematical Analysis by Wiley in Back Matter
- Understanding Analysis by Stephen Abbott in Back Matter
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