The Fifth Edition of this leading text offers substantial training in vectors and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. Numerical methods are touched upon at various points, because of their practical value and the insights they give about theory.

Computer graphics is important in many areas including engineering design, architecture, education, and computer art and animation. This book examines a wide array of current methods used in creating real-looking objects in the computer, one of the main aims of computer graphics.

This volume presents the subject of image processing and analysis to the point of view of the user. The standard algorithms, procedures, and rules of thumb are explained in the context of successful application to biological or medical images and chapters cover image acquisition, processing, analysis, and pattern recognition. This approach equips the user with the necessary background for informed use of image processing software, and the ability to write their own programs. There are explanations of more advanced techniques, and each has reference to specific applications. This is an extremely usable, practical guide for the beginning postgraduate biologist or medical researcher.

The major thrust of this book is the analysis of pointwise behavior of Sobolev functions of integer order and BV functions (functions whose partial derivatives are measures with finite total variation). The development of Sobolev functions includes an analysis of their continuity properties in terms of Lebesgue points, approximate continuity, and fine continuity as well as a discussion of their higher order regularity properties in terms of Lp-derivatives. This provides the foundation for further results such as a strong approximation theorem and the comparison of Lp and distributional derivatives. Also included is a treatment of Sobolev-Poincaré type inequalities which unifies virtually all inequalities of this type. Although the techniques required for the discussion of BV functions are completely different from those required for Sobolev functions, there are similarities between their developments such as a unifying treatment of Poincaré-type inequalities for BV functions. This book is intended for graduate students and researchers whose interests may include aspects of approximation theory, the calculus of variations, partial differential equations, potential theory and related areas. The only prerequisite is a standard graduate course in real analysis since almost all of the material is accessible through real variable techniques.

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods.

Contains basic definitions, complete and clear theorems, and gives attention to the topics of algebraic geometry, computers, homology, and representations. For individuals interested in a self-study guide to learning advanced algebra and its related topics.

Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and homology: the cornerstones of contemporary algebraic topology.

Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.

This book is an introduction to level set methods and dynamic implicit surfaces. These are powerful techniques for analyzing and computing moving fronts in a variety of different settings. While it gives many examples of the utility of the methods to a diverse set of applications, it also gives complete numerical analysis and recipes, which will enable users to quickly apply the techniques to real problems.

"This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." –Publicationes Mathematicae

"This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises." –Newsletter of the EMS

"In the reviewer's opinion, this is a superb book which makes learning a real pleasure."
—Revue Romaine de Mathematiques Pures et Appliquees

"This mainstream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises."

—Monatshefte F. Mathematik

This practical course in complex calculus explains the applications, without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical sciences and engineering.

Editorial Reviews
Volume I "Throughout the notation is carefully organized and all proofs are complete and rigorous. The text is completed by carefully worked examples, many of them are illustrated by drawings. A special feature of the book is the extensive collection of exercises … The book is a good preparation for readers who wish to go on to more advanced studies in analysis. It can be also highly recommended as a text for a course or for self study."-Zentralblatt fur Mathematik

Volume II ''Throughout the text is carefully organized, proofs are complete and rigorous and the material is completed by carefully worked examples.'- Zentralblatt fur Mathematik

This book is a well-organized and thoroughly readable introduction to a number of subjects. Beginning with two chapters on set theory and the real number system, one can purue various paths. There is a treatment of Lebesgue measure and integral followed by sections on the L and on the relationship between derivative and integral. One might choose at this point to skip over several chapters and continue with the third portion of the text, general measure and integration. Another introductory course, this one in topology and functional analysis, can be obtained by proceeding from Chapters one and two to Part Two of the text, which deals with metric spaces, topological spaces, compact spaces, and Banach spaces. Naturally, other combinations of the material are quite reasonable. The final portion on general measure and integration might serve as an almost independent presentation of measure theory and as an introduction to a course in probability.