Infinite Sequences And Series

Author : Ludmila Bourchtein,Andrei Bourchtein
Publisher : Springer Nature
Page : 388 pages
File Size : 51,8 Mb
Release : 2021-11-13
Category : Mathematics
ISBN : 9783030794316

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Theory of Infinite Sequences and Series by Ludmila Bourchtein,Andrei Bourchtein Pdf

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 : 212 pages
File Size : 51,9 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9780486152042

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Infinite Sequences and Series by Konrad Knopp Pdf

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
Page : 0 pages
File Size : 46,6 Mb
Release : 2003
Category : Applied mathematics
ISBN : 0130457868

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Introduction to Real Analysis by William F. Trench Pdf

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
Page : 201 pages
File Size : 53,5 Mb
Release : 2018-05-17
Category : Mathematics
ISBN : 9781107059825

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A Student's Guide to Infinite Series and Sequences by Bernhard W. Bach, Jr. Pdf

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,Kee L. Teo,Bruce van Brunt
Publisher : Springer
Page : 476 pages
File Size : 51,5 Mb
Release : 2015-05-28
Category : Mathematics
ISBN : 9781493926510

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Real Analysis via Sequences and Series by Charles H.C. Little,Kee L. Teo,Bruce van Brunt Pdf

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 : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 500 pages
File Size : 54,7 Mb
Release : 2017-09-14
Category : Mathematics
ISBN : 0980232759

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Calculus by Gilbert Strang Pdf

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.

Author : James M Hyslop
Publisher : Courier Corporation
Page : 146 pages
File Size : 47,6 Mb
Release : 2012-05-11
Category : Mathematics
ISBN : 9780486154855

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Infinite Series by James M Hyslop Pdf

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 : Godfrey Harold Hardy
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 41,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821826492

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Divergent Series by Godfrey Harold Hardy Pdf

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 : Matthew Boelkins
Publisher : Createspace Independent Publishing Platform
Page : 560 pages
File Size : 45,8 Mb
Release : 2018-08-13
Category : Electronic
ISBN : 1724458329

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Active Calculus 2018 by Matthew Boelkins Pdf

Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.

Author : Daniel D. Bonar,Michael J. Khoury Jr.
Publisher : American Mathematical Soc.
Page : 261 pages
File Size : 55,6 Mb
Release : 2018-12-12
Category : Electronic
ISBN : 9781470447823

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Real Infinite Series by Daniel D. Bonar,Michael J. Khoury Jr. Pdf

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 : Charles H. C. Little,Kee L. Teo,Bruce van Brunt
Publisher : Springer Nature
Page : 258 pages
File Size : 48,6 Mb
Release : 2022-01-10
Category : Mathematics
ISBN : 9783030906467

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An Introduction to Infinite Products by Charles H. C. Little,Kee L. Teo,Bruce van Brunt Pdf

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 : Demetrios P. Kanoussis
Publisher : Unknown
Page : 141 pages
File Size : 55,5 Mb
Release : 2018-10-15
Category : Electronic
ISBN : 1728828600

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Infinite Series and Products by Demetrios P. Kanoussis Pdf

This book is a complete and self contained presentation on the fundamentals of Infinite Series and Products and has been designed to be an excellent supplementary textbook for University and College students in all areas of Math, Physics and Engineering.Infinite Series and Products is a branch of Applied Mathematics with an enormous range of applications in various areas of Applied Sciences and Engineering.The Theory of Infinite Series and Products relies heavily on the Theory of Infinite Sequences and therefore the reader of this text is urged to refresh his/her background on Sequences and related topics.In our e-book "Sequences of Real and Complex Numbers" the reader will find an excellent introduction to the subject that will help him/her to follow readily the matter developed in the current text.The content of this book is divided into 11 chapters.In Chapter 1 we introduce the Σ and the Π notation which is widely used to denote infinite series and infinite products, respectively. In Chapter 2 we present some basic, fundamental concepts and definitions pertaining to infinite series, such as convergent series, divergent series, the infinite geometric series, etc.In Chapter 3 we introduce the extremely important concept of Telescoping Series and show how this concept is used in order to find the sum of an infinite series in closed form (when possible). In this chapter we also present a list of Telescoping Trigonometric Series, which arise often on various applications.In Chapter 4 we develop some general Theorems on Infinite Series, for example deleting or inserting or grouping terms in a series, the Cauchy's necessary and sufficient condition for convergence, the widely used necessary test for convergence, the Harmonic Series, etc.In Chapter 5 we study the Convergence Test for Series with Positive Terms, i.e. the Comparison Test, the Limit Comparison Test, the D' Alembert's Test, the Cauchy's n-th Root Test, the Raabe's Test, the extremely important Cauchy's Integral Test, the Cauchy's Condensation Test etc.In Chapter 6 we study the Alternating Series and the investigation of such series with the aid of the Leibnitz's Theorem.In Chapter 7 we introduce and investigate the Absolutely Convergent Series and the Conditionally Convergent Series, state some Theorems on Absolute and Conditional Convergence and define the Cauchy Product of two absolutely convergent series.In Chapter 8 we give a brief review of Complex Numbers and Hyperbolic Functions, needed for the development of series from real to complex numbers. We define the Complex Numbers and their Algebraic Operations and give the three representations i.e. the Cartesian, the Polar and the Exponential representation of the Complex Numbers. The famous Euler's Formulas and the important De Moivre's Theorem are presented and various interesting applications are given. In this chapter we also define the so called Hyperbolic Functions of real and complex arguments.In Chapter 9 we introduce the theory of Series with Complex Terms, define the convergence in the complex plane and present a few important Theorems which are particularly useful for the investigation of series with complex terms.In Chapter 10 we define the Multiple Series and show how to treat simple cases of such series.In Chapter 11 we present the fundamentals of the Infinite Products, give the necessary and sufficient condition for the convergence of Infinite Products and define the Absolute and Conditional Convergence of Products. In particular in this chapter we present the Euler's product formula for the sine function and show how Euler used this product to solve the famous Basel problem.The 63 illustrative examples and the 176 characteristic problems are designed to help students sharpen their analytical skills on the subject.

Author : N. P. Bali
Publisher : Firewall Media
Page : 342 pages
File Size : 42,8 Mb
Release : 2007
Category : Electronic
ISBN : 8131800555

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Golden Sequences and Infinite Series by N. P. Bali Pdf

Author : Robert C. Wrede,Murray R Spiegel
Publisher : McGraw Hill Professional
Page : 460 pages
File Size : 52,8 Mb
Release : 2002-02-20
Category : Mathematics
ISBN : 0071375678

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Schaums Outline of Advanced Calculus, Second Edition by Robert C. Wrede,Murray R Spiegel Pdf

Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, theres Schaums Outlines. More than 40 million students have trusted Schaums to help them succeed in the classroom and on exams. Schaums is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaums Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaums highlights all the important facts you need to know. Use Schaums to shorten your study time-and get your best test scores! Schaums Outlines-Problem Solved.

Author : Konrad Knopp
Publisher : Legare Street Press
Page : 0 pages
File Size : 43,8 Mb
Release : 2022-10-26
Category : Electronic
ISBN : 101546646X

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Theory And Application Of Infinite Series by Konrad Knopp Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.