This concisely written book gives an elementary introduction to a
classical area of mathematicsa "approximation theorya "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
(Weierstrassa (TM) and Taylora (TM)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 FBIa (TM)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.
General
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