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Author : Konrad Knopp
Publisher :
Page : 596 pages
File Size : 32,10 MB
Release : 1928
Category : Series, Infinite
ISBN :
Trans from the 2nd German ed , pub 1923.
Author : Ludmila Bourchtein
Publisher : Springer Nature
Page : 388 pages
File Size : 40,53 MB
Release : 2021-11-13
Category : Mathematics
ISBN : 3030794318
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
Page : 596 pages
File Size : 44,83 MB
Release : 1990-01-01
Category : Mathematics
ISBN : 0486661652
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 : Konrad Knopp
Publisher : Courier Corporation
Page : 212 pages
File Size : 13,41 MB
Release : 2012-09-14
Category : Mathematics
ISBN : 0486152049
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 : Bernhard W. Bach, Jr.
Publisher : Cambridge University Press
Page : 201 pages
File Size : 24,51 MB
Release : 2018-05-17
Category : Mathematics
ISBN : 1107059828
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 : Isidore Isaac Hirschman
Publisher : Courier Corporation
Page : 193 pages
File Size : 30,80 MB
Release : 2014-08-18
Category : Mathematics
ISBN : 0486798240
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.
Author : Charles H. C. Little
Publisher : Springer Nature
Page : 258 pages
File Size : 26,58 MB
Release : 2022-01-10
Category : Mathematics
ISBN : 3030906469
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 : Leonhard Euler
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 25,55 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461210216
From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."
Author : Dan Pedoe
Publisher : Courier Corporation
Page : 466 pages
File Size : 42,43 MB
Release : 2013-04-02
Category : Mathematics
ISBN : 0486131734
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.
Author : Daniel D. Bonar
Publisher : American Mathematical Soc.
Page : 261 pages
File Size : 39,28 MB
Release : 2018-12-12
Category :
ISBN : 1470447827
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.