Approximation Theory: From Taylor Polynomials to Wavelets - Paperback
by Ole Christensen (Author), Khadija Laghrida Christensen (Author)
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. Included are classical, illustrative examples and constructions, exercises, and a discussion of the role of wavelets to areas such as digital signal processing and data compression.
One of the few books to describe wavelets in words rather than mathematical symbols, the work will be an excellent textbook or self-study reference for advanced undergraduate/beginning graduate 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.
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.
Ole Christensen is the author of An Introduction to Frames and Riesz Bases (0-8176-4295-1).
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