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More (Almost) Impossible Integrals, Sums, and Series

A New Collection of Fiendish Problems and Surprising Solutions

  • Textbook
  • © 2023

Overview

Authors:
  1. Cornel Ioan Vălean

    1. Timis, Romania

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  • Presents a whole new collection of fiendish problems and solutions devised by the author
  • Contains over 500 integrals, sums, and series throughout the book, most being new
  • Includes ‘Hints’ sections to guide the reader toward obtaining a solution or to more information about a problem

Part of the book series: Problem Books in Mathematics (PBM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxxiv
    Download chapter PDF

  2. Integrals

    • Cornel Ioan Vălean
    Pages 1-76

  3. Hints

    • Cornel Ioan Vălean
    Pages 77-88

  4. Solutions

    • Cornel Ioan Vălean
    Pages 89-391

  5. Sums and Series

    • Cornel Ioan Vălean
    Pages 393-456

  6. Hints

    • Cornel Ioan Vălean
    Pages 457-469

  7. Solutions

    • Cornel Ioan Vălean
    Pages 471-811

  8. Back Matter

    Pages 813-816
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Keywords

About this book

This book, the much-anticipated sequel to (Almost) Impossible, Integrals, Sums, and Series, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author’s previous book, these fascinating mathematical problems are shown in new and engaging ways, 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. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers wholove a good integral or series and aren’t afraid of a challenge.

Authors and Affiliations

  • Timis, Romania

    Cornel Ioan Vălean

About the author

Cornel Ioan Vălean lives in Romania. While his background is in accounting and business informatics, he is also an independent researcher and self-educated in the area of the calculation of integrals, series and limits. He has published his work in the Journal of Classical Analysis and the Mediterranean Journal of Mathematics, and has made several contributions to the Problems section of the American Mathematical Monthly.

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