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Theory of infinite sequences and series

Bourchtein, Ludmila.

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Theory of infinite sequences and series

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theory of infinite sequences and series/ by Ludmila Bourchtein, Andrei Bourchtein.
Author:	Bourchtein, Ludmila.
other author:	Bourchtein, Andrei.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xiv, 377 p. :ill., digital ;24 cm.
[NT 15003449]:	Sequences of numbers -- Series of numbers -- Sequences of functions -- Series of functions -- Power series.
Contained By:	Springer Nature eBook
Subject:	Sequences (Mathematics) -
Online resource:	https://doi.org/10.1007/978-3-030-79431-6
ISBN:	9783030794316

Theory of infinite sequences and series
Bourchtein, Ludmila.

Theory of infinite sequences and series[electronic resource] /by Ludmila Bourchtein, Andrei Bourchtein. - Cham :Springer International Publishing :2022. - xiv, 377 p. :ill., digital ;24 cm.

Sequences of numbers -- Series of numbers -- Sequences of functions -- Series of functions -- Power series.

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.

ISBN: 9783030794316

Standard No.: 10.1007/978-3-030-79431-6doiSubjects--Topical Terms:

555869
Sequences (Mathematics)

LC Class. No.: QA292

Dewey Class. No.: 515.24

Theory of infinite sequences and series
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100 1 $a Bourchtein, Ludmila. $3 2184832
245 1 0 $a Theory of infinite sequences and series $h [electronic resource] / $c by Ludmila Bourchtein, Andrei Bourchtein.
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300 $a xiv, 377 p. : $b ill., digital ; $c 24 cm.
505 0 $a Sequences of numbers -- Series of numbers -- Sequences of functions -- Series of functions -- Power series.
520 $a 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.
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