Real analysis, real variables

A two-volume advanced text for graduate students.

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

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.

This book is intended as a survey of latest results on weighted inequalities in Lorentz, Orlicz spaces and Zygmund classes.

In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations.

Kiyosi Ito, the founder of stochastic calculus, is one of the few central figures of the twentieth century mathematics who reshaped the mathematical world.

Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians.

This book is meant as a text for a first year graduate course in analysis.

Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable.

This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms.

47 brauchen nur den Nenner n so groß zu wählen, daß das Intervall [0, IJn] kleiner wird als das fragliche Intervall [A, B], dann muß mindestens einer der Brüche m/n innerhalb des Intervalls liegen.

This book is an introductory text on real analysis for undergraduate students.

Hypersingular Integral Equations in Fracture Analysis explains how plane elastostatic crack problems may be formulated and solved in terms of hypersingular integral equations.

A study of large deviations for empirical measures and vector-valued additive functionals of general state space Markov chains.

The understanding of results and notions for a student in mathematics requires solving ex- ercises.

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.

This book is an English translation of the last French edition of Bourbaki's Fonctions d'une Variable Reelle.

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.

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

The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak-Orlicz Hardy-type function spaces, and to lay the foundations for further applications.

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization.

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.

The subject of real analysis dates to the mid-nineteenth century - the days of Riemann and Cauchy and Weierstrass.

The 12th International Conference in Methodologies and Intelligent Systems for Technology Enhanced Learning was hosted by the University of L'Aquila and was held in L'Aquila (Italy) from July 13 to 15, 2022.

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.

A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

From the reviews: "e;In the world of mathematics, the 1980's might well be described as the "e;decade of the fractal"e;.

The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics.

Advanced Data Analysis and Modeling in Chemical Engineering provides the mathematical foundations of different areas of chemical engineering and describes typical applications.

Mathematik ist nicht jedermanns Sache.

Building on the basic concepts through a careful discussion of covalence, (while adhering resolutely to sequences where possible), the main part of the book concerns the central topics of continuity, differentiation and integration of real functions.

This book provides a concise and meticulous introduction to functional analysis.

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

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.

The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent.

The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications.

Modern text examining the interplay between measure theory and Fourier analysis.

Broadly speaking, analysis is the study of limiting processes such as sum- ming infinite series and differentiating and integrating functions, and in any of these processes there are two issues to consider; first, there is the question of whether or not the limit exists, and second, assuming that it does, there is the problem of finding its numerical value.

From the reviews: "e;A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics.

The purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica- tions which accompany them.

Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "e;applied real analysis"e;.

Engineers and physicists are more and more encountering integrations involving nonelementary integrals and higher transcendental functions.

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