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Graduate Texts in Mathematics Ser.: Functions of One Complex Variable I by John

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Specificaties

Objectstaat
Goed: Een boek dat is gelezen, maar zich in goede staat bevindt. De kaft is zeer minimaal beschadigd ...
Subject
Mathematics
ISBN
9780387903286
Publication Name
Functions of One Complex Variable I
Item Length
9.2in
Publisher
Springer New York
Series
Graduate Texts in Mathematics Ser.
Publication Year
1995
Type
Textbook
Format
Hardcover
Language
English
Item Height
0.3in
Author
John B. Conway
Features
Revised
Item Width
6.1in
Item Weight
50.8 Oz
Number of Pages
Xiv, 322 Pages

Over dit product

Product Information

This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre­ requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ­ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe­ matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

Product Identifiers

Publisher
Springer New York
ISBN-10
0387903283
ISBN-13
9780387903286
eBay Product ID (ePID)
156436

Product Key Features

Author
John B. Conway
Publication Name
Functions of One Complex Variable I
Format
Hardcover
Language
English
Features
Revised
Series
Graduate Texts in Mathematics Ser.
Publication Year
1995
Type
Textbook
Number of Pages
Xiv, 322 Pages

Dimensions

Item Length
9.2in
Item Height
0.3in
Item Width
6.1in
Item Weight
50.8 Oz

Additional Product Features

Series Volume Number
11
Number of Volumes
1 Vol.
Lc Classification Number
Qa402.5-402.6
Edition Description
Revised Edition
Edition Number
2
Reviews
"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book for classroom use or self-study."   --MathSciNet
Table of Content
I. The Complex Number System.- §1. The real numbers.- §2. The field of complex numbers.- §3. The complex plane.- §4. Polar representation and roots of complex numbers.- §5. Lines and half planes in the complex plane.- §6. The extended plane and its spherical representation.- II. Metric Spaces and the Topology of ?.- §1. Definition and examples of metric spaces.- §2. Connectedness.- §3. Sequences and completeness.- §4. Compactness.- §5. Continuity.- §6. Uniform convergence.- III. Elementary Properties and Examples of Analytic Functions.- §1. Power series.- §2. Analytic functions.- §3. Analytic functions as mapping, Möbius transformations.- IV. Complex Integration.- §1. Riemann-Stieltjes integrals.- §2. Power series representation of analytic functions.- §3. Zeros of an analytic function.- §4. The index of a closed curve.- §5. Cauchy's Theorem and Integral Formula.- §6. The homotopic version of Cauchy's Theorem and simple connectivity.- §7. Counting zeros; the Open Mapping Theorem.- §8. Goursat's Theorem.- V. Singularities.- §1. Classification of singularities.- §2. Residues.- §3. The Argument Principle.- VI. The Maximum Modulus Theorem.- §1. The Maximum Principle.- §2. Schwarz's Lemma.- §3. Convex functions and Hadamard's Three Circles Theorem.- §4. Phragm>én-Lindel>üf Theorem.- VII. Compactness and Convergence in ihe Space of Analytic Functions.- §1. The space of continuous functions C(G, ?).- §2. Spaccs of analytic functions.- §3. Spaccs of meromorphic functions.- §4. The Riemann Mapping Theorem.- §5. Weierstrass Factorization Theorem.- §6. Factorization of the sine function.- $7. The gamma function.- §8. The Riemann zeta function.- VIII. Runge's Theorem.- §1. Runge's Theorem.- §2. Simple connectedness.- §3.Mittag-Leffler's Theorem.- IX. Analytic Continuation and Riemann Surfaces.- §1. Schwarz Reflection Principle.- $2. Analytic Continuation Along A Path.- §3. Monodromy Theorem.- §4. Topological Spaces and Neighborhood Systems.- $5. The Sheaf of Germs of Analytic Functions on an Open Set.- $6. Analytic Manifolds.- §7. Covering spaccs.- X. Harmonic Functions.- §1. Basic Properties of harmonic functions.- §2. Harmonic functions on a disk.- §3. Subharmonic and superharmonic functions.- §4. The Dirichlet Problem.- §5. Green's Functions.- XI. Entire Functions.- §1. Jensen's Formula.- §2. The genus and order of an entire function.- §3. Hadamard Factorization Theorem.- XII. The Range of an Analytic Function.- §1. Bloch's Theorem.- §2. The Little Picard Theorem.- §3. Schottky's Theorem.- §4. The Great Picard Theorem.- Appendix A: Calculus for Complex Valued Functions on an Interval.- Appendix B: Suggestions for Further Study and Bibliographical Notes.- References.- List of Symbols.
Copyright Date
1978
Topic
Functional Analysis, Algebra / General, Optimization, Mathematical Analysis, Complex Analysis
Lccn
78-018836
Intended Audience
Scholarly & Professional
Illustrated
Yes
Genre
Mathematics

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