**Author**: Kenneth B. Howell

**Publisher:** CRC Press

**ISBN:** 1498734138

**Category : **Mathematics

**Languages : **en

**Pages : **792

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**Book Description**
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

**Author**: Kenneth B. Howell

**Publisher:** CRC Press

**ISBN:** 1498734138

**Category : **Mathematics

**Languages : **en

**Pages : **792

**View**

**Book Description**
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

**Author**: Gilbert G. Walter

**Publisher:** CRC Press

**ISBN:** 9781584882275

**Category : **Mathematics

**Languages : **en

**Pages : **392

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**Book Description**
A bestseller in its first edition, Wavelets and Other Orthogonal Systems: Second Edition has been fully updated to reflect the recent growth and development of this field, especially in the area of multiwavelets. The authors have incorporated more examples and numerous illustrations to help clarify concepts. They have also added a considerable amount of new material, including sections addressing impulse trains, an alternate approach to periodic wavelets, and positive wavelet s. Other new discussions include irregular sampling in wavelet subspaces, hybrid wavelet sampling, interpolating multiwavelets, and several new statistics topics. With cutting-edge applications in data compression, image analysis, numerical analysis, and acoustics wavelets remain at the forefront of current research. Wavelets and Other Orthogonal Systems maintains its mathematical perspective in presenting wavelets in the same setting as other orthogonal systems, thus allowing their advantages and disadvantages to be seen more directly. Now even more student friendly, the second edition forms an outstanding text not only for graduate students in mathematics, but also for those interested in scientific and engineering applications.

**Author**: John R. Heckenlively

**Publisher:** MIT Press

**ISBN:** 0262083469

**Category : **Medical

**Languages : **en

**Pages : **1016

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**Book Description**
The long-awaited second edition of an authoritative reference on electrophysiologic vision testing, including detailed information on techniques and problems, basic physiology and anatomy, theoretical concepts, and clinical findings; with extensive new material. This authoritative text is the only comprehensive reference available on electrophysiologic vision testing, offering both practical information on techniques and problems as well as basic physiology and anatomy, theoretical concepts, and clinical correlations. The second edition, of the widely used text, offers extensive new material and updated information: 65 of the 84 chapters are completely new, with the changes reflecting recent advances in the field. The book will continue to be an essential resource for practitioners and scholars from a range of disciplines within vision science. The contributions not only cover new information—important material that is likely to become more important in the next decade—but also offer a long-range perspective on the field and its remarkable development in the last century. After discussing the history and background of clinical electrophysiology, the book introduces the anatomy of the retina and principles of cell biology in the visual pathways at the molecular, physiological, and biochemical levels. It relates these new findings to the techniques and interpretations of clinical tests, including the electro-oculogram (EOG), electroretinogram (ERG), and visual evoked potentials (VEP), which are discussed in detail, as are equipment, data acquisition and analysis, principles and protocols for clinical testing, diseases and dysfunction, and animal testing. Notable additions for this edition include chapters on the origin of electroretinogram waveforms, multifocal techniques, testing in standard laboratory animals, recent advances in analysis of abnormalities in disease, and the applications of these techniques to the study of genetic abnormalities.

**Author**: Steven G. Krantz

**Publisher:** CRC Press

**ISBN:** 9781584884835

**Category : **Mathematics

**Languages : **en

**Pages : **474

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**Book Description**
Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-depth understanding of the subject. Further complicating this, the field has not changed much over the past 150 years, prompting few authors to address the lackluster or overly complex dichotomy existing among the available texts. The enormously popular first edition of Real Analysis and Foundations gave students the appropriate combination of authority, rigor, and readability that made the topic accessible while retaining the strict discourse necessary to advance their understanding. The second edition maintains this feature while further integrating new concepts built on Fourier analysis and ideas about wavelets to indicate their application to the theory of signal processing. The author also introduces relevance to the material and surpasses a purely theoretical treatment by emphasizing the applications of real analysis to concrete engineering problems in higher dimensions. Expanded and updated, this text continues to build upon the foundations of real analysis to present novel applications to ordinary and partial differential equations, elliptic boundary value problems on the disc, and multivariable analysis. These qualities, along with more figures, streamlined proofs, and revamped exercises make this an even more lively and vital text than the popular first edition.

**Author**: Eric Stade

**Publisher:** John Wiley & Sons

**ISBN:** 1118165519

**Category : **Mathematics

**Languages : **en

**Pages : **520

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**Book Description**
A reader-friendly, systematic introduction to Fourieranalysis Rich in both theory and application, Fourier Analysispresents a unique and thorough approach to a key topic in advancedcalculus. This pioneering resource tells the full story of Fourieranalysis, including its history and its impact on the developmentof modern mathematical analysis, and also discusses essentialconcepts and today's applications. Written at a rigorous level, yet in an engaging style that doesnot dilute the material, Fourier Analysis brings twoprofound aspects of the discipline to the forefront: the wealth ofapplications of Fourier analysis in the natural sciences and theenormous impact Fourier analysis has had on the development ofmathematics as a whole. Systematic and comprehensive, the book: Presents material using a cause-and-effect approach,illustrating where ideas originated and what necessitated them Includes material on wavelets, Lebesgue integration, L2 spaces,and related concepts Conveys information in a lucid, readable style, inspiringfurther reading and research on the subject Provides exercises at the end of each section, as well asillustrations and worked examples throughout the text Based upon the principle that theory and practice arefundamentally linked, Fourier Analysis is the ideal text andreference for students in mathematics, engineering, and physics, aswell as scientists and technicians in a broad range of disciplineswho use Fourier analysis in real-world situations.

**Author**: James Kraft

**Publisher:** CRC Press

**ISBN:** 1315161001

**Category : **Computers

**Languages : **en

**Pages : **578

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**Book Description**
Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

**Author**: William P. Fox

**Publisher:** CRC Press

**ISBN:** 1351368249

**Category : **Business & Economics

**Languages : **en

**Pages : **430

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**Book Description**
Mathematical Modeling for Business Analytics is written for decision makers at all levels. This book presents the latest tools and techniques available to help in the decision process. The interpretation and explanation of the results are crucial to understanding the strengths and limitations of modeling. This book emphasizes and focuses on the aspects of constructing a useful model formulation, as well as building the skills required for decision analysis. The book also focuses on sensitivity analysis. The author encourages readers to formally think about solving problems by using a thorough process. Many scenarios and illustrative examples are provided to help solve problems. Each chapter is also comprehensively arranged so that readers gain an in-depth understanding of the subject which includes introductions, background information and analysis. Both undergraduate and graduate students taking methods courses in methods and discrete mathematical modeling courses will greatly benefit from using this book. Boasts many illustrative examples to help solve problems Provides many solutions for each chapter Emphasizes model formulation and helps create model building skills for decision analysis Provides the tools to support analysis and interpretation

**Author**: Steven G. Krantz

**Publisher:** CRC Press

**ISBN:** 1351642944

**Category : **Mathematics

**Languages : **en

**Pages : **323

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**Book Description**
Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathematical studies. The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in today’s world. The book explains: What goes behind a Google search algorithm How to calculate the odds in a lottery The value of Big Data How the nefarious Ponzi scheme operates Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.

**Author**: Crista Arangala

**Publisher:** CRC Press

**ISBN:** 1498770738

**Category : **Mathematics

**Languages : **en

**Pages : **304

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**Book Description**
Mathematical Modeling: Branching Beyond Calculus reveals the versatility of mathematical modeling. The authors present the subject in an attractive manner and flexibley manner. Students will discover that the topic not only focuses on math, but biology, engineering, and both social and physical sciences. The book is written in a way to meet the needs of any modeling course. Each chapter includes examples, exercises, and projects offering opportunities for more in-depth investigations into the world of mathematical models. The authors encourage students to approach the models from various angles while creating a more complete understanding. The assortment of disciplines covered within the book and its flexible structure produce an intriguing and promising foundation for any mathematical modeling course or for self-study. Key Features: Chapter projects guide more thorough investigations of the models The text aims to expand a student’s communication skills and perspectives WThe widespread applications are incorporated, even includinge biology and social sciences Its structure allows it to serve as either primary or supplemental text Uses Mathematica and MATLAB are used to develop models and computations

**Author**: Kenneth Kuttler

**Publisher:** CRC Press

**ISBN:** 1351727265

**Category : **Mathematics

**Languages : **en

**Pages : **604

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**Book Description**
Elementary Differential Equations presents the standard material in a first course on differential equations, including all standard methods which have been a part of the subject since the time of Newton and the Bernoulli brothers. The emphasis in this book is on theory and methods and differential equations as a part of analysis. Differential equations is worth studying, rather than merely some recipes to be used in physical science. The text gives substantial emphasis to methods which are generally presented first with theoretical considerations following. Essentially all proofs of the theorems used are included, making the book more useful as a reference. The book mentions the main computer algebra systems, yet the emphasis is placed on MATLAB and numerical methods which include graphing the solutions and obtaining tables of values. Featured applications are easily understood. Complete explanations of the mathematics and emphasis on methods for finding solutions are included.