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An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ... a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.

Real analysis is the section of mathematics that studies the functions of real variables such as measurements, integrations, and topology results. This new edition of the widely used analysis book continues to cover real analysis in detail.

An exciting approach to the history and mathematics of number theory ... the author s style is totally lucid and very easy to read... the result is indeed a wonderful story.

This set features: "Linear Algebra and Its Applications, Second Edition" (978-0-471-75156-4) and "Functional Analysis" (978-0-471-55604-6) both by Peter D. Lax.

Written by authors at the forefront of their field, this Second Edition discusses problems with periodic solutions, and presents new information on initial boundary value problems and numerical methods for partial differential equations.

This book brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike. The Second Edition features new exercises and an updated bibliography. A new discussion provides a different method for computing the Galois group of a quartic polynomial.

This pioneering resource tells the full story of Fourier analysis-its history, its impact on the development of modern mathematical analysis, and today's applications. The topics are presented using a cause-and-effect approach, illustrating where ideas originated and what necessitated them.

Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves.

The primary purpose of this text is to introduce math majors, who have completed a calculus sequence, to the axiomatic makeup of modern mathematics. Heavy emphasis is placed on the writing of clear and understandable proofs.

Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.

This book reflects the most recent developments in finite element methods and is accessible to students of mathematics, engineering, and physics due to its approach. An overview and consolidation of the basic knowledge of linear spaces and PDEs is presented, which is followed by this discussion of finite element methods and its applications.

Reflecting the emerging role of topology, this book is uniquely innovative in its cross-disciplinary approach. * Includes topological applications in the scientific fields of physics, chemistry, biology, engineering, and economics. * Applets are available via a related website.

A posteriori error estimators have been intensely studied in recent years, owing to their remarkable capacity to enhance both speed and accuracy in computing. By effectively estimating error, the door has been opened for the possibility of controlling the entire computational process through new adaptive algorithms.

This book provides an excellent introduction to the subject designed for readers from a variety of mathematical backgrounds. It features introductory properties of metric spaces and Banach spaces, and an appendix contains a summary of the concepts of set theory.

This introduction to linear algebra by world-renowned mathematician Peter Lax is unique in its emphasis on the analytical aspects of the subject as well as its numerous applications. The book grew out of Dr. Lax's course notes for the linear algebra classes he taught at New York University.

This straight-forward, concise book is made up of carefully selected topics and is written in an accessible that requires minimal background knowledge. It provides the reader with a sense of unity in the subject's development and fully explains the essential concepts, outlining the logic behind the steps to familiarize the reader with the theories.

This introductory textbook on nonlinear partial differential equations is technique oriented with an emphasis on applications and is designed to build a foundation for studying advanced treatises in the field. The Second Edition features an updated bibliography as well as an increase in the number of exercises.

This precise and highly readable book provides a complete and concise introduction to classical topics in the numerical solution of ordinary differential equations (ODEs). It contains many up-to-date references to both analytical and numerical ODE literature while offering new unifying views on different problem classes.

This book covers the Hilbert transform of distribution and the space of periodic distributions with period. It includes inversion formulas worked out for the Hilbert transform and applied to solve singular integral equation occurring in elasticity and elsewhere.

A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic... ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems.

Advanced algebra in the service of contemporary mathematical research-- a unique introduction. This volume takes an altogether new approach to advanced algebra. Its intriguing title, inspired by the term postmodernism, denotes a departure from van der Waerden's Modern Algebra--a book that has dominated the field for nearly seventy years.

Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry. "Conformal Differential Geometry and Its Generalizations" systematically presents the foundations and manifestations of conformal differential geometry.

Modeling is one of the most appealing areas in engineering and applied sciences. Engineers need to build models to solve real life problems. The aim of a model consists of reproducing the reality as faithfully as possible, trying to understand how the real world behaves, and obtaining the expected responses to given actions or inputs.

An authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects.

A novel, practical introduction to functional analysis In the twenty years since the first edition of Applied Functional Analysis was published, there has been an explosion in the number of books on functional analysis. Yet none of these offers the unique perspective of this new edition.

A superb text on the fundamentals of Lebesgue measure and integration. This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R.

This book presents the mathematics of finite dimensional constrained optimization problems. It offers a solid presentation of real analysis and provides a basis for the mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems.