Real analysis, real variables

In many problems arising in engineering and science one requires approxi- tion methods to reproduce physical reality as well as possible.

One of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quantities in a system and transformations of a system.

Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established.

This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions.

The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems.

This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

A unifying approach suitable for graduate students and mathematicians.

Introduction to singularity theory based on MSc course taught by author; novel synthesis, with new results not found elsewhere.

This book is an extensive introductory text to mathematical analysis for graduate students and advanced undergraduates, complete with 500 exercises and numerous examples.

Part two of comprehensive text on multidimensional real analysis.

Part one of a comprehensive text on multidimensional real analysis, including numerous exercises with partial solutions.

This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

This book presents a complete proof of Connes'' Index Theorem generalized to foliated spaces, including coverage of new developments and applications.

This classic text offers a clear exposition of modern probability theory.

A uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs.

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

An Introduction to Complex Analysis in Several Variables

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems.

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

The theory of series in the 17th and 18th centuries poses several interesting problems to historians.

This is the second edition of an undergraduate one-variable analysis text.

This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs.

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

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

This book is a revised and expanded edition of a successful graduate and reference text.

Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications.

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

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.

The approach taken by this book is based on two beliefs.

What differential calculus, and, in general, analysis ofthe infinite, might be can hardly be explainedto those innocent ofany knowledge ofit.

The core of this book, Chapters three through five, presents a course on metric, normed, and Hilbert spaces at the senior/graduate level.

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.

Was plane geometry your favorite math course in high school?

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.

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

Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas.

A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs.

Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology.

Project practitioners and decision makers complain that both parametric and Monte Carlo methods fail to produce accurate project duration and cost contingencies in majority of cases.

Project practitioners and decision makers complain that both parametric and Monte Carlo methods fail to produce accurate project duration and cost contingencies in majority of cases.

Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis.

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

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