By Ole Christensen

This concisely written booklet offers an effortless creation to a classical zone of mathematics—approximation theory—in a fashion that clearly ends up in the trendy box of wavelets. The exposition, pushed by means of principles instead of technical info and proofs, demonstrates the dynamic nature of arithmetic and the effect of classical disciplines on many parts of recent arithmetic and functions.

Key positive aspects and issues:

* Description of wavelets in phrases instead of mathematical symbols

* trouble-free creation to approximation utilizing polynomials (Weierstrass’ and Taylor’s theorems)

* advent to countless sequence, with emphasis on approximation-theoretic aspects

* advent to Fourier analysis

* various classical, illustrative examples and constructions

* dialogue of the position of wavelets in electronic sign processing and information compression, resembling the FBI’s use of wavelets to shop fingerprints

* minimum necessities: user-friendly calculus

* workouts that could be utilized in undergraduate and graduate classes on limitless sequence and Fourier series

*Approximation idea: From Taylor Polynomials to Wavelets* can be an outstanding textbook or self-study reference for college students and teachers in natural and utilized arithmetic, mathematical physics, and engineering. Readers will locate motivation and history fabric pointing towards complex literature and study themes in natural and utilized harmonic research and comparable areas.