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Haar Wavelets

With Applications

  • Book
  • © 2014

Overview

Authors:
  1. Ülo Lepik

    1. Institute of Mathematics, University of Tartu, Tartu, Estonia

  2. Helle Hein

    1. Institute of Computer Science, University of Tartu, Tartu, Estonia

  • Provides a comprehensive introduction to Haar wavelets
  • Presents a broad range of applications of Haar wavelet theory
  • Written by experts in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematical Engineering (MATHENGIN)

  • 31k Accesses

  • 194 Citations

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About this book

This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Preliminaries

    • Ülo Lepik, Helle Hein
    Pages 1-6

  3. Haar Wavelets

    • Ülo Lepik, Helle Hein
    Pages 7-20

  4. Solution of Ordinary Differential Equations (ODEs)

    • Ülo Lepik, Helle Hein
    Pages 21-43

  5. Stiff Equations

    • Ülo Lepik, Helle Hein
    Pages 45-57

  6. Integral Equations

    • Ülo Lepik, Helle Hein
    Pages 59-82

  7. Evolution Equations

    • Ülo Lepik, Helle Hein
    Pages 83-95

  8. Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

    • Ülo Lepik, Helle Hein
    Pages 97-105

  9. Fractional Calculus

    • Ülo Lepik, Helle Hein
    Pages 107-122

  10. Applying Haar Wavelets in the Optimal Control Theory

    • Ülo Lepik, Helle Hein
    Pages 123-135

  11. Buckling of Elastic Beams

    • Ülo Lepik, Helle Hein
    Pages 137-149

  12. Vibrations of Cracked Euler-Bernoulli Beams

    • Ülo Lepik, Helle Hein
    Pages 151-165

  13. Free Vibrations on Non-uniform and Axially Functionally Graded Euler-Bernoulli Beams

    • Ülo Lepik, Helle Hein
    Pages 167-176

  14. Vibrations of Functionally Graded Timoshenko Beams

    • Ülo Lepik, Helle Hein
    Pages 177-187

  15. Applying Haar Wavelets in Damage Detection Using Machine Learning Methods

    • Ülo Lepik, Helle Hein
    Pages 189-202

  16. Back Matter

    Pages 203-207
    Download chapter PDF
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Reviews

From the reviews:

“This textbook presents a comprehensive overview of different applications of the Haar wavelet method. … This useful book is mainly written for students and researchers in applied mathematics, physics and engineering. The authors demonstrate the efficiency and accuracy of the Haar wavelet method by numerous examples.” (Manfred Tasche, zbMATH, Vol. 1287, 2014)

Authors and Affiliations

  • Institute of Mathematics, University of Tartu, Tartu, Estonia

    Ülo Lepik

  • Institute of Computer Science, University of Tartu, Tartu, Estonia

    Helle Hein

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