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Discovering Mathematics

A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA® and Maple™

  • Textbook
  • © 2011

Overview

Authors:
  1. Jiří Gregor

    1. Department of Mathematics, Czech Technical University, Praha 6, Czech Republic

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    You can also search for this author in PubMed   Google Scholar

  2. Jaroslav Tišer

    1. Department of Mathematics, Czech Technical University, Praha 6, Czech Republic

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    You can also search for this author in PubMed   Google Scholar

  • May be applied to a wide range of disciplines

  • Contains a net of hyperlinked problems, hints, plans of solutions, definitions and theorems with solutions provided separately, thus enabling the reader to choose preferred level of difficulty

  • Problems mostly assume the use of advanced mathematical software, avoiding routine calculations wherever possible and enabling quick hypotheses checks when necessary

  • Includes supplementary material: sn.pub/extras

  • 26k Accesses

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction

    • Jiří Gregor, Jaroslav Tišer
    Pages 1-8

  3. Concepts

    1. Front Matter

      Pages 9-9
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    2. Mappings, Composite and Inverse Functions

      • Jiří Gregor, Jaroslav Tišer
      Pages 11-29

    3. Infinite Sequences

      • Jiří Gregor, Jaroslav Tišer
      Pages 31-56

    4. Periodicity

      • Jiří Gregor, Jaroslav Tišer
      Pages 57-71

  4. Tools

    1. Front Matter

      Pages 73-73
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    2. Finite Sums

      • Jiří Gregor, Jaroslav Tišer
      Pages 75-93

    3. Inequalities

      • Jiří Gregor, Jaroslav Tišer
      Pages 95-111

    4. Collocation and Least Squares Methods

      • Jiří Gregor, Jaroslav Tišer
      Pages 113-128

  5. Applications

    1. Front Matter

      Pages 129-129
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    2. Maximal and Minimal Values

      • Jiří Gregor, Jaroslav Tišer
      Pages 131-142

    3. Arcs and Curves

      • Jiří Gregor, Jaroslav Tišer
      Pages 143-162

    4. Center of Mass and Moments

      • Jiří Gregor, Jaroslav Tišer
      Pages 163-176

    5. Miscellaneous

      • Jiří Gregor, Jaroslav Tišer
      Pages 177-186

  6. Appendix

    1. Front Matter

      Pages 187-187
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    2. Answers to Problems

      • Jiří Gregor, Jaroslav Tišer
      Pages 189-241

  7. Back Matter

    Pages 243-247
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Keywords

About this book

The book contains chapters of structured approach to problem solving in mathematical analysis on an intermediate level. It follows the ideas of G.Polya and others, distinguishing between exercises and problem solving in mathematics. Interrelated concepts are connected by hyperlinks, pointing toward easier or more difficult problems so as to show paths of mathematical reasoning. Basic definitions and theorems can also be found by hyperlinks from relevant places. Problems are open to alternative formulations, generalizations, simplifications, and verification of hypotheses by the reader; this is shown to be helpful in solving problems. The book presents how advanced mathematical software can aid all stages of mathematical reasoning while the mathematical content remains in foreground. The authors show how software can contribute to deeper understanding and to enlarging the scope of teaching for students and teachers of mathematics.

Authors and Affiliations

  • Department of Mathematics, Czech Technical University, Praha 6, Czech Republic

    Jiří Gregor, Jaroslav Tišer

Bibliographic Information

  • Book Title: Discovering Mathematics

  • Book Subtitle: A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA® and Maple™

  • Authors: Jiří Gregor, Jaroslav Tišer

  • DOI: https://doi.org/10.1007/978-0-85729-064-9

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London Limited 2011

  • Softcover ISBN: 978-0-85729-054-0Published: 27 December 2010

  • eBook ISBN: 978-0-85729-064-9Published: 21 December 2010

  • Edition Number: 1

  • Number of Pages: VII, 247

  • Number of Illustrations: 16 b/w illustrations

  • Topics: Analysis

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