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Analysis and Synthesis in Mathematics

Author: Michael Otte

Publisher: Springer Science & Business Media

Published: 1997

Total Pages: 476

ISBN-13: 9780792345701

The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

The Cambridge Companion to Newton

Author: I. Bernard Cohen

Publisher: Cambridge University Press

Published: 2002-04-25

Total Pages: 785

ISBN-13: 1139826026

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Sir Isaac Newton (1642–1727) was one of the greatest scientists of all time, a thinker of extraordinary range and creativity who has left enduring legacies in mathematics and the natural sciences. In this volume a team of distinguished contributors examine all the main aspects of Newton's thought, including not only his approach to space, time, mechanics, and universal gravity in his Principia, his research in optics, and his contributions to mathematics, but also his more clandestine investigations into alchemy, theology, and prophecy, which have sometimes been overshadowed by his mathematical and scientific interests.

The Fundamentals of Analysis for Talented Freshmen

Author: Peter M. Luthy

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 84

ISBN-13: 3031024095

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This book assumes the students know some of the basic facts about Calculus. We are very rigorous and expose them to the proofs and the ideas which produce them. In three chapters, this book covers these number systems and the material usually found in a junior-senior advanced Calculus course. It is designed to be a one-semester course for "talented" freshmen. Moreover, it presents a way of thinking about mathematics that will make it much easier to learn more of this subject and be a good preparation for more of the undergraduate curriculum.

Analysis and Synthesis As Problem-Solving Methods

Author: National Council of Teachers of Mathematics

Publisher:

Published: 1969

Total Pages: 171

ISBN-13: 9780873531580

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Sound Analysis and Synthesis with R

Author: Jérôme Sueur

Publisher: Springer

Published: 2018-06-06

Total Pages: 637

ISBN-13: 3319776479

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Sound is almost always around us, anywhere, at any time, reaching our ears and stimulating our brains for better or worse. Sound can be the disturbing noise of a drill, a merry little tune sung by a friend, the song of a bird in the morning or a clap of thunder at night. The science of sound, or acoustics, studies all types of sounds and therefore covers a wide range of scientific disciplines, from pure to applied acoustics. Research dealing with acoustics requires a sound to be recorded, analyzed, manipulated and, possibly, changed. This is particularly, but not exclusively, the case in bioacoustics and ecoacoustics, two life sciences disciplines that attempt to understand and to eavesdrop on the sound produced by animals. Sound analysis and synthesis can be challenging for students, researchers and practitioners who have few skills in mathematics or physics. However, deciphering the structure of a sound can be useful in behavioral and ecological research – and also very amusing. This book is dedicated to anyone who wants to practice acoustics but does not know much about sound. Acoustic analysis and synthesis are possible, with little effort, using the free and open-source software R with a few specific packages. Combining a bit of theory, a lot of step-by-step examples and a few cases studies, this book shows beginners and experts alike how to record, read, play, decompose, visualize, parametrize, change, and synthesize sound with R, opening a new way of working in bioacoustics and ecoacoustics but also in other acoustic disciplines.

Sequential Logic

Author: Joseph Cavanagh

Publisher: CRC Press

Published: 2018-10-03

Total Pages: 912

ISBN-13: 1420007858

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Until now, there was no single resource for actual digital system design. Using both basic and advanced concepts, Sequential Logic: Analysis and Synthesis offers a thorough exposition of the analysis and synthesis of both synchronous and asynchronous sequential machines. With 25 years of experience in designing computing equipment, the author stresses the practical design of state machines. He clearly delineates each step of the structured and rigorous design principles that can be applied to practical applications. The book begins by reviewing the analysis of combinatorial logic and Boolean algebra, and goes on to define sequential machines and discuss traditional and alternative methods for synthesizing synchronous sequential machines. The final chapters deal with asynchronous sequential machines and pulse-mode asynchronous sequential machines. Because this volume is technology-independent, these techniques can be used in a variety of fields, such as electrical and computer engineering as well as nanotechnology. By presenting each method in detail, expounding on several corresponding examples, and providing over 500 useful figures, Sequential Logic is an excellent tutorial on analysis and synthesis procedures.

An Introduction to Multivariable Mathematics

Author: Leon Simon

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 132

ISBN-13: 3031023943

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The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in the first ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds. The book then concludes with further essential linear algebra, including the theory of determinants, eigenvalues, and the spectral theorem for real symmetric matrices, and further multivariable analysis, including the contraction mapping principle and the inverse and implicit function theorems. There is also an appendix which provides a nine-lecture introduction to real analysis. There are various ways in which the additional material in the appendix could be integrated into a course--for example in the Stanford Mathematics honors program, run as a four-lecture per week program in the Autumn Quarter each year, the first six lectures of the nine-lecture appendix are presented at the rate of one lecture per week in weeks two through seven of the quarter, with the remaining three lectures per week during those weeks being devoted to the main chapters of the text. It is hoped that the text would be suitable for a quarter or semester course for students who have scored well in the BC Calculus advanced placement examination (or equivalent), particularly those who are considering a possible major in mathematics. The author has attempted to make the presentation rigorous and complete, with the clarity and simplicity needed to make it accessible to an appropriately large group of students. Table of Contents: Linear Algebra / Analysis in R / More Linear Algebra / More Analysis in R / Appendix: Introductory Lectures on Real Analysis

Hadamard Matrix Analysis and Synthesis

Author: Rao K. Yarlagadda

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 120

ISBN-13: 1461563135

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Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing presents the basic concepts of Sylvester's construction of Hadamard matrices, the eigenvalue-eigenvector decompositions, along with its relationship to Fourier transforms. Relevant computational structures are included for those interested in implementing the Hadamard transform. The 2-dimensional Hadamard transform is discussed in terms of a 1- dimensional transform. The applications presented touch on statistics, error correction coding theory, communications signaling, Boolean function analysis and synthesis, image processing, sequence theory (maximal length binary sequences, composite sequences, and Thue-Morse sequences) and signal representation. An interesting application of the Hadamard transform to images is the Naturalness Preserving Transform (NPT), which is presented. The NPT provides a way to encode an image that can be reconstructed when it is transmitted through a noisy or an unfriendly channel. The potential applications of the Hadamard transform are wide and the book samples many of the important concepts among a vast field of applications of the transform. Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing serves as an excellent reference source and may be used as a text for advanced courses on the topic.

Analysis and Synthesis of Logics

Author: Walter Carnielli

Publisher: Springer Science & Business Media

Published: 2008-01-22

Total Pages: 612

ISBN-13: 1402067828

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Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.

Analysis and Synthesis of Computer Systems

Author: Erol Gelenbe

Publisher: World Scientific

Published: 2010-04-14

Total Pages: 324

ISBN-13: 1908978422

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Analysis and Synthesis of Computer Systems presents a broad overview of methods that are used to evaluate the performance of computer systems and networks, manufacturing systems, and interconnected services systems. Aside from a highly readable style that rigorously addresses all subjects, this second edition includes new chapters on numerical methods for queueing models and on G-networks, the latter being a new area of queuing theory that one of the authors has pioneered. This book will have a broad appeal to students, practitioners and researchers in several different areas, including practicing computer engineers as well as computer science and engineering students. Contents:Basic Tools of Probabilistic ModellingThe Queue with Server of Walking Type and Its Applications to Computer System ModellingQueueing Network ModelsQueueing Networks with Multiple Classes of Positive and Negative Customers and Product Form SolutionMarkov-Modulated QueuesDiffusion Approximation Methods for General Queueing NetworksApproximate Decomposition and Iterative Techniques for Closed Model SolutionSynthesis Problems in Single-Resource Systems: Characterisation and Control of Achievable PerformanceControl of Performance in Mutliple-Resource SystemsA Queue with Server of Walking Type Readership: Academic, students, professionals, telecommunications industry, operations management and industry. Keywords:Computer Systems;Computer Networks;Queuing Theory;Quality of Service;Performance Evaluation