Mathematical Analysis

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...

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...

Tracing a path from the earliest beginnings of Fourier series through to the latest research A Panorama of Harmonic Analysis discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and...

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...

Thomas' Calculus goes beyond memorizing formulas and routine procedures to help you develop deeper understanding. It guides you to a level of mathematical proficiency, with additional support if needed through its clear and intuitive explanations,...

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 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;...

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...

This volume reflects the variety of areas where Maz'ya's results are fundamental, influential and/or pioneering. New advantages in such areas are presented by world-recognized experts and include, in particularly, Beurling's minimum principle, inverse...

An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach...

Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out...

This new edition provides an updated approach for students, engineers, and researchers to apply numerical methods for solving problems using MATLAB (R) This accessible book makes use of MATLAB (R) software to teach the fundamental concepts for applying...

The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors' original approach combines rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into...

Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text...

Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.Lectures on a unified theory of and practical procedures for the numerical solution of...

The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for...

The subject of multivariate splines has become a rapidly growing field of mathematical research. The author presents the subject from an elementary point of view that parallels the theory and development of univariate spline analysis. To compensate for...

A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting...

This book serves as a textbook for an undergraduate calculus course. It is written for readers with some previous exposure to the techniques of calculus who would like to see the subject in a conceptual framework. The book combines a review of methods of...

By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation, with little attention paid to the relationships between...

Tikhonov regularization is the most popular general-purpose method for regularization, a mathematical technique to suppress the effect of noise in data, and uses much of the machinery of Hilbert space theory. This book develops the theory of Tikhonov...