Linear Differential Equations And Oscillators
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Linear Differential Equations And Oscillators
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Author : Luis Manuel Braga da Costa Campos
language : en
Publisher: CRC Press
Release Date : 2019-11-05
Linear Differential Equations And Oscillators written by Luis Manuel Braga da Costa Campos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Mathematics categories.
Linear Differential Equations and Oscillators is the first book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This first book consists of chapters 1 and 2 of the fourth volume. The first chapter covers linear differential equations of any order whose unforced solution can be obtained from the roots of a characteristic polynomial, namely those: (i) with constant coefficients; (ii) with homogeneous power coefficients with the exponent equal to the order of derivation. The method of characteristic polynomials is also applied to (iii) linear finite difference equations of any order with constant coefficients. The unforced and forced solutions of (i,ii,iii) are examples of some general properties of ordinary differential equations. The second chapter applies the theory of the first chapter to linear second-order oscillators with one degree-of-freedom, such as the mechanical mass-damper-spring-force system and the electrical self-resistor-capacitor-battery circuit. In both cases are treated free undamped, damped, and amplified oscillations; also forced oscillations including beats, resonance, discrete and continuous spectra, and impulsive inputs. Describes general properties of differential and finite difference equations, with focus on linear equations and constant and some power coefficients Presents particular and general solutions for all cases of differential and finite difference equations Provides complete solutions for many cases of forcing including resonant cases Discusses applications to linear second-order mechanical and electrical oscillators with damping Provides solutions with forcing including resonance using the characteristic polynomial, Green' s functions, trigonometrical series, Fourier integrals and Laplace transforms
Comparison And Oscillation Theory Of Linear Differential Equations By C A Swanson
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Author :
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Comparison And Oscillation Theory Of Linear Differential Equations By C A Swanson written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Oscillation Theory Of Partial Differential Equations
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Author : Norio Yoshida
language : en
Publisher: World Scientific
Release Date : 2008
Oscillation Theory Of Partial Differential Equations written by Norio Yoshida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This unique book is designed to provide the reader with an exposition of interesting aspects ? encompassing both rudimentary and advanced knowledge ? of oscillation theory of partial differential equations, which dates back to the publication in 1955 of a paper by Ph Hartman and A Wintner. The objective of oscillation theory is to acquire as much information as possible about the qualitative properties of solutions of differential equations through the analysis of laws governing the distribution of zeros of solutions as well as the asymptotic behavior of solutions of differential equations under consideration.This textbook on oscillation theory of partial differential equations is useful for both specialists and graduate students working in the field of differential equations. The book will also help to stimulate further progress in the study of oscillation theory and related subjects.
Theory Of Oscillators
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Author : Aleksandr Aleksandrovich Andronov
language : en
Publisher: Courier Dover Publications
Release Date : 1987
Theory Of Oscillators written by Aleksandr Aleksandrovich Andronov and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Science categories.
This classic offers detailed, thorough discussions of linear systems, nonlinear conservative systems, dynamic systems with a first-order differential equation, dynamic systems of the second order, much more.
Sturmian Theory For Ordinary Differential Equations
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Author : William T. Reid
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sturmian Theory For Ordinary Differential Equations written by William T. Reid 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.
Stability And Oscillations In Delay Differential Equations Of Population Dynamics
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Author : K. Gopalsamy
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-03-31
Stability And Oscillations In Delay Differential Equations Of Population Dynamics written by K. Gopalsamy 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 1992-03-31 with Mathematics categories.
This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.
U S Government Research Reports
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Author :
language : en
Publisher:
Release Date : 1962
U S Government Research Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Science categories.
Coupled Oscillator Based Active Array Antennas
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Author : Ronald J. Pogorzelski
language : en
Publisher: John Wiley & Sons
Release Date : 2012-07-18
Coupled Oscillator Based Active Array Antennas written by Ronald J. Pogorzelski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-18 with Technology & Engineering categories.
