Theory and Application of Infinite Series PDF Download

Author: Konrad Knopp
Publisher:
ISBN:
Category : Series, Infinite
Languages : en
Pages : 596

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Book Description
Trans from the 2nd German ed , pub 1923.

Author: Ludmila Bourchtein
Publisher: Springer Nature
ISBN: 3030794318
Category : Mathematics
Languages : en
Pages : 388

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Book Description
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: 0486152049
Category : Mathematics
Languages : en
Pages : 212

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Book Description
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: James M Hyslop
Publisher: Courier Corporation
ISBN: 0486154858
Category : Mathematics
Languages : en
Pages : 146

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Book Description
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: Bernhard W. Bach, Jr.
Publisher: Cambridge University Press
ISBN: 1107059828
Category : Mathematics
Languages : en
Pages : 201

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Book Description
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: Daniel D. Bonar
Publisher: American Mathematical Soc.
ISBN: 1470447827
Category : Mathematics
Languages : en
Pages : 278

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Book Description
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: Tian-Xiao He
Publisher: CRC Press
ISBN: 1000534332
Category : Mathematics
Languages : en
Pages : 458

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Book Description
This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

Author: Isidore Isaac Hirschman
Publisher: Courier Corporation
ISBN: 0486798240
Category : Mathematics
Languages : en
Pages : 193

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Book Description
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: Dan Pedoe
Publisher: Courier Corporation
ISBN: 0486131734
Category : Mathematics
Languages : en
Pages : 466

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Book Description
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: Giovanni Ferraro
Publisher: Springer Science & Business Media
ISBN: 0387734686
Category : Mathematics
Languages : en
Pages : 392

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Book Description
The manuscript gives a coherent and detailed account of the theory of series in the eighteenth and early nineteenth centuries. It provides in one place an account of many results that are generally to be found - if at all - scattered throughout the historical and textbook literature. It presents the subject from the viewpoint of the mathematicians of the period, and is careful to distinguish earlier conceptions from ones that prevail today.