Sergei Aliukov

Approximation Theory and Applications (eBook, ePUB)

Piecewise Linear and Generalized Functions

• Format: ePub

Produktbeschreibung

Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics. The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure. However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice. This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields. Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics. Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access. - Offers clear, comprehensive coverage of approximation theory and applications, with full consideration for newly evolved implications of piecewise linear and generalized functions - Features practical examples across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, and heat engineering, among other fields - Includes questions for review, sample problems, and a separate Solutions Manual hosted for instructor access - Considers numerical verification of approximation methods

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Produktdetails

• Verlag: Elsevier Science & Techn.
• Seitenzahl: 304
• Erscheinungstermin: 4. Februar 2025
• Englisch
• ISBN-13: 9780443291425
• Artikelnr.: 73252586

Autorenporträt

Sergei Aliukov is a Professor at South Ural State University, Chelyabinsk, Russia. He received his Ph.D. degree in mechanical engineering from South Ural State University in 1983 and the Doctor's degree in the field of mechanical engineering from the South Ural State University in 2005. He has more than 150 publications, and 10 inventions to his name, and his research interests include mathematical modeling processes and applications and non-linear dynamic systems. He is a Guest Editor of the Special Issue of the journal Mathematics.

Inhaltsangabe

1. Basic provisions and methods of approximation theory The main idea of
the approximation of the original function.
2. New methods of approximation of piecewise-linear and generalized
functions
3. Practical application and examples of using the developed approximation
methods
4. Numerical verification of the proposed approximation methods
5. Basics of a new macroeconomic theory with impulse and jump
characteristics