Describing an innovative approach to phased-array control in antenna design This book explores in detail phased-array antennas that use coupled-oscillator arrays, an arrangement featuring a remarkably simple beam steering control system and a major reduction in complexity compared with traditional methods of phased-array control. It brings together in one convenient, self-contained volume the many salient research results obtained over the past ten to fifteen years in laboratories around the world, including the California Institute of Technology's Jet Propulsion Laboratory. The authors examine the underlying theoretical framework of coupled-oscillator systems, clearly explaining the linear and nonlinear formalisms used in the development of coupled-oscillator arrays, while introducing a variety of state-of-the-art methodologies, design solutions, and tools for applying this control scheme. Readers will find: Numerous implementation examples of coupled-oscillator array prototypes A continuum model that permits application of diffusion theory to the analysis of phase dynamics A demonstration of the array behavior through experimental results that validate the linearized theory Examples of how incorporating coupling delay restores causality, including the latest published results Guidance on how to accurately analyze and optimize coupled-oscillator arrays using modern simulation tools A review of current developments, including the design of compact couple-oscillator array antennas Complete with 150 diagrams and photographs, Coupled-Oscillator Based Active-Array Antennas is a highly useful tutorial for antenna designers and a valuable reference for researchers and engineers wishing to learn about this cutting-edge technology.
El Ni O Southern Oscillation In A Changing Climate
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Author : Michael J. McPhaden
language : en
Publisher: John Wiley & Sons
Release Date : 2020-11-24
El Ni O Southern Oscillation In A Changing Climate written by Michael J. McPhaden and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-24 with Science categories.
Comprehensive and up-to-date information on Earth’s most dominant year-to-year climate variation The El Niño Southern Oscillation (ENSO) in the Pacific Ocean has major worldwide social and economic consequences through its global scale effects on atmospheric and oceanic circulation, marine and terrestrial ecosystems, and other natural systems. Ongoing climate change is projected to significantly alter ENSO's dynamics and impacts. El Niño Southern Oscillation in a Changing Climate presents the latest theories, models, and observations, and explores the challenges of forecasting ENSO as the climate continues to change. Volume highlights include: Historical background on ENSO and its societal consequences Review of key El Niño (ENSO warm phase) and La Niña (ENSO cold phase) characteristics Mathematical description of the underlying physical processes that generate ENSO variations Conceptual framework for understanding ENSO changes on decadal and longer time scales, including the response to greenhouse gas forcing ENSO impacts on extreme ocean, weather, and climate events, including tropical cyclones, and how ENSO affects fisheries and the global carbon cycle Advances in modeling, paleo-reconstructions, and operational climate forecasting Future projections of ENSO and its impacts Factors influencing ENSO events, such as inter-basin climate interactions and volcanic eruptions The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals. Find out more about this book from this Q&A with the editors.
Classical Mechanics
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Author : Christopher W. Kulp
language : en
Publisher: CRC Press
Release Date : 2025-08-22
Classical Mechanics written by Christopher W. Kulp and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-22 with Science categories.
Classical Mechanics: A Computational Approach with Examples using Python and Mathematica provides a unique, contemporary introduction to classical mechanics, with a focus on computational methods. In addition to providing clear and thorough coverage of key topics, this textbook includes integrated instructions and treatments of computation. This newly updated and revised second edition includes two new appendices instructing the reader in both the Python and Mathematica languages. All worked example problems in the second edition contain both Python and Mathematica code. New end-of-chapter problems explore the application of computational methods to classical mechanics problems. Full of pedagogy, it contains both analytical and computational example problems within the body of each chapter. The example problems teach readers both analytical methods and how to use computer algebra systems and computer programming to solve problems in classical mechanics. End-of-chapter problems allow students to hone their skills in problem solving with and without the use of a computer. The methods presented in this book can then be used by students when solving problems in other fields both within and outside of physics. It is an ideal textbook for undergraduate students in physics, mathematics, and engineering studying classical mechanics. Key Features: Gives readers the "big picture" of classical mechanics and the importance of computation in the solution of problems in physics Numerous example problems using both analytical and computational methods, as well as explanations as to how and why specific techniques were used Online resources containing specific example codes to help students learn computational methods and write their own algorithms A solutions manual is available via the Routledge Instructor Hub and all example codes in the book are available via the Support Material tab, and at the book’s GitHub page: https://github.com/vpagonis/Classical_Mechanics_2nd_Edition