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Fourier Analysis and Related Topics
Aim of this note is to provide mathematical tools used in applications, and a certain theoretical background that would make other parts of mathematical analysis accessible to the student of physical science. Topics covered includes: Power series and trigonometric series, Fourier integrals, Pointwise convergence of Fourier series, Summability of Fourier series, Periodic distributions and Fourier series, Metric, normed and inner product spaces, Orthogonal expansions and Fourier series, Classical orthogonal systems and series, Eigenvalue problems related to differential equations, Fourier transformation of well-behaved functions, Fourier transformation of tempered distributions, General distributions and Laplace transforms.
Author(s): J. Korevaar
341 Pages 
A gentle introduction to Fourier analysis
This note covers fourier series, 1D fourier transform, 2D fourier transform, Convolution theorem, Understanding the sampling theorem.
Author(s): NA
101 Pages
Fourier Analysis for Beginners
This PDF book covers the following topics related to Fourier analysis : Mathematical Preliminaries, Sinusoids, Phasors, and Matrices, Fourier Analysis of Discrete Functions, The Frequency Domain, Continuous Functions, Fourier Analysis of Continuous Functions, Sampling Theory, Statistical Description of Fourier Coefficients, Hypothesis Testing for Fourier Coefficients, Directional Data Analysis, The Fourier Transform, Properties of The Fourier Transform, Signal Analysis, Fourier Optics.
Author(s): L.N. Thibos, Indiana University School of Optometry
201 Pages
Fourier Analysis by Prof. John A. Peacock
This PDF covers the following topics related to Fourier Analysis : Introduction, Introduction to the Dirac delta function, Fourier Series, Fourier Transforms, The Dirac delta function, Convolution, Parseval’s theorem for FTs, Correlations and cross-correlations, Fourier analysis in multiple dimensions, Digital analysis and sampling, Discrete Fourier Transforms & the FFT, Ordinary Differential Equations, Green’s functions, Partial Differential Equations and Fourier methods, Separation of Variables, PDEs in curved coordinates.
Author(s): Prof. John A. Peacock
91 Pages
Notes on Fourier Analysis byJeffrey Chang
This page covers the following topics related to Fourier Analysis : Introduction, Fourier Series, Periodicity, Monsieur Fourier, Finding Coefficients, Interpretation, Hot Rings, Orthogonality, Fourier Transforms, Motivation, Inversion and Examples, Duality and Symmetry, Scaling and Derivatives, Convolution.
Author(s): Jeffrey Chang, Graduate Student, Department of Physics, Harvard University
NA Pages
A Quick Introduction to Fourier Analysis by UCF
This PDF covers the following topics related to Fourier Analysis : Introduction, The Dirac Delta Function, The Fourier Transform, Fourier’s Theorem, Some Common Fourier Transforms, Properties of the Fourier Transform, Green’s Function for ODE, The Airy Function, The Heat Equation, The Wave Equation, The Fourier Series 16 4.1 Derivation, Properties of Fourier Series, The Heat Equation, Poisson Summation, Parseval’s Identity, The Fourier Transform, Causal Green’s Functions , Poisson’s Equation, The Brane World and Large Extra Dimensions, Appendix: Some Mathematical Niceties.
Author(s): University of Central Florida
48 Pages
Fourier analysis and distribution theory by Pu Zhao Kow
This PDF covers the following topics related to Fourier Analysis : Fourier series, Weak derivatives, 1-dimensional Fourier series, n-dimensional Fourier series, Pointwise convergence and Gibbs-Wilbraham phenomenon,Absolute convergence and uniform convergence, Pointwise convergence: Dini's criterion,. Cesàro summability of Fourier series, Fourier transform, Motivations, Schwartz space, Fourier transform on Schwartz space, The space of tempered distributions,The space of compactly supported distributions, Convolution of functions, Tensor products, Convolution of distributions, Convolution between distributions and functions, Convolution of distributions with non-compact supports, etc.
Author(s): Pu-Zhao Kow, Department of Mathematics and Statistics, University of Jyvaskyla, Finland
67 Pages
This note explains the following topics: Infinite Sequences, Infinite Series and Improper Integrals, Fourier Series, The One-Dimensional Wave Equation, The Two-Dimensional Wave Equation, Fourier Transform, Applications of the Fourier Transform, Bessel’s Equation.
Author(s): Arthur L. Schoenstadt
182 Pages
Fourier Analysis and Related Topics
Aim of this note is to provide mathematical tools used in applications, and a certain theoretical background that would make other parts of mathematical analysis accessible to the student of physical science. Topics covered includes: Power series and trigonometric series, Fourier integrals, Pointwise convergence of Fourier series, Summability of Fourier series, Periodic distributions and Fourier series, Metric, normed and inner product spaces, Orthogonal expansions and Fourier series, Classical orthogonal systems and series, Eigenvalue problems related to differential equations, Fourier transformation of well-behaved functions, Fourier transformation of tempered distributions, General distributions and Laplace transforms.
Author(s): J. Korevaar
341 Pages