Infinite Sequences And Series

Author : Ludmila Bourchtein
Publisher : Springer Nature
ISBN 13 : 3030794318
Total Pages : 388 pages
Book Rating : 4.16/5 ( download)

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Download or read book Theory of Infinite Sequences and Series written by Ludmila Bourchtein and published by Springer Nature. This book was released on 2021-11-13 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 0486152049
Total Pages : 212 pages
Book Rating : 4.42/5 ( download)

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Download or read book Infinite Sequences and Series written by Konrad Knopp and published by Courier Corporation. This book was released on 2012-09-14 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : William F. Trench
Publisher : Prentice Hall
ISBN 13 : 9780130457868
Total Pages : 0 pages
Book Rating : 4.68/5 ( download)

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Download or read book Introduction to Real Analysis written by William F. Trench and published by Prentice Hall. This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.

Author : Bernhard W. Bach, Jr.
Publisher : Cambridge University Press
ISBN 13 : 1107059828
Total Pages : 201 pages
Book Rating : 4.25/5 ( download)

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Download or read book A Student's Guide to Infinite Series and Sequences written by Bernhard W. Bach, Jr. and published by Cambridge University Press. This book was released on 2018-05-17 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 1493926519
Total Pages : 476 pages
Book Rating : 4.10/5 ( download)

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Download or read book Real Analysis via Sequences and Series written by Charles H.C. Little and published by Springer. This book was released on 2015-05-28 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

Author : Konrad Knopp
Publisher :
ISBN 13 :
Total Pages : 596 pages
Book Rating : 4.65/5 ( download)

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Download or read book Theory and Application of Infinite Series written by Konrad Knopp and published by . This book was released on 1928 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trans from the 2nd German ed , pub 1923.

Author : James M Hyslop
Publisher : Courier Corporation
ISBN 13 : 0486154858
Total Pages : 146 pages
Book Rating : 4.55/5 ( download)

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Download or read book Infinite Series written by James M Hyslop and published by Courier Corporation. This book was released on 2012-05-11 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Charles H. C. Little
Publisher : Springer Nature
ISBN 13 : 3030906469
Total Pages : 258 pages
Book Rating : 4.67/5 ( download)

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Download or read book An Introduction to Infinite Products written by Charles H. C. Little and published by Springer Nature. This book was released on 2022-01-10 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Godfrey Harold Hardy
Publisher : American Mathematical Soc.
ISBN 13 : 0821826492
Total Pages : 418 pages
Book Rating : 4.92/5 ( download)

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Download or read book Divergent Series written by Godfrey Harold Hardy and published by American Mathematical Soc.. This book was released on 2000 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface by J. E. Littlewood: "All [Hardy's] books gave him some degree of pleasure, but this one, his last, was his favourite. When embarking on it he told me that he believed in its value (as well he might), and also that he looked forward to the task with enthusiasm. He had actually given lectures on the subject at intervals ever since his return to Cambridge in 1931, and he had at one time or another lectured on everything in the book except Chapter XIII [TheEuler-MacLaurin sum formula] ... [I]n the early years of the century the subject [Divergent Series], while in no way mystical or unrigorous, was regarded as sensational, and about the present title, now colourless, there hung an aroma of paradox and audacity."

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
ISBN 13 : 9780980232752
Total Pages : 500 pages
Book Rating : 4.59/5 ( download)

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Download or read book Calculus written by Gilbert Strang and published by Wellesley-Cambridge Press. This book was released on 2017-09-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gilbert Strang's clear, direct style and detailed, intensive explanations make this textbook ideal as both a course companion and for self-study. Single variable and multivariable calculus are covered in depth. Key examples of the application of calculus to areas such as physics, engineering and economics are included in order to enhance students' understanding. New to the third edition is a chapter on the 'Highlights of calculus', which accompanies the popular video lectures by the author on MIT's OpenCourseWare. These can be accessed from math.mit.edu/~gs.