Introductory Complex Analysis (Dover Books on Mathematics)
by Richard A. Silverman, Mathematics
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Book Summary Information
Author: Mathematics, Richard A. SilvermanEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1984-05-01
ISBN: 0486646866
Number of pages: 400
Publisher: Dover Publications
Book Reviews of Introductory Complex Analysis (Dover Books on Mathematics)
Book Review: An excellent(and cheap!) text
Summary: 5 Stars
This book might just be the best Dover text out there-which isn't really saying much, considering how many of their books are total stinkers. To me, this is nearly an ideal math book: clear logical development punctuated with very well-chosen exercises. I know of no better book on the basics of complex analysis. If you've seen basic material about complex numbers and functions, as well as a few basic facts about real analysis, you can start in chapter seven, where complex integration is introduced, and used to prove all sorts of wonderful things. But if you haven't seen these basics, they are well-presented in the opening chapters, making this book extremely accessible. But it is in chapter seven that the book really begins, which is where the fundamental theorems of complex analysis start being proved. All of these proofs and chapters are extremely well-written, making the logical structure of the whole theory entirely transparent. This book is just an introduction, as the title says, and there is lots of advanced material not touched here, but this book provides an excellent foundation for further study. Chapter Titles: 1. Complex Numbers, Functions, and Sequences 2. Limits and Continuity 3. Differentiation. Analytic Functions 4. Polynomials and Rational Functions 5. Mobius Transforms 6. Exponentials and Logarithms 7. Complex Integrals. Cauchy's Integral Theorem 8. Cauchy's Integral Formula and Its Implications 9. Complex Series. Uniform Convergence 10. Power Series 11. Laurent Series. Singular points 12. The Reside Theorem and Its Implications 13. Harmonic Functions 14. Infinite Product and Partial Fraction Expansions 15. Conformal Mapping 16. Analytic Continuation
Summary of Introductory Complex Analysis (Dover Books on Mathematics)
A shorter version of A. I. Markushevich's masterly three-volume Theory of Functions of a Complex Variable, this edition is appropriate for advanced undergraduate and graduate courses in complex analysis. Numerous worked-out examples and more than 300 problems, some with hints and answers, make it suitable for independent study. 1967 edition.
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