Elementary Real and Complex Analysis

Elementary Real Analysis is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the “big picture” and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory, uniform continuity of functions and uniform convergence of sequences of functions. Covers metric spaces. Ideal for readers interested in mathematics, particularly in advanced calculus and real analysis.

354097766XThis text covers many principal topics in the theory of functions of a complex variable. These include, in real analysis, set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces. In complex analysis, they include polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems....

Complex analysis is a classic and central area of mathematics, which is studies and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much-awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter....

This nicely written manuscript takes a gentler approach than other functional analysis graduate texts, and includes an improved approach along with a better choice of topics. The concise treatment makes this ideal for a one-semester course. The exercises in this manuscript are numerous and of a very high quality. Interesting historical tidbits are scattered throughout the text, many of which will be new to most readers. The main prerequisites are basic undergraduate courses in real analysis, linear algebra, and point set topology.

0444104526This book has its origin in lectures given at the Tata Institute of Fundamental Research, Bombay in the winter of 1964/65. The aim of the lectures was to present various topics in analysis, both on real and on complex manifolds. It is unnecessary to add that the topics actually chosen were determined entirely by personal taste. The contents were issued as lecture notes by the Tata Institute, and the present book is based on these notes. ...

This nice little book by Volkovyskii et al (translated from Russian) is a collection of exercises, and it covers the central aspects of and themes in complex function theory, elementary geometry, harmonic and analytic functions. It contains graphics and illustrations, and the last third of the book consists of answers and solutions.

This text is a rigorous introduction on an elementary level to the theory of analytic functions of one complex variable. At American universities it is intended to be used by first-year graduate and advanced undergraduate students. Since the time the first edition was published there has been a marked change in the quality of American students of mathematics. They enter college better prepared, and they are confronted with true mathematical reasoning at an earlier stage. To a lesser degree the same is true abroad. ...

Basic book on rudimentary methods of analyzing complex variables with essential information about the techniques of complex analysis. Exercise material and examples. Bibliography

3540963022This book originated with a series of lectures on nineteenth-century analysis which I gave at the University of Calabria in 1977-79. The study of nineteenth-century mathematics presents an extraordinarily rich and fertile field for historical research, particularly when we realize that the production of mathematics in the last century was greater than in all the preceding centuries put together, and that many contemporary theories have their roots in this period. ...

A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory. ...