Real analysis, real variables

Comprehensive coverage of recent, exciting developments in Fourier restriction theory, including applications to number theory and PDEs.

A thorough, self-contained and easily accessible treatment of the theory on the polynomial best approximation of functions with respect to maximum norms.

A quantity can be made smaller and smaller without it ever vanishing.

Intended for a one- or two-semester course, this text applies basic, one-variable calculus to analyze the motion both of planets in their orbits as well as interplanetary spacecraft in their trajectories.

Optimal control theory has numerous applications in both science and engineering.

Convex functions play an important role in almost all branches of mathematics as well as other areas of science and engineering.

This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak-Orlicz spaces) with minimal assumptions on the generating F-function.

Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis - providing a mathematically sophisticated introduction to functional analytical concepts.

From the reviews: "e;Volume 1 covers a basic course in real analysis of one variable and Fourier series.

A Concrete Introduction to Analysis, Second Edition offers a major reorganization of the previous edition with the goal of making it a much more comprehensive and accessible for students.

The first volume of three providing a full and detailed account of undergraduate mathematical analysis.

Mathematics students generally meet the Riemann integral early in their undergraduate studies, then at advanced undergraduate or graduate level they receive a course on measure and integration dealing with the Lebesgue theory.

This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral.

In the ideal world, major decisions would be made based on complete and reliable information available to the decision maker.

A revised and updated edition, providing hundreds of exercises to help students gradually transition from school to university-level calculus.

This textbook provides a gentle overview of fundamental concepts related to one-variable calculus.

Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform.

Dieses Buch ist Band 5 in der Serie Gestufte Italienische Lesebücher.

This book investigates sequences and series with a clear and focused approach, presenting key theoretical concepts alongside a diverse range of examples and proposed problems, complete with solutions.

This second edition of "e;Polynomial representations of GL (K)"e; consists of n two parts.

An introduction to Griffiths'' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds.

A typical source of mistakes that frequently lead to a wrong or incomplete solution for the antiderivative of a given real function of one real variable is a misuse of the technique of change of variable.

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years.

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level.

Norm inequalities relating (i) a function and two of itsderivatives and (ii) a sequence and two of its differencesare studied.

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlomilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions.

This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

This book provides a self-contained and rigorous introduction to calculus of functions of one variable.

Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology.

This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas ~n what measure theory every would-be analyst should learn, and to detail my approach to the subject.

What's the point of calculating definite integrals since you can't possibly do them all?

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems.

This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line.

Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings.

Responses from colleagues and students concerning the first edition indicate that the text still answers a pedagogical need which is not addressed by other texts.

From the author of the highly acclaimed "e;A First Course in Real Analysis"e; comes a volume designed specifically for a short one- semester course in real analysis.

This brief explores the Krasnosel'skii-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.

The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations.

Designed for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration.