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Fourier analysis and distributions = a first course with applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Fourier analysis and distributions/ by Rolf Brigola.
其他題名:	a first course with applications /
作者:	Brigola, Rolf.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xii, 543 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Analysis. -
電子資源:	https://doi.org/10.1007/978-3-031-81311-5
ISBN:	9783031813115

Fourier analysis and distributions = a first course with applications /
Brigola, Rolf.

Fourier analysis and distributionsa first course with applications /[electronic resource] :by Rolf Brigola. - Cham :Springer Nature Switzerland :2025. - xii, 543 p. :ill. (some col.), digital ;24 cm. - Texts in applied mathematics,v. 792196-9949 ;. - Texts in applied mathematics ;40..

Preface -- Introduction -- Trigonometric Polynomials, Fourier Coefficients -- Fourier Series -- Calculating with Fourier Series -- Application Examples for Fourier Series -- Discrete Fourier Transforms, First Applications -- Convergence of Fourier Series -- Fundamentals of Distribution Theory -- Application Examples for Distributions -- The Fourier Transform -- Basics of Linear Filters -- Further Applications of the Fourier Transform -- The Malgrange-Ehrenpreis Theorem -- Outlook on Further Concepts -- A The Residue Theorem and the Fundamental Theorem of Algebra -- B Tools from Integration Theory -- C Solutions to the Exercises -- References -- List of Symbols and Physical Quantities -- Index.

This comprehensive book offers an accessible introduction to Fourier analysis and distribution theory, blending classical mathematical theory with a wide range of practical applications. Designed for undergraduate and beginning Master's students in mathematics and engineering. Key Features: Balanced Approach: The book is structured to include both theoretical and application-based chapters, providing readers with a solid understanding of the fundamentals alongside real-world scenarios. Diverse Applications: Topics include Fourier series, ordinary differential equations, AC circuit calculations, heat and wave equations, digital signal processing, and image compression. These applications demonstrate the versatility of Fourier analysis in solving complex problems in engineering, physics, and computational sciences. Advanced Topics: The text covers convolution theorems, linear filters, the Shannon Sampling Theorem, multi-carrier transmission with OFDM, wavelets, and a first insight into quantum mechanics. It also introduces readers to the finite element method (FEM) and offers an elementary proof of the Malgrange-Ehrenpreis theorem, showcasing advanced concepts in a clear and approachable manner. Practical Insights: Includes a detailed discussion of Hilbert spaces, orthonormal systems, and their applications to topics like the periodic table in chemistry and the structure of water molecules. The book also explores continuous and discrete wavelet transforms, providing insights into modern data compression and denoising techniques. Comprehensive Support: Appendices cover essential theorems in function theory and Lebesgue integration, complete with solutions to exercises, a reference list, and an index. With its focus on practical applications, clear explanations, and a wealth of examples, Fourier Analysis and Distributions bridges the gap between classical theory and modern computational methods. This text will appeal to students and practitioners looking to deepen their understanding of Fourier analysis and its far-reaching implications in science and engineering.

ISBN: 9783031813115

Standard No.: 10.1007/978-3-031-81311-5doiSubjects--Topical Terms:

669490
Analysis.

LC Class. No.: QA403.5

Dewey Class. No.: 515.2433

Fourier analysis and distributions = a first course with applications /
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505 0 $a Preface -- Introduction -- Trigonometric Polynomials, Fourier Coefficients -- Fourier Series -- Calculating with Fourier Series -- Application Examples for Fourier Series -- Discrete Fourier Transforms, First Applications -- Convergence of Fourier Series -- Fundamentals of Distribution Theory -- Application Examples for Distributions -- The Fourier Transform -- Basics of Linear Filters -- Further Applications of the Fourier Transform -- The Malgrange-Ehrenpreis Theorem -- Outlook on Further Concepts -- A The Residue Theorem and the Fundamental Theorem of Algebra -- B Tools from Integration Theory -- C Solutions to the Exercises -- References -- List of Symbols and Physical Quantities -- Index.
520 $a This comprehensive book offers an accessible introduction to Fourier analysis and distribution theory, blending classical mathematical theory with a wide range of practical applications. Designed for undergraduate and beginning Master's students in mathematics and engineering. Key Features: Balanced Approach: The book is structured to include both theoretical and application-based chapters, providing readers with a solid understanding of the fundamentals alongside real-world scenarios. Diverse Applications: Topics include Fourier series, ordinary differential equations, AC circuit calculations, heat and wave equations, digital signal processing, and image compression. These applications demonstrate the versatility of Fourier analysis in solving complex problems in engineering, physics, and computational sciences. Advanced Topics: The text covers convolution theorems, linear filters, the Shannon Sampling Theorem, multi-carrier transmission with OFDM, wavelets, and a first insight into quantum mechanics. It also introduces readers to the finite element method (FEM) and offers an elementary proof of the Malgrange-Ehrenpreis theorem, showcasing advanced concepts in a clear and approachable manner. Practical Insights: Includes a detailed discussion of Hilbert spaces, orthonormal systems, and their applications to topics like the periodic table in chemistry and the structure of water molecules. The book also explores continuous and discrete wavelet transforms, providing insights into modern data compression and denoising techniques. Comprehensive Support: Appendices cover essential theorems in function theory and Lebesgue integration, complete with solutions to exercises, a reference list, and an index. With its focus on practical applications, clear explanations, and a wealth of examples, Fourier Analysis and Distributions bridges the gap between classical theory and modern computational methods. This text will appeal to students and practitioners looking to deepen their understanding of Fourier analysis and its far-reaching implications in science and engineering.
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