Real analysis, real variables

The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable.

In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory.

This book contains survey papers based on the lectures presented at the 3rd International Winter School "e;Modern Problems of Mathematics and Mechanics"e; held in January 2010 at the Belarusian State University, Minsk.

Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups.

Automorphic forms on the upper half plane have been studied for a long time.

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

This monograph uncovers the full capabilities of the Riemann integral.

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations.

This volume explores A.

This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques.

This book provides new contributions to the theory of inequalities for integral and sum, and includes four chapters.

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

This textbook covers key topics of Elementary Calculus through selected exercises, in a sequence that facilitates development of problem-solving abilities and techniques.

This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications.

This book sketches a path for newcomers into the theory of harmonic analysis on the real line.

This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning - the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series.

This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying.

This volume features recent development and techniques in evolution equations by renown experts in the field.

This volume is part of the collaboration agreement between Springer and the ISAAC society.

This volume is part of the collaboration agreement between Springer and the ISAAC society.

This textbook offers a rigorous presentation of mathematics before the advent of calculus.

This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics.

This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area.

This book presents a compact and self-contained introduction to the theory of measure and integration.

This textbook offers a comprehensive undergraduate course in real analysis in one variable.

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

Motivated by recent increased activity of research on time scales, the book  provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales.

This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums.

This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S.

This textbook offers an extensive list of completely solved problems in mathematical analysis.

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones.

This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications.

Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book.

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.

This book provides an in depth discussion of Loewner's theorem on the characterization of matrix monotone functions.

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

The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results.

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

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.

This book presents eleven peer-reviewed papers from the 3rd International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE2017) held in Tbilisi, Georgia in December 2017.

This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration.

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks.

Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single-variable calculus.

This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature.

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.

Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook.

This text gives a rigorous treatment of the foundations of calculus.

In preparing this second edition I have restricted myself to making small corrections and changes to the first edition.

This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques.