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Problems in Real Analysis

Advanced Calculus on the Real Axis

  • Teodora-Liliana Radulescu
  • Vicentiu D. Radulescu
  • Titu Andreescu

Table of contents

  1. Front Matter
    Pages 1-15
  2. Sequences, Series, and Limits

    1. Front Matter
      Pages 1-2
    2. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 3-57
    3. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 59-114
    4. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 115-135
  3. Qualitative Properties of Continuous and Differentiable Functions

    1. Front Matter
      Pages 237-238
    2. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 139-181
    3. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 183-259
  4. Applications to Convex Functions and Optimization

    1. Front Matter
      Pages 261-262
    2. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 263-287
    3. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 289-310
  5. Antiderivatives, Riemann Integrability, and Applications

    1. Front Matter
      Pages 311-312
    2. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 313-324
    3. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 325-372
    4. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 373-414
  6. Appendix

    1. Front Matter
      Pages 415-416
    2. Teodora-Liliana T. Rădulescu, Vicenţiu D. Rădulescu, Titu Andreescu
      Pages 417-420
  7. Back Matter
    Pages 1-31

About this book

Introduction

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

Key features:

*Uses competition-inspired problems as a platform for training typical inventive skills;

*Develops basic valuable techniques for solving problems in mathematical analysis on the real axis and provides solid preparation for deeper study of real analysis;

*Includes numerous examples and interesting, valuable historical accounts of ideas and methods in analysis;

*Offers a systematic path to organizing a natural transition that bridges elementary problem-solving activity to independent exploration of new results and properties.

Keywords

Carleman's inequalities Differentiability Hardy's inequalities Real Analysis analysis mathematical physics numerical analysis optimization

Authors and affiliations

  • Teodora-Liliana Radulescu
    • 1
  • Vicentiu D. Radulescu
    • 2
  • Titu Andreescu
    • 3
  1. 1."Fratii Buzesti" CollegeUniversity CraiovaCraiovaRomania
  2. 2.Fac. Mathematics & Computer ScienceUniversity of CraiovaCraiovaRomania
  3. 3.School of Natural Sciences &University of Texas, DallasRichardsonUSA

Bibliographic information