The authors provide discussions on such topics as differential equations, vector analysis, matrix algebra, complex analysis, boundary value problems and numerical methods. Features of the book include its clarity of presentation and the number and calibre of the exercises and examples. For flexibility in topic selection the book is divided into ...
Appropriate for an elementary undergraduate first course of varying lengths. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics.Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential ...
Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus. There are ...
This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, ...
The book was written from lectures given at the University of Cambridge and maintains throughout a high level of rigour whilst remaining a highly readable and lucid account. Topics covered include the Planchard theory of the existence of Fourier transforms of a function of L2 and Tauberian theorems. The influence of G. H. Hardy is apparent from ...
Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics. Emphasizing the physical interpretation of mathematical solutions, this book introduces ...
This classic text is one of the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. Includes 190 problems, approximately half with answers. 1893 edition.
This updated edition has been revised to include changes that consist of the addition of new material on integral transforms, discrete and fast Fourier transforms, series solutions, harmonic analysis, spherical harmonics, and a glance at some of the numerical techniques for the solution of boundary value problems. The text offers a full ...
Classic, graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition.
This monograph on generalised functions, Fourier integrals and Fourier series is intended for readers who, while accepting that a theory where each point is proved is better than one based on conjecture, nevertheless seek a treatment as elementary and free from complications as possible. Little detailed knowledge of particular mathematical ...
This reputable translation covers trigonometric Fourier series, orthogonal systems, double Fourier series, Bessel functions, the Eigenfunction method and its applications to mathematical physics, operations on Fourier series, more. Over 100 problems. 1962 edition.
The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the mid-nineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number ...
A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley begins with a physical problem and applies the results to different situations. 1966 edition ...
An incisive text combining theory and practical example to introduce Fourier series, orthogonal functions and applications of the Fourier method to boundary-value problems. Includes 570 exercises. Answers and notes.
This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 1970s, beginning with Fefferman's famous disc counterexample. The ...
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 ...
Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the ...
This book uses techniques of Fourier series and functional analysis to deal with certain problems in differential equations. The Fourier series and functional analysis are merely tools; the authors' real interest lies in the differential equations that they study. It has been known since 1967 that a wide variety of sets {ewikt of complex ...
This book is a self-contained introduction to Laplace Transforms and Fourier Series; emphasising the applications of Laplace transforms throughout, the book also provides coverage of the underlying pure mathematical structures. Alongside the Laplace transform, the notion of Fourier series is developed from first principles. Exercises are provided ...
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