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This book describes and analyses how a mathematics student can develop into a sophisticated and rigorous thinker.

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Offers a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and some applications.

¿The book The E. M. Stein Lectures on Hardy Spaces is based on a graduate course on real variable Hardy spaces which was given by E.M. Stein at Princeton University in the academic year 1973-1974. Stein, along with C. Fefferman and G. Weiss, pioneered this subject area, removing the theory of Hardy spaces from its traditional dependence on complex variables, and to reveal its real-variable underpinnings. This book is based on Steven G. Krantz¿...

Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.

This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to pr...

This edition offers a more instructive Preface to assist instructors on developing the course they prefer. The prerequisites are more explicit and provide a roadmap for the course. Sample syllabi are included.

This new edition is re-organized to make it more useful and more accessible. The most frequently taught topics are now up front. And the major applications are isolated in their own chapters. This makes this edition the most useable and flexible of any previous editions.

The Handbook of Complex Analysis will be an entree for advanced undergraduates and beginning graduate students in the subject of complex analysis. The subject of complex analysis of increasing importance. Even the function theory of several complex variables has seen applications in cosmology, geophysics, and engineering.

This new edition continues the effort to make the book accessible to a broader audience. Many students who take a real analysis course do not have the ideal background. The new edition offers chapters on background material like set theory, logic, and methods of proof. The more advanced material in the book is made more apparent.

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A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike.

Partial Differential Equations and Complex Analysis is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and he examines how those results apply to the boundary regularity of...

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The book showcases convexity in the context of mathematical analysis. It introduces analytic tools for studying convexity and provides analytical applications of the concept. The book includes a general background in classical geometric theory which allows readers to obtain a glimpse of how modern mathematics is developed and how geometric ideas may be studied analytically. Featuring a user-friendly approach, the book contains copious examples...

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research:  complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis.  The monograp...

Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.

As both readers and writers, we are all aware of blogs, chat rooms, and preprint servers. The truly new feature of this second edition is an extensive discussion of technological developments. Similar to the first edition, Krantz's frank and straightforward approach makes this book particularly suitable as a textbook for an undergraduate course.

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This textbook offers a rare opportunity to teach Lebesgue integration to undergraduates. Focusing on the real line, the author introduces the topic in an accessible way, thus encouraging students to dig into this mainstay of mathematical analysis earlier than the traditional graduate level course.