On Sums on Numerical Series and the Fourier Series PDF Download

Author: H. Germano Pavão
Publisher:
ISBN:
Category : Fourier analysis
Languages : en
Pages : 14

View

Book Description

Author: Rupert Lasser
Publisher: CRC Press
ISBN: 100010527X
Category : Mathematics
Languages : en
Pages : 300

View

Book Description
This work addresses all of the major topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. It stresses throughout the idea of homogenous Banach spaces and provides recent results. Techniques from functional analysis and measure theory are utilized.;College and university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.

Author: Horatio Scott Carslaw
Publisher:
ISBN:
Category : Definite integrals
Languages : en
Pages : 342

View

Book Description

Author: Cornelius Lanczos
Publisher: SIAM
ISBN: 1611974526
Category : Mathematics
Languages : en
Pages : 272

View

Book Description
Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. Many modern textbooks are filled with specialized terms and equations that may be confusing, but this book uses a friendly, conversational tone to clarify the material and engage the reader. The author meticulously develops the topic and uses 161 problems integrated into the text to walk the student down the simplest path to a solution. Intended for students of engineering, physics, and mathematics at both advanced undergraduate and graduate levels.

Author: Gerlind Plonka
Publisher: Springer Nature
ISBN: 3031350057
Category : Mathematics
Languages : en
Pages : 676

View

Book Description
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

Author: Georgi P. Tolstov
Publisher: Courier Corporation
ISBN: 0486141748
Category : Mathematics
Languages : en
Pages : 354

View

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.

Author: Steven L. Brunton
Publisher: Cambridge University Press
ISBN: 1009098489
Category : Computers
Languages : en
Pages : 615

View

Book Description
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Author: Sujaul Chowdhury
Publisher: Springer Nature
ISBN: 3031346645
Category : Science
Languages : en
Pages : 113

View

Book Description
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a function of time. This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform. This book: Aids readers to numerically calculate or obtain frequencies that are present in numerical data Explores the use of the discrete Fourier transform and demonstrates practical numerical calculation Utilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equation

Author: Richard Bernatz
Publisher: John Wiley & Sons
ISBN: 0470651377
Category : Mathematics
Languages : en
Pages : 336

View

Book Description
The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.

Author: Jean-Pierre Kahane
Publisher: Routledge
ISBN:
Category : Mathematics
Languages : en
Pages : 414

View

Book Description
Consists of two sections: the first, by Jean-Pierre Kahane, deals with Fourier series in the classical sense; the second, by Pierre-Gilles Lemarié-Rieusset, expounds the modern theory of wavelets. Includes original papers by Fourier, Dirichlet, Riemann, and Cantor.