Theory of infinite sequences and series / Ludmila Bourchtein, Andrei Bourchtein.
Bourchtein, Ludmila, author.; Bourchtein, Andrei, author.
2022
QA292
Available Online

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Title Theory of infinite sequences and series / Ludmila Bourchtein, Andrei Bourchtein.
Author Bourchtein, Ludmila, author.
ISBN 9783030794316 (electronic bk.)
3030794318 (electronic bk.)
303079430X
9783030794309
DOI https://doi.org/10.1007/978-3-030-79431-6
Imprint Cham, Switzerland : Birkhäuser, [2022]
Language English
Description 1 online resource
Other Standard Identifiers 10.1007/978-3-030-79431-6 doi
Call Number QA292
Dewey Decimal Classification 515/.24
Summary This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed November 19, 2021).
Added Author Bourchtein, Andrei, author.
Available in Other Form Print version: 9783030794309
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Sequences of numbers
Series of numbers
Sequences of functions
Series of functions
Power series.

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