Theory Of Infinite Sequences And Series
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Theory Of Infinite Sequences And Series
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Author : Ludmila Bourchtein
language : en
Publisher: Springer Nature
Release Date : 2021-11-13
Theory Of Infinite Sequences And Series written by Ludmila Bourchtein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-13 with Mathematics categories.
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.
Infinite Sequences And Series
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Author : Konrad Knopp
language : en
Publisher: Courier Corporation
Release Date : 2012-09-14
Infinite Sequences And Series written by Konrad Knopp and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
A Student S Guide To Infinite Series And Sequences
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Author : Bernhard W. Bach, Jr.
language : en
Publisher: Cambridge University Press
Release Date : 2018-05-17
A Student S Guide To Infinite Series And Sequences written by Bernhard W. Bach, Jr. and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-17 with Mathematics categories.
An informal and practically focused introduction for undergraduate students exploring infinite series and sequences in engineering and the physical sciences. With a focus on practical applications in real world situations, it helps students to conceptualize the theory with real-world examples and to build their skill set.
Infinite Series
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Author : Isidore Isaac Hirschman
language : en
Publisher: Courier Corporation
Release Date : 2014-08-18
Infinite Series written by Isidore Isaac Hirschman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-18 with Mathematics categories.
Text for advanced undergraduate and graduate students examines Taylor series, Fourier series, uniform convergence, power series, and real analytic functions. Appendix covers set and sequence operations and continuous functions. 1962 edition.
An Introduction To Infinite Products
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Author : Charles H. C. Little
language : en
Publisher: Springer Nature
Release Date : 2022-01-10
An Introduction To Infinite Products written by Charles H. C. Little and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-10 with Mathematics categories.
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.
Problems And Theorems In Analysis I
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Author : George Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-12-11
Problems And Theorems In Analysis I written by George Polya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-11 with Mathematics categories.
From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems." Bulletin of the American Mathematical Society
Automatic Sequences
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Author : Jean-Paul Allouche
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-21
Automatic Sequences written by Jean-Paul Allouche and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-21 with Computers categories.
Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.
Geometry A Comprehensive Course
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Author : Dan Pedoe
language : en
Publisher: Courier Corporation
Release Date : 2013-04-02
Geometry A Comprehensive Course written by Dan Pedoe and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-02 with Mathematics categories.
Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.