A First Course in Wavelets with Fourier Analysis

  • Filename: a-first-course-in-wavelets-with-fourier-analysis.
  • ISBN: 9781118211151
  • Release Date: 2011-09-20
  • Number of pages: 336
  • Author: Albert Boggess
  • Publisher: John Wiley & Sons



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.

A First Course in Fourier Analysis

  • Filename: a-first-course-in-fourier-analysis.
  • ISBN: 9781139469036
  • Release Date: 2008-01-17
  • Number of pages:
  • Author: David W. Kammler
  • Publisher: Cambridge University Press



This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

A First Course in Harmonic Analysis

  • Filename: a-first-course-in-harmonic-analysis.
  • ISBN: 9780387275611
  • Release Date: 2006-03-30
  • Number of pages: 192
  • Author: Anton Deitmar
  • Publisher: Springer Science & Business Media



Affordable softcover second edition of bestselling title (over 1000 copies sold of previous edition) A primer in harmonic analysis on the undergraduate level Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Almost all proofs are given in full and all central concepts are presented clearly. Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. Introduces the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

A First Course in Numerical Analysis

  • Filename: a-first-course-in-numerical-analysis.
  • ISBN: 048641454X
  • Release Date: 2001
  • Number of pages: 606
  • Author: Anthony Ralston
  • Publisher: Courier Corporation



Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.

A First Course in Real Analysis

  • Filename: a-first-course-in-real-analysis.
  • ISBN: 0387974377
  • Release Date: 1997-03-07
  • Number of pages: 536
  • Author: Murray H. Protter
  • Publisher: Springer Science & Business Media



Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.

A First Course on Wavelets

  • Filename: a-first-course-on-wavelets.
  • ISBN: 1420049984
  • Release Date: 1996-09-12
  • Number of pages: 489
  • Author: Eugenio Hernandez
  • Publisher: CRC Press



Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: Several bases generated by a single function via translations and dilations Multiresolution analysis, compactly supported wavelets, and spline wavelets Band-limited wavelets Unconditionality of wavelet bases Characterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided, and constructions of splines wavelets are presented. Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.

A First Course in Computational Physics

  • Filename: a-first-course-in-computational-physics.
  • ISBN: 9781449636197
  • Release Date: 2011-01-28
  • Number of pages: 433
  • Author: Paul L. DeVries
  • Publisher: Jones & Bartlett Publishers



Computers and computation are extremely important components of physics and should be integral parts of a physicist s education. Furthermore, computational physics is reshaping the way calculations are made in all areas of physics. Intended for the physics and engineering students who have completed the introductory physics course, A First Course in Computational Physics, Second Edition covers the different types of computational problems using MATLAB with exercises developed around problems of physical interest. Topics such as root finding, Newton-Cotes integration, and ordinary differential equations are included and presented in the context of physics problems. A few topics rarely seen at this level such as computerized tomography, are also included. Within each chapter, the student is led from relatively elementary problems and simple numerical approaches through derivations of more complex and sophisticated methods, often culminating in the solution to problems of significant difficulty. The goal is to demonstrate how numerical methods are used to solve the problems that physicists face. Read the review published in Computing in Science & Engineering magazine, March/April 2011 (Vol. 13, No. 2) (c) 2011 IEEE, Published by the IEEE Computer Society"

A First Course in Partial Differential Equations with Complex Variables and Transform Methods

  • Filename: a-first-course-in-partial-differential-equations-with-complex-variables-and-transform-methods.
  • ISBN: 048668640X
  • Release Date: 1995
  • Number of pages: 446
  • Author: Hans F. Weinberger
  • Publisher: Courier Corporation



Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Topics include one-dimensional wave equation, properties of elliptic and parabolic equations, separation of variables and Fourier series, nonhomogeneous problems, and analytic functions of a complex variable. Solutions. 1965 edition.

A First Course on Numerical Methods

  • Filename: a-first-course-on-numerical-methods.
  • ISBN: 9780898719970
  • Release Date: 2011-07-14
  • Number of pages: 552
  • Author: Uri M. Ascher
  • Publisher: SIAM



Offers students a practical knowledge of modern techniques in scientific computing.

A First Course in Complex Analysis with Applications

  • Filename: a-first-course-in-complex-analysis-with-applications.
  • ISBN: 0763778346
  • Release Date: 2009-09-09
  • Number of pages: 193
  • Author: Patrick D. Shanahan
  • Publisher: Jones & Bartlett Learning



The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

A First Course in the Numerical Analysis of Differential Equations

  • Filename: a-first-course-in-the-numerical-analysis-of-differential-equations.
  • ISBN: 9780521734905
  • Release Date: 2009
  • Number of pages: 459
  • Author: A. Iserles
  • Publisher: Cambridge University Press



lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

A First Course in Functional Analysis

  • Filename: a-first-course-in-functional-analysis.
  • ISBN: 9781783083244
  • Release Date: 2014-11-01
  • Number of pages: 486
  • Author: Rabindranath Sen
  • Publisher: Anthem Press



This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.

The Fourier Transform and Its Applications

  • Filename: the-fourier-transform-and-its-applications.
  • ISBN: UCSD:31822031267685
  • Release Date: 2000
  • Number of pages: 616
  • Author: Ronald Newbold Bracewell
  • Publisher: McGraw-Hill Science Engineering



This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other fourier transform books in its emphasis on applications. Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms.The pedagogy in this classic text is excellent. The author has included such tools as the pictorial dictionary of transforms and bibliographic references. In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions. To aid students further, discussions of many of the problems can be found at the end of the book.

Fourier Analysis on Finite Abelian Groups

  • Filename: fourier-analysis-on-finite-abelian-groups.
  • ISBN: 9780817649166
  • Release Date: 2009-08-14
  • Number of pages: 159
  • Author: Bao Luong
  • Publisher: Springer Science & Business Media



This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.

A Second Course in Mathematical Analysis

  • Filename: a-second-course-in-mathematical-analysis.
  • ISBN: 0521523435
  • Release Date: 2002-10-24
  • Number of pages: 526
  • Author: J. C. Burkill
  • Publisher: Cambridge University Press



Classic calculus text reissued in Cambridge Mathematical Library. Clear, logical with many examples.

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