Theory Of Infinite Sequences And Series PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Theory Of Infinite Sequences And Series PDF full book. Access full book title Theory Of Infinite Sequences And Series.
Author | : Ludmila Bourchtein |
Publisher | : Springer Nature |
Total Pages | : 388 |
Release | : 2021-11-13 |
Genre | : Mathematics |
ISBN | : 3030794318 |
Download Theory of Infinite Sequences and Series Book in PDF, ePub and Kindle
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.
Author | : Konrad Knopp |
Publisher | : Courier Corporation |
Total Pages | : 212 |
Release | : 2012-09-14 |
Genre | : Mathematics |
ISBN | : 0486152049 |
Download Infinite Sequences and Series Book in PDF, ePub and Kindle
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.
Author | : Konrad Knopp |
Publisher | : |
Total Pages | : 596 |
Release | : 1928 |
Genre | : Series, Infinite |
ISBN | : |
Download Theory and Application of Infinite Series Book in PDF, ePub and Kindle
Trans from the 2nd German ed , pub 1923.
Author | : Konrad Knopp |
Publisher | : Courier Corporation |
Total Pages | : 596 |
Release | : 1990-01-01 |
Genre | : Mathematics |
ISBN | : 0486661652 |
Download Theory and Application of Infinite Series Book in PDF, ePub and Kindle
This unusually clear and interesting classic offers a thorough and reliable treatment of an important branch of higher analysis. The work covers real numbers and sequences, foundations of the theory of infinite series, and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, and other topics). Exercises throughout. Ideal for self-study.
Author | : Bernhard W. Bach, Jr. |
Publisher | : Cambridge University Press |
Total Pages | : 201 |
Release | : 2018-05-17 |
Genre | : Mathematics |
ISBN | : 1107059828 |
Download A Student's Guide to Infinite Series and Sequences Book in PDF, ePub and Kindle
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.
Author | : Charles H. C. Little |
Publisher | : Springer Nature |
Total Pages | : 258 |
Release | : 2022-01-10 |
Genre | : Mathematics |
ISBN | : 3030906469 |
Download An Introduction to Infinite Products Book in PDF, ePub and Kindle
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.
Author | : James M Hyslop |
Publisher | : Courier Corporation |
Total Pages | : 146 |
Release | : 2012-05-11 |
Genre | : Mathematics |
ISBN | : 0486154858 |
Download Infinite Series Book in PDF, ePub and Kindle
This concise text focuses on the convergence of real series. Topics include functions and limits, real sequences and series, series of non-negative terms, general series, series of functions, the multiplication of series, more. 1959 edition.
Author | : Daniel D. Bonar |
Publisher | : American Mathematical Soc. |
Total Pages | : 261 |
Release | : 2018-12-12 |
Genre | : |
ISBN | : 1470447827 |
Download Real Infinite Series Book in PDF, ePub and Kindle
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
Author | : Jean-Paul Allouche |
Publisher | : Cambridge University Press |
Total Pages | : 592 |
Release | : 2003-07-21 |
Genre | : Computers |
ISBN | : 9780521823326 |
Download Automatic Sequences Book in PDF, ePub and Kindle
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.
Author | : Valérie Berthé |
Publisher | : Birkhäuser |
Total Pages | : 578 |
Release | : 2018-04-09 |
Genre | : Mathematics |
ISBN | : 331969152X |
Download Sequences, Groups, and Number Theory Book in PDF, ePub and Kindle
This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.