From Continuous To Discrete
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From Continuous To Discrete
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Author : Dean Banerjee
language : en
Publisher:
Release Date : 2014-04
From Continuous To Discrete written by Dean Banerjee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04 with Mathematics categories.
A great resource for those who want to understand integer equations, difference equations, and digital electronics This book builds on algebra, differential equations, and analog electronics to better understand integer equations, difference equations, and digital electronics. Readers who are unfamiliar with differential equations or analog electronics will still be able to follow most of this book, although knowledge of them will certainly be a benefit. By building upon this knowledge and establishing some key connections between analog concepts and their discrete equivalents, it is possible to cover a large amount of topics in a relatively short amount of time while still maintaining a solid understanding. Some of the topics covered include modulus equations, music theory, integer equations, difference equations, the Mandelbrot set, Z transforms, sampling theory, analog to digital converters, digital filters, and digital communications. Although these topics may seem broad and scattered, the underlying mathematics that supports them is much more universal. Striking a good balance between practical applications and theoretical concepts, From Continuous to Discrete, gives practical examples and methods to real world problems with sufficient theoretical background to understand why the methods work.
From Continuous To Discrete
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Author : Dean Banerjee
language : en
Publisher:
Release Date : 2023-07-30
From Continuous To Discrete written by Dean Banerjee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-30 with categories.
Embark on a compelling mathematical journey that seamlessly transitions from the continuous domain of algebra, differential equations, and analog electronics to discover vital connections with their discrete counterparts: integer equations, difference equations, and digital electronics. While a familiarity with differential equations and analog electronics can certainly enrich the experience, it is not a prerequisite. By leveraging a foundation in continuous mathematics, this book skillfully navigates a diverse array of discrete subjects within a remarkably efficient timeframe, all the while nurturing a solid grasp of the underlying principles. Immerse yourself in an enthralling expedition through modulus equations, the harmonies of music theory, the intricacies of integer equations, the dance of difference equations, the enigmatic Mandelbrot set, the transformative power of Z transforms, the subtleties of sampling theory, the evolution of analog to digital converters, the delicate craftsmanship of digital filters, and the captivating realm of digital communications. Despite the apparent diversity of these topics, they share a common thread of foundational mathematics that unites them. Harmonizing practical applications with theoretical principles, "From Continuous to Discrete" offers effective methodologies for solving real-world problems while still providing a robust theoretical foundation that supports these methods.
Problems From The Discrete To The Continuous
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Author : Ross G. Pinsky
language : en
Publisher: Springer
Release Date : 2014-08-09
Problems From The Discrete To The Continuous written by Ross G. Pinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-09 with Mathematics categories.
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
Continuous And Discrete Modules
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Author : Saad H. Mohamed
language : en
Publisher: Cambridge University Press
Release Date : 1990-02-22
Continuous And Discrete Modules written by Saad H. Mohamed and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-02-22 with Mathematics categories.
Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory.
Excursions In Calculus
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Author : Robert M. Young
language : en
Publisher: Cambridge University Press
Release Date : 1992
Excursions In Calculus written by Robert M. Young and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book explores the interplay between the two main currents of mathematics, the continuous and the discrete.
Stochastic Control In Discrete And Continuous Time
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Author : Atle Seierstad
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-03
Stochastic Control In Discrete And Continuous Time written by Atle Seierstad and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-03 with Mathematics categories.
This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.
Discrete And Continuous Models In The Theory Of Networks
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Author : Fatihcan M. Atay
language : en
Publisher: Birkhäuser
Release Date : 2021-09-04
Discrete And Continuous Models In The Theory Of Networks written by Fatihcan M. Atay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-04 with Mathematics categories.
This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the state-of-the-art results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models - a subject that has been blooming in the last twenty years - are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book.
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics
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Author : John L. Bell
language : en
Publisher: Springer Nature
Release Date : 2019-09-09
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics written by John L. Bell and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Signals Systems Continuous And Discrete 4 E
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Author : Ziemer
language : en
Publisher: Pearson Education India
Release Date : 1998-09
Signals Systems Continuous And Discrete 4 E written by Ziemer and has been published by Pearson Education India this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09 with categories.
Impulsive Control In Continuous And Discrete Continuous Systems
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Author : Boris M. Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Impulsive Control In Continuous And Discrete Continuous Systems written by Boris M. Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Impulsive Control in Continuous and Discrete-Continuous Systems is an up-to-date introduction to the theory of impulsive control in nonlinear systems. This is a new branch of the Optimal Control Theory, which is tightly connected to the Theory of Hybrid Systems. The text introduces the reader to the interesting area of optimal control problems with discontinuous solutions, discussing the application of a new and effective method of discontinuous time-transformation. With a large number of examples, illustrations, and applied problems arising in the area of observation control, this book is excellent as a textbook or reference for a senior or graduate-level course on the subject, as well as a reference for researchers in related fields.
