Описание: This classic work, written in a clear and interesting style, with many exercises, offers a thorough and reliable treatment of an important branch of higher analysis. It lends itself well to use in course work; however, because of its consistent clear illustrations of theoretical difficulties, the book is also ideal for self-study. Since all higher analysis depends on the theory of numbers, Professor Knopp (formerly Professor of Mathematics, University of T bingen) begins with an introduction to the theory of real numbers, an indispensable foundation for what is to come. This introduction is followed by an extensive account of the theory of sequences and the actual theory of infinite series. The latter is covered in two stages: (1) the classical theory (2) later developments of the 19th century. Carefully selected exercises have been included throughout, emphasizing applications of the theory, rather than purely theoretical considerations. Aimed at students already acquainted with the elements of differential and integral calculus, this work grew out of the author's lectures and course work at the universities of Berlin and K nigsberg. This pedagogical background helped him achieve a work of utmost clarity and precision -- one that belongs in the library of every serious mathematician or student of higher analysis.
Автор: Hyslop James Название: Infinite Series ISBN: 0486450333 ISBN-13(EAN): 9780486450339 Издательство: Dover Рейтинг: Цена: 1144 р. Наличие на складе: Нет в наличии.
Автор: Gelfand S. I. Название: Sequences, Combinations, Limits ISBN: 0486425665 ISBN-13(EAN): 9780486425665 Издательство: Dover Рейтинг: Цена: 1259 р. Наличие на складе: Нет в наличии.
Описание: In a departure from traditional teaching methods, this text focuses on theory more than computations, relying on independent study. Its material is geared toward aspects of high-school mathematics that promise to prove particularly useful for future studies and work. The first of three chapters deals with sequences, their definitions, and methods of mathematic induction. The next chapter addresses combinations, and the final chapter examines limits through a series of introductory problems, problems related to the definition of limit, and problems related to the computation of limits. Answers and hints to the test problems are provided, and "road signs" appear in the margins, marking passages requiring particular attention. 1969 edition.
Описание: Students progressing to advanced calculus are frequently confounded by the dramatic shift from mechanical to theoretical and from concrete to abstract. This text bridges the gap, offering a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. The first five chapters consist of a systematic development of many of the important properties of the real number system, plus detailed treatment of such concepts as mappings, sequences, limits, and continuity. The sixth and final chapter discusses metric spaces and generalizes many of the earlier concepts and results involving arbitrary metric spaces. An index of axioms and key theorems appears at the end of the book, and more than 300 problems amplify and supplement the material within the text. Geared toward students who have taken several semesters of basic calculus, this volume is an ideal prerequisite for mathematics majors preparing for a two-semester course in advanced calculus.
Автор: Kuipers L. Название: Uniform Distribution of Sequences ISBN: 0486450198 ISBN-13(EAN): 9780486450193 Издательство: Dover Рейтинг: Цена: 2638 р. Наличие на складе: Нет в наличии.
Описание: The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.
Автор: Isidore Isaac Hirschman Название: Infinite Series ISBN: 0486789756 ISBN-13(EAN): 9780486789750 Издательство: Dover Рейтинг: Цена: 1718 р. Наличие на складе: Нет в наличии.
Описание: This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book. The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the applications of uniform convergence; double series, changes in the order of summation, and summability; power series and real analytic functions; and additional topics in Fourier series. The text concludes with an appendix containing material on set and sequence operations and continuous functions.
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