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

Christensen, Ole

Softcover

ISBN 10: 0817636005 ISBN 13: 9780817636005

Verlag: Birkhäuser Boston, 2004

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

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

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Birkhäuser Boston
• Erscheinungsdatum: 2004
• Sprache: Englisch
• ISBN 10: 0817636005
• ISBN 13: 9780817636005
• Einband: Taschenbuch
• Anzahl der Seiten: 172
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland