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 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: 9780521883405
  • Release Date: 2007
  • Number of pages: 864
  • Author: David W. Kammler
  • Publisher: Cambridge University Press



This book introduces applied mathematics through Fourier analysis, with applications to studying sampling theory, PDEs, probability, diffraction, musical tones, and wavelets.

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 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 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.

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.

Computational Neuroscience

  • Filename: computational-neuroscience.
  • ISBN: 9783319008615
  • Release Date: 2013-05-23
  • Number of pages: 135
  • Author: Hanspeter Mallot
  • Publisher: Springer Science & Business Media



Computational Neuroscience - A First Course provides an essential introduction to computational neuroscience and equips readers with a fundamental understanding of modeling the nervous system at the membrane, cellular, and network level. The book, which grew out of a lecture series held regularly for more than ten years to graduate students in neuroscience with backgrounds in biology, psychology and medicine, takes its readers on a journey through three fundamental domains of computational neuroscience: membrane biophysics, systems theory and artificial neural networks. The required mathematical concepts are kept as intuitive and simple as possible throughout the book, making it fully accessible to readers who are less familiar with mathematics. Overall, Computational Neuroscience - A First Course represents an essential reference guide for all neuroscientists who use computational methods in their daily work, as well as for any theoretical scientist approaching the field of computational neuroscience.

A First Course in Computational Physics

  • Filename: a-first-course-in-computational-physics.
  • ISBN: 9780763773144
  • Release Date: 2011-01-28
  • Number of pages: 433
  • Author: Paul L. DeVries
  • Publisher: Jones & Bartlett Learning



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) © 2011 IEEE, Published by the IEEE Computer Society

Principles of Harmonic Analysis

  • Filename: principles-of-harmonic-analysis.
  • ISBN: 9780387854687
  • Release Date: 2008-11-21
  • Number of pages: 333
  • Author: Anton Deitmar
  • Publisher: Springer Science & Business Media



The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. We ?rst prove both for locally compact abelian groups. For non-abelian groups we discuss the Plancherel Theorem in the general situation for Type I groups. The generalization of the Poisson Summation Formula to non-abelian groups is the S- berg Trace Formula, which we prove for arbitrary groups admitting uniform lattices. As examples for the application of the Trace F- mula we treat the Heisenberg group and the group SL (R). In the 2 2 former case the trace formula yields a decomposition of the L -space of the Heisenberg group modulo a lattice. In the case SL (R), the 2 trace formula is used to derive results like the Weil asymptotic law for hyperbolic surfaces and to provide the analytic continuation of the Selberg zeta function. We ?nally include a chapter on the app- cations of abstract Harmonic Analysis on the theory of wavelets. The present book is a text book for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up of the First Course in Harmonic Analysis, [9], or indep- dently, if the students have required a modest knowledge of Fourier Analysis already. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in [9].

A First Course in Calculus

  • Filename: a-first-course-in-calculus.
  • ISBN: 9781441985323
  • Release Date: 2012-09-17
  • Number of pages: 731
  • Author: Serge Lang
  • Publisher: Springer Science & Business Media



This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.

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