Mathematical Analysis

A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend...

This book is an introduction to basic topics in inequalities and their applications. These include the arithmetic mean-geometric mean inequality, Cauchy-Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and...

A concise introduction to computational methods for solving large linear systems of equations. This is the only textbook that treats iteration methods for symmetric linear systems from a polynomial point of view. This particular feature enables readers...

There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in...

This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be...

This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen...

The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The...

This volume contains the proceedings of the AMS Special Sessions on Frames, Wavelets and Gabor Systems and Frames, Harmonic Analysis, and Operator Theory, held from April 16-17, 2016, at North Dakota State University in Fargo, North Dakota.The papers...

A Passage to Modern Analysis is an extremely well-written and reader-friendly invitation to real analysis. An introductory text for students of mathematics and its applications at the advanced undergraduate and beginning graduate level, it strikes an...

Systems of linear equations are ubiquitous in numerical analysis and scientific computing. and iterative methods are indispensable for the numerical treatment of such systems. This book offers a rigorous introduction to fundamental iterative methods for...

Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence...

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology...

Targeting talented students who seek a deeper understanding of calculus and its applications, this book contains enrichment material for courses in first- and second-year calculus, differential equations, modelling, and introductory real analysis...

The Calculus Collection is a useful resource for everyone who teaches calculus, in secondary school or in a college or university. It consists of 123 articles selected by a panel of veteran secondary school teachers. The articles focus on engaging...

Multilevel adaptive methods play an increasingly important role in the solution of many scientific and engineering problems. Fast adaptive methods techniques are widely used by specialists to execute and analyze simulation and optimization problems. This...

This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds.The local...

We consider in Rn a differential operator P(D), P a polynomial, with constant coefficients. Let U be an open set in Rn and A(U) be the space of real analytic functions on U. We consider the equation P(D)u=f, for f in A(U) and look for a solution in A(U)...

An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. It was during the nineteenth century that the diverse mathematical formulae...

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for...

This volume collects two articles by Christine Laurent-Thiebaut and Jurgen Leiterer which were submitted to, and accepted by the Annali della Scuola Normale Superiore, Classe di Scienze: The q-convex case; the q-concave case. Owing to the character of...

In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study...

This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds.Oka theory is the field of complex...

Larson/Edwards' student-oriented CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 8th INTERNATIONAL METRIC Edition with WebAssign digital resources and online tutorials clearly introduces the concepts and rules behind calculus. Updated content is designed to...

Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical...

This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long...

The purpose of this book is to present modern developments and applications of the techniques of modulus or extremal length of path families in the study of m- n pings in R , n? 2, and in metric spaces. The modulus method was initiated by Lars Ahlfors...

For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors. This much anticipated second edition of the most successful new calculus text published in the...

The aim of this work is to present a unified approach to the modern field of control theory and to provide a technique for making problems involving deterministic, stochastic, and adaptive processes of both linear and nonlinear type amenable to machine...

The present volume reflects both the diversity of Bochner's pursuits in pure mathematics and the influence his example and thought have had upon contemporary researchers. Originally published in 1971. The Princeton Legacy Library uses the latest...

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is...

Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to...

Alberto P. Calderon (1920-1998) was one of the 20th century's leading mathematical analysts. His contributions have changed the way researchers approach and think about a variety of topics in mathematics and its applications, including harmonic analysis,...

This text, based on the author's teaching at Ecole Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces;...

Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They...

Working Analysis is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular, effective numerical...

With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter...

Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors...

These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis,...

Continuous optimization is the study of problems in which we wish to opti mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in...

The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented...