10 Best Books on Fourier Analysis

“A Guide to Distributions and Fourier Transforms” Book Review: The book presents fundamental principles and key concepts of the theory of distribution and Fourier transforms. The chapters of this book contain ideas, statements of theorems, and explanations of ideas behind the proofs. The latest topics like pseudodifferential operators, wave front sets, wavelets, and quasicrystals are discussed in detail. The applications of Fourier transform and featured techniques in partial differential equations and various problems are highlighted in this book. The multidimensional calculus and basic complex variables are used as tools for dealing with the featured concepts. The book is basically for the course on applied analysis or methods of mathematical physics.

“Fourier Analysis: An Introduction” Book Review: The book is intended for the beginners in mathematical analysis and Fourier analysis. It begins with a history of Fourier. The chapters of this book cover all the major topics related to genesis of Fourier analysis, basic properties of Fourier series, convergence of Fourier series, Fourier transform, finite Fourier analysis, and Dirichet’s theorem. The applications of Fourier series in various equations and theorems are highlighted in this book. Each chapter ends with a number of exercises and problems. The content of this book is illustrated and supported with several examples, figures, and graphs.

“Introduction to Fourier Analysis” Book Review: The book is a great source of information on Fourier analysis and FFT. The chapters of this book are majorly based on Fourier series for periodic functions, Fourier integral, Fourier Transform, successive differentiation, frequency-domain analysis, time-domain analysis, sampling theorems, discrete Fourier Transform, errors in Fourier Transforms estimation, and convolution. The topics like time and frequency domains, representation of waveforms in terms of complex exponentials and sinusoids, convolution, impulse response, frequency transfer function, modulation, and demodulation are thoroughly explained. For self-assessment and practice of the readers, the book consists of many exercises. The book will be suitable for the engineering students.

“Schaum’s Outline of Fourier Analysis with Applications to Boundary Value Problems” Book Review: The book is a well-structured and self-sufficient text, describing the relevant and most important topics of Fourier analysis. The chapters of this book describe all the major topics related to boundary value problems, Fourier series, orthogonal functions, gamma and beta functions, Fourier integrals, Bessel functions and applications, Legendre functions, Hermite and Laguerre polynomials. The applications of featured concepts and topics are highlighted. The topics presented in this book are reader friendly and explained quite efficiently. Many examples, solved problems, and practice exercises are included in this book for self-study and self-assessment of the readers.

“Fourier Analysis and Its Applications” Book Review: The book is a balanced piece of text, featuring both theory and applications of Fourier series, integrals, and Eigenfunction expansions. The initial chapters of this book cover all the major concepts of Bessel functions, Orthogonal polynomials, and Laplace transforms. The final section of the book deals with generalized functions and Green’s functions for ordinary and partial differential equations. The topics are explained with the help of figures and graphs. The book highlights numerous applications of Fourier analysis. The analyses featured in this book are used for developing concepts and reasoning behind various techniques. The book will be useful for the students and professionals of physics and engineering.

“Fourier Analysis on Finite Groups and Applications” Book Review: The book reflects the development of Fourier analysis on the real line and the circle, and then moves on to analogues of higher dimensional Euclidean space. The matrix groups such as the Heisenberg group of upper triangular 2×2 matrices and zeta functions on finite graphs are discussed in detail. It presents the applications of Fourier analysis on chemistry, error-correcting codes, data analysis, graph theory, number theory, and probability. The theory presented in this book is illustrated with the help of examples, pictures, and computer experiments. The book will be a great resource of the students of mathematics, engineering, and the physical sciences. It will be ideal for both beginners and researchers.

“Applied Mathematics: Data Compression, Spectral Methods, Fourier Analysis, Wavelets” Book Review: The book revolves around the basic aspects of applied mathematics. The chapters of this book are reader-friendly and easy-to-understand. The latest topics like information data manipulation, information coding, data approximation, data dimensionality reduction, data compression, time-frequency and time scale bases, image manipulation, and image noise removal are thoroughly explained. The methods like spectral representation and concept of wavelets are discussed. The content of this book is supported with examples and exercises. The book will be a good choice for teachers and the readers interested in self-study.

“Fourier Series” Book Review: The book aims at presenting the fundamental principles and basic concepts of Fourier series. The initial section of this book covers trigonometric Fourier series, orthogonal systems, convergence of trigonometric Fourier series, trigonometric series with decreasing coefficients, and operations on Fourier series. Moving on, the topics like summation of trigonometric Fourier series, double Fourier series and the Fourier integral, Bessel functions, Fourier-Bessel series, and Eigenfunction method are discussed. The chapters of this book describe each topic efficiently and the theorems are explained along with their proofs. Many solved and unsolved problems are given throughout the book. It highlights the applications of the Fourier series in mathematical physics. The book is basically for the students, professionals, and researchers of mathematics, physics, and engineering.

“Real Analysis and Applications: Including Fourier Series and the Calculus of Variations” Book Review: The book will be suitable for the undergraduate courses of mathematics and engineering. It is divided into five sections covering major topics of real numbers and limits, topology, calculus, Fourier series, and calculus of variations, respectively. The chapters of this book begin with detailed theory, thus enabling the readers in understanding basic concepts and core of real analysis. Moving on to Fourier series and calculus, the chapters deal with many mathematical tools. The applications of real analysis in various fields, subjects, and equations are clearly illustrated. The book is a great source of information, enriched with several problems, exercises, and hints for their solutions.