Mathematical Analysis

With numerous applications, particularly in fluid dynamics, the semi-Lagrangian approximation scheme is an essential part of the numerical analyst's toolkit. This largely self-contained book provides a framework for the semi-Lagrangian strategy for...

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...

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...

Excursions in Classical Analysis introduces undergraduate students to advanced problem solving and undergraduate research in two ways. Firstly, it provides a colourful tour of classical analysis which places a wide variety of problems in their historical...

Nilsystems play a key role in the structure theory of measure preserving systems, arising as the natural objects that describe the behavior of multiple ergodic averages. This book is a comprehensive treatment of their role in ergodic theory, covering...

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...

This new book from the authors of the classic book Numerical Methods addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines...

Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in...

Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted...

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Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three...

Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques...

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...

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...

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...

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...

This set includes An Introduction to Numerical Methods and Analysis, 2nd Edition & Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis, 2nd Edition An Introduction to Numerical Methods and Analysis, 2nd Edition explores where...

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...

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;...

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,...

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...

Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fields of engineering, economics, management sciences,...

The emergence of social networks, OpenCourseWare, Massive Open Online Courses, informal remote learning and connectivist approaches to learning has made the analysis and evaluation of Digital Learning Environments more complex. Modeling these complex...

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...

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...

Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is...

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...