Approximation Theory: From Taylor Polynomials to Wavelets (Applied and Numerical Harmonic Analysis) - Brossura

Christensen, Ole

Brossura

ISBN 10: 0817636005 ISBN 13: 9780817636005

Casa editrice: Birkhäuser Boston, 2004

Riassunto

This concisely written book gives an elementary introduction to a classical area of mathematics---approximation theory---in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass' and Taylor's theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI's use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series "Approximation Theory: From Taylor Polynomials" to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.

Su questo libro

Informazioni sull?autore

Ole Christensen is the author of An Introduction to Frames and Riesz Bases (0-8176-4295-1).

Dalla quarta di copertina

This concisely written book gives an elementary introduction to a classical area of mathematics―approximation theory―in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.

Key features and topics:

* Description of wavelets in words rather than mathematical symbols

* Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems)

* Introduction to infinite series, with emphasis on approximation-theoretic aspects

* Introduction to Fourier analysis

* Numerous classical, illustrative examples and constructions

* Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints

* Minimal prerequisites: elementary calculus

* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series

Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.

Dettagli dell'edizione

• Editore: Birkhäuser Boston
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 0817636005
• ISBN 13: 9780817636005
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 172
• Contatto del produttore: non disponibile
• Persona responsabile: Palgrave Macmillan; ProductSafety@springernature.com; ; Crinan Street 4; London; N1 9XW; Regno Unito