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Strikingly different from typical presentations, Principles of Fourier Analysis provides an introduction to and comprehensive overview of the mathematical theory of Fourier analysis as it is used in applications in engineering, science, and mathematics. It presents the general results and formulas most useful to those who use Fourier analysis in their work, complete with indications of the limitations of those results and formulas. The author's uniquely accessible approach stimulates readers' understanding and appreciation of the fundamental concepts and helps them develop the ability to handle the more sophisticated mathematics ultimately required by Fourier analysis.

Harmonic analysis. Fourier analysis --- 517.518.5 --- Fourier analysis --- Analysis, Fourier --- Mathematical analysis --- Theory of the Fourier integral --- Fourier analysis. --- 517.518.5 Theory of the Fourier integral

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Harmonic analysis. --- Almost periodic functions. --- Fourier series. --- 517.518.5 --- 517.518.5 Theory of the Fourier integral --- Theory of the Fourier integral

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Fourier series --- 517.518.5 --- 517.518.4 --- wiskunde --- Fourier-analyse --- integraaltransformaties --- #TCPW W5.0 --- #TELE:SISTA --- Theory of the Fourier integral --- Trigonometric series --- 517.518.4 Trigonometric series --- 517.518.5 Theory of the Fourier integral --- FOURIER TRANSFORM

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Analytical spaces --- 517.518.5 --- Theory of the Fourier integral --- Topological imbeddings. --- Isometrics (Mathematics) --- Metric spaces. --- Lp spaces. --- Isometrics (Mathematics). --- 517.518.5 Theory of the Fourier integral --- Topological imbeddings --- Metric spaces --- Lp spaces --- Isométrie (Mathématiques) --- Espaces Lp --- Espaces métriques --- Espaces fonctionnels --- Function spaces

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The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.

Fourier series --- Integral transforms. --- 517.518.4 --- 517.518.5 --- Integral transforms --- #KVIV:BB --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Theory of the Fourier integral --- Fourier series. --- 517.518.5 Theory of the Fourier integral --- 517.518.4 Trigonometric series