On Sums on Numerical Series and the Fourier Series
Author : H. Germano Pavão
Publisher :
Page : 14 pages
File Size : 23,46 MB
Release : 2007
Category : Fourier analysis
ISBN :
Data-Driven Science and Engineering
Author : Steven L. Brunton
Publisher : Cambridge University Press
Page : 615 pages
File Size : 22,73 MB
Release : 2022-05-05
Category : Computers
ISBN : 1009098489
Book Description
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
A Student's Guide to Infinite Series and Sequences
Author : Bernhard W. Bach, Jr.
Publisher : Cambridge University Press
Page : 201 pages
File Size : 21,24 MB
Release : 2018-05-17
Category : Mathematics
ISBN : 1107059828
Book Description
An informal and practically focused introduction for undergraduate students exploring infinite series and sequences in engineering and the physical sciences. With a focus on practical applications in real world situations, it helps students to conceptualize the theory with real-world examples and to build their skill set.
Fourier Analysis
Author : Elias M. Stein
Publisher : Princeton University Press
Page : 326 pages
File Size : 16,55 MB
Release : 2011-02-11
Category : Mathematics
ISBN : 1400831237
Book Description
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Mathematics for Engineers and Scientists, 5th Edition
Author : Alan Jeffrey
Publisher : CRC Press
Page : 934 pages
File Size : 46,99 MB
Release : 1996-06-13
Category : Mathematics
ISBN : 9780412621505
Book Description
This edition of the book has been revised with the needs of present-day first-year engineering students in mind. Apart from many significant extensions to the text, attention has been paid to the inclusion of additional explanatory material wherever it seems likely to be helpful and to a lowering of the rigour of proofs given in previous editions - without losing sight of the necessity to justify results. New problem sets are included for use with commonly available software products. The mathematical requirements common to first year engineering students of every discipline are covered in detail with numerous illustrative worked examples given throughout the text. Extensive problem sets are given at the end of each chapter with answers to odd-numbered questions provided at the end of the book.
A First Course in Wavelets with Fourier Analysis
Author : Albert Boggess
Publisher : John Wiley & Sons
Page : 248 pages
File Size : 49,15 MB
Release : 2011-09-20
Category : Mathematics
ISBN : 1118211154
Book Description
A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
Fourier Analysis and Its Applications
Author : G. B. Folland
Publisher : American Mathematical Soc.
Page : 447 pages
File Size : 38,10 MB
Release : 2009
Category : Fourier analysis
ISBN : 0821847902
Book Description
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.
The Fourier Transform and Its Applications
Author : Ronald Newbold Bracewell
Publisher :
Page : pages
File Size : 29,87 MB
Release : 1978
Category : Fourier transformations
ISBN :
Book Description
Fourier Series
Author : Georgi P. Tolstov
Publisher : Courier Corporation
Page : 354 pages
File Size : 34,89 MB
Release : 2012-03-14
Category : Mathematics
ISBN : 0486141748
Book Description
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, and more. Over 100 problems. 1962 edition.
Differential Equations, Fourier Series, and Hilbert Spaces
Author : Raffaele Chiappinelli
Publisher : Walter de Gruyter GmbH & Co KG
Page : 220 pages
File Size : 27,19 MB
Release : 2023-09-18
Category : Mathematics
ISBN : 3111302520
Book Description
This book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on "Basic Mathematical Physics", and is organized as a short presentation of few important points on the arguments indicated in the title. It aims at completing the students' basic knowledge on Ordinary Differential Equations (ODE) - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations (PDE) of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable and consistent discussion of the latter argument, some elementary results on Hilbert spaces and series expansion in othonormal vectors are treated with some detail in Chapter 2. Prerequisites for a satisfactory reading of the present Notes are not only a course of Calculus for functions of one or several variables, but also a course in Mathematical Analysis where - among others - some basic knowledge of the topology of normed spaces is supposed to be included. For the reader's convenience some notions in this context are explicitly recalled here and there, and in particular as an Appendix in Section 1.4. An excellent reference for this general background material is W. Rudin's classic Principles of Mathematical Analysis. On the other hand, a complete discussion of the results on ODE and PDE that are here just sketched are to be found in other books, specifically and more deeply devoted to these subjects, some of which are listed in the Bibliography. In conclusion and in brief, my hope is that the present Notes can serve as a second quick reading on the theme of ODE, and as a first introductory reading on Fourier series, Hilbert spaces, and PDE
