Mathematical Analysis

Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to...

Mathematical Analysis: Theory and Applications provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics. Readers will discover numerous valuable tools and...

TIMELY UPDATE OF A POPULAR EDITION ON PERMUTATION TESTING WITH NUMEROUS CASE STUDIES INCLUDED THROUGHOUT The newly revised and updated Second Edition of Permutation Tests for Complex Data describes permutation tests from the point of view of experimental...

Finite Mathematics: An Introduction with Applications in Business, Social Sciences, and Music presents core concepts of finite mathematics in a clear, intuitive fashion designed to reinforce understanding. The book begins with finite mathematics...

This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the...

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years. These additions are essential for grasping the practical applications of convex function theory in...

This book covers contemporary topics in mathematical analysis and its applications and relevance in other areas of research. It provides a better understanding of methods, problems, and applications in mathematical analysis. It also covers applications...

This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces...

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded...

The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap proximation of possibly irregular functions and surfaces and was successfully applied in data compression,...

The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of...

The Springer edition of this book is an unchanged reprint of Courant and Friedrich's classical treatise which was first published in 1948. The basic research for it took place during World War II, but there are many aspects which still make the book...

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of...

The authors' aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics should provide the reader with methods and results that are applicable in a...

This book is both a text and a paean to twentieth-century real variables, measure theory, and integration theory. As a text, the book is aimed at graduate students. As an exposition, extolling this area of analysis, the book is necessarily limited in...

The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in...

Univariate statistical analysis is concerned with techniques for the analysis of a single random variable. This book is about applied multivariate analysis. It was written to p- vide students and researchers with an introduction to statistical techniques...

The late Professor G. N. Watson wrote his monumental 1995 treatise on the theory of Bessel functions with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables; and the second...

The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during 1925-1926. Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. V. Stepanov, N. N...

This updated edition provides detailed information on the amendments to the standard including IEEE 802.15.4a, IEEE 802.15.4c, IEEE 802.15.4d, IEEE 802.15.4e, IEEE 802.15.4f, and IEEE 802.15.4g, as well as an update on the ZigBee Alliance. This book...

The term convexity used to describe these lectures given at the Univer sity of Lund in 1991-92 should be understood in a wide sense. Only Chap ters I and II are devoted to convex sets and functions in the traditional sense of convexity. The following...

For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This...

For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found...

This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the...

This book is to serve as a text for engineering students at the senior or beginning graduate level in a second course in dynamics. It grew out of many years experience in teaching such a course to senior students in mechanical engineering at the...

For courses in precalculus. Prepare. Practice. Review. MichaelSullivan's time-tested approach focuses students on the fundamental skills theyneed for the course: preparing for class, practicing withhomework, and reviewing the concepts. The...

Fixed point theory is a powerful tool in nonlinear analysis, with applications in fractional differential equations and other areas. The most prominent application/conclusion of this theory is the Banach contraction principal. The notion of invisible...

Targeted to upper-undergraduate and graduate students of mathematics, this book discusses special integrals and their applications in finding certain series sums. It starts with the differentiation and the integration methods for summing a series that is...

This book is a straightforward and comprehensive presentation of the concepts and methodology of elementary real analysis. Targeted to undergraduate students of mathematics and engineering, it serves as the foundation for mathematical reasoning and...

Designed for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration. It acts as a pivotal link bridging the Riemann integral and the Lebesgue integral, with a primary...

This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have...

Up to a certain time the attention of mathematicians was concentrated on the study of individual objects, for example, specific elementary functions or curves defined by special equations. With the creation of the method of Fourier series, which allowed...

One service mathematics has rendered the 'Et moi, ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded...

Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations. When solving such problems, in many cases it is fairly easy to obtain the Laplace transform, while it is very demanding to...

This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and...

The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of...

The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other...

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of...

The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical...

This book provides an overview of recent advances in the theory of dynamical systems, with a particular emphasis on their connections to other areas of mathematical research, including number theory, geometry, mathematical physics, complex analysis, and...