(Almost) Impossible Integrals, Sums, and Series

(Almost) Impossible Integrals, Sums, and Series

Author: Cornel Ioan Vălean

Publisher: Springer

Published: 2019-05-10

Total Pages: 572

ISBN-13: 3030024628

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This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.


(Almost) Impossible Integrals, Sums, and Series

(Almost) Impossible Integrals, Sums, and Series

Author: Cornel Ioan Vălean

Publisher: Springer

Published: 2019-05-24

Total Pages: 0

ISBN-13: 9783030024611

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This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.


Irresistible Integrals

Irresistible Integrals

Author: George Boros

Publisher: Cambridge University Press

Published: 2004-06-21

Total Pages: 326

ISBN-13: 9780521796361

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This book, first published in 2004, uses the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.


Inside Interesting Integrals

Inside Interesting Integrals

Author: Paul J. Nahin

Publisher: Springer Nature

Published: 2020-06-27

Total Pages: 542

ISBN-13: 3030437884

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What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book, now in its second edition, is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.


Special Techniques For Solving Integrals: Examples And Problems

Special Techniques For Solving Integrals: Examples And Problems

Author: Khristo N Boyadzhiev

Publisher: World Scientific

Published: 2021-12-10

Total Pages: 401

ISBN-13: 9811235775

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This volume contains techniques of integration which are not found in standard calculus and advanced calculus books. It can be considered as a map to explore many classical approaches to evaluate integrals. It is intended for students and professionals who need to solve integrals or like to solve integrals and yearn to learn more about the various methods they could apply. Undergraduate and graduate students whose studies include mathematical analysis or mathematical physics will strongly benefit from this material. Mathematicians involved in research and teaching in areas related to calculus, advanced calculus and real analysis will find it invaluable.The volume contains numerous solved examples and problems for the reader. These examples can be used in classwork or for home assignments, as well as a supplement to student projects and student research.


Problems in Probability

Problems in Probability

Author: Albert N. Shiryaev

Publisher: Springer Science & Business Media

Published: 2012-08-07

Total Pages: 432

ISBN-13: 1461436885

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For the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises. Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the course of many years while working on many interesting topics. Many of the exercises resulted from discussions that took place during special seminars for graduate and undergraduate students. Many of the exercises included in the book contain helpful hints and other relevant information. Lastly, the author has included an appendix at the end of the book that contains a summary of the main results, notation and terminology from Probability Theory that are used throughout the present book. This Appendix also contains additional material from Combinatorics, Potential Theory and Markov Chains, which is not covered in the book, but is nevertheless needed for many of the exercises included here.


Geometric Inequalities

Geometric Inequalities

Author: Hayk Sedrakyan

Publisher: Springer

Published: 2017-05-27

Total Pages: 454

ISBN-13: 3319550802

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This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.


Table of Integrals, Series, and Products

Table of Integrals, Series, and Products

Author: I. S. Gradshteyn

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 1207

ISBN-13: 1483265641

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Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.


Measure, Integral and Probability

Measure, Integral and Probability

Author: Marek Capinski

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 229

ISBN-13: 1447136314

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This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.


An Introduction to the Harmonic Series and Logarithmic Integrals

An Introduction to the Harmonic Series and Logarithmic Integrals

Author: Ali Olaikhan

Publisher:

Published: 2021-04-15

Total Pages:

ISBN-13: 9781736736005

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This book provides a broad panel of results about the harmonic series and logarithmic integrals, some of which are, as far as I know, new in the mathematical literature. One goal of the book is to introduce the harmonic series in a way that will be approachable by anyone with a good knowledge of calculus-from high school students to researchers. The other goal is to present this book as a good reference resource for such series, as they are not commonly found in the standard textbooks and only very few books address them, apart from articles that are highly specialized and addressed in general to a small audience. The book will equip the reader with plenty of important tools that are necessary to solve (challenging) problems involving the harmonic series, and will also help the reader explore advanced results.