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Approximation Theory and Applications,

Edition 1 Piecewise Linear and Generalized Functions

Editors: By Sergei Aliukov

Publication Date: 10 Mar 2025

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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.

Key Features

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

About the author

By Sergei Aliukov, Professor, South Ural State University, Chelyabinsk, Russia

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

Title Reviews

"...presents the main provisions of approximation theory, and considers existing and new methods... 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." Review by Sergei Aliukov, MathSciNet, September 2025

Approximation Theory and Applications,

Editors: By Sergei Aliukov

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About the author

Title Reviews