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Harmonic analysis. Fourier analysis --- Fluid mechanics --- Plasma physics

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Ergodic theory. Information theory --- Mathematical control systems --- Numerical analysis --- Harmonic analysis. Fourier analysis --- Computer. Automation --- Engineering mathematics --- 51-7 --- Mathematics --- 51 --- Wiskunde --- Math --- Science --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Engineering mathematics - Problems, exercises, etc.

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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.

Approximation theory. --- Approximations and Expansions. --- Applications of Mathematics. --- Mathematics. --- Harmonic analysis. --- Fourier analysis. --- Functional analysis. --- Applied mathematics. --- Engineering mathematics. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Signal, Image and Speech Processing. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Math --- Science --- Analysis, Fourier --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Engineering --- Engineering analysis

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517.518.8 --- 519.64 --- 519.65 --- 681.3*G12 --- 681.3*G14 --- 681.3*G14 Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 519.65 Approximation. Interpolation --- Approximation. Interpolation --- 519.64 Numerical methods for solution of integral equations. Quadrature formulae --- Numerical methods for solution of integral equations. Quadrature formulae --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Orthogonal polynomials. --- Orthogonal polynomials --- Polynômes orthogonaux --- Fourier analysis --- Functions, Orthogonal --- Polynomials