Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one s own time. An unfortunate effect of the predominance of fads is that if a student doesn t learn about such worthwhile topics as the wave equation, Gauss s hypergeometric function, the gamma function, and the basic problems of the calculus of variations among others as an undergraduate, then he/she is unlikely to do so later.
The natural place for an informal acquaintance with such ideas is a leisurely introductory...
Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the ach...
Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon delta methods. Students can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness.
The book is suitable for a calculus course at the undergraduate or high school level or for...
Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approac...
Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.
Convex Analysis introduces analytic tools for studying convexity and provides analytical applications of the concept. The book includes a general background on classical geometric theory which allows readers to obtain a glimpse of how modern...
Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a f...
Numerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical methods, especially their applications, limitations, and potentials.
Each chapter contains many computational examples, as well as a section on applications that contain additional engineering examples. Each chapter also includes a set of exercise problems.
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Numerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving c...
Advanced Linear Algebra, Second Edition takes a gentle approach that starts with familiar concepts and then gradually builds to deeper results. Each section begins with an outline of previously introduced concepts and results necessary for mastering the new material. By reviewing what students need to know before moving forward, the text builds a solid foundation upon which to progress.
The new edition of this successful text focuses on vector spaces and the maps between them that preserve their structure (linear transformations). Designed for advanced...
Advanced Linear Algebra, Second Edition takes a gentle approach that starts with familiar concepts and then gradually builds to de...
Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.
Topics covered include a quick review of abstract measure theory, theorems and differentiation in n, Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions as well as functions of...
Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of meas...
Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With emphasis on mathematical thinking and problem solving, the text draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games. This updated edition of a widely adopted textbook considers a number of popular games and diversions that are mathematically based or can be studied from a...
Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistic...
Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups. This new edition of a widely adopted textbook covers applications from biology, science, and engineering. It offers numerous updates based on feedback from first edition adopters, as well as improved and simplified proofs of a number of important theorems. Many new exercises...
Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and th...
Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial differential equations (PDEs), boundary value problems, numerical methods, and dynamical systems. Lively historical notes and mathematical nuggets of information enrich the reading experience by offering perspective on the lives of...
Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge tec...
ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a language such as MATLAB(r). Supplying students with a bridge between the functions of complex variable theory and MATLAB, this supplemental text enables instructors to easily add a MATLAB component to their complex variables courses. A MATLAB(r) Companion to Complex Variables provides readers with a clear understanding of the utility of MATLAB in complex variable calculus. An ideal adjunct to standard texts on the functions of complex variables,...
ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a lang...