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Author  Title  Accn#  Year  Item Type  Claims 
1 
Grigorieva, Elena V 
Asymptotic Representation of Relaxation Oscillations in Lasers 
I10175 
2017 
eBook 

2 
Schuch, Dieter 
Quantum Theory from a Nonlinear Perspective 
I10013 
2018 
eBook 

3 
Maximon, Leonard C 
Differential and Difference Equations 
I09655 
2016 
eBook 

4 
Papachristou, Costas J 
Aspects of Integrability of Differential Systems and Fields 
I09485 
2019 
eBook 

5 
Akhmet, Marat 
Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities 
I08930 
2017 
eBook 

6 
TahirKheli, Raza 
Ordinary Differential Equations 
I08768 
2018 
eBook 

7 
Coley, A.A 
Dynamical Systems and Cosmology 
I11465 
2003 
eBook 

8 
Contopoulos, George 
Order and Chaos in Dynamical Astronomy 
I11280 
2002 
eBook 

9 
Vakakis, Alexander F 
Normal Modes and Localization in Nonlinear Systems 
I10997 
2001 
eBook 

10 
Lynch, Stephen 
Dynamical Systems with Applications using MAPLE 
I10751 
2001 
eBook 


1.


Title  Asymptotic Representation of Relaxation Oscillations in Lasers 
Author(s)  Grigorieva, Elena V;Kaschenko, Sergey A 
Publication  Cham, Springer International Publishing, 2017. 
Description  VIII, 230 p. 73 illus : online resource 
Abstract Note  In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differentialdifference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of largeamplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations 
ISBN,Price  9783319428604 
Keyword(s)  1. DIFFERENTIAL EQUATIONS
2. EBOOK
3. EBOOK  SPRINGER
4. Engineering Fluid Dynamics
5. FLUID MECHANICS
6. LASERS
7. MATHEMATICAL PHYSICS
8. Optics, Lasers, Photonics, Optical Devices
9. ORDINARY DIFFERENTIAL EQUATIONS
10. PHOTONICS
11. Theoretical, Mathematical and Computational Physics

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I10175 


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2.


Title  Quantum Theory from a Nonlinear Perspective : Riccati Equations in Fundamental Physics 
Author(s)  Schuch, Dieter 
Publication  Cham, Springer International Publishing, 2018. 
Description  XIV, 258 p. 15 illus., 7 illus. in color : online resource 
Abstract Note  This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under timereversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phaseamplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from BoseEinsteincondensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws 
ISBN,Price  9783319655949 
Keyword(s)  1. Applications of Nonlinear Dynamics and Chaos Theory
2. DIFFERENTIAL EQUATIONS
3. EBOOK
4. EBOOK  SPRINGER
5. History and Philosophical Foundations of Physics
6. ORDINARY DIFFERENTIAL EQUATIONS
7. PHYSICS
8. QUANTUM PHYSICS
9. STATISTICAL PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I10013 


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3.


Title  Differential and Difference Equations : A Comparison of Methods of Solution 
Author(s)  Maximon, Leonard C 
Publication  Cham, Springer International Publishing, 2016. 
Description  XV, 162 p : online resource 
Abstract Note  This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations  variation of constants, reduction of order, Laplace transforms and generating functions  bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green???s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer???s rule, a detailed consideration of the role of the superposition principal in the Green???s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients 
ISBN,Price  9783319297361 
Keyword(s)  1. APPLIED MATHEMATICS
2. Difference and Functional Equations
3. DIFFERENCE EQUATIONS
4. DIFFERENTIAL EQUATIONS
5. EBOOK
6. EBOOK  SPRINGER
7. ENGINEERING MATHEMATICS
8. FUNCTIONAL EQUATIONS
9. Mathematical and Computational Engineering
10. Mathematical Applications in the Physical Sciences
11. Mathematical Methods in Physics
12. MATHEMATICAL PHYSICS
13. ORDINARY DIFFERENTIAL EQUATIONS
14. PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I09655 


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5.


Title  Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities 
Author(s)  Akhmet, Marat;Kashkynbayev, Ardak 
Publication  Singapore, Springer Singapore, 2017. 
Description  XI, 166 p. 31 illus., 26 illus. in color : online resource 
Abstract Note  This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the righthandside or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for ??beginners and experts in the field. For the former group of specialists, that is, undergraduate and graduate students, the book will be useful since it provides a strong impression that bifurcation theory can be developed not only for discrete and continuous systems, but those which combine these systems in very different ways. The latter group of specialists will find in this book several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impacts, differential equations with piecewise constant arguments of generalized type and Filippov systems. A significant benefit of the present book is expected to be for those who consider bifurcations in systems with impulses since they are presumably nonautonomous systems 
ISBN,Price  9789811031809 
Keyword(s)  1. Applications of Nonlinear Dynamics and Chaos Theory
2. Control and Systems Theory
3. Control engineering
4. Difference and Functional Equations
5. DIFFERENCE EQUATIONS
6. DIFFERENTIAL EQUATIONS
7. Dynamical Systems and Ergodic Theory
8. DYNAMICS
9. EBOOK
10. EBOOK  SPRINGER
11. ERGODIC THEORY
12. FUNCTIONAL EQUATIONS
13. ORDINARY DIFFERENTIAL EQUATIONS
14. STATISTICAL PHYSICS

Item Type  eBook 
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Call#  Status  Issued To  Return Due On  Physical Location 
I08930 


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6.


Title  Ordinary Differential Equations : Mathematical Tools for Physicists 
Author(s)  TahirKheli, Raza 
Publication  Cham, Springer International Publishing, 2018. 
Description  XXII, 408 p. 65 illus., 1 illus. in color : online resource 
Abstract Note  This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE ). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail. 
ISBN,Price  9783319764061 
Keyword(s)  1. DIFFERENTIAL EQUATIONS
2. EBOOK
3. EBOOK  SPRINGER
4. Mathematical Applications in the Physical Sciences
5. Mathematical Methods in Physics
6. MATHEMATICAL PHYSICS
7. MECHANICS
8. Mechanics, Applied
9. ORDINARY DIFFERENTIAL EQUATIONS
10. PHYSICS
11. Theoretical and Applied Mechanics

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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I08768 


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7.


Title  Dynamical Systems and Cosmology 
Author(s)  Coley, A.A 
Publication  Dordrecht, Springer Netherlands, 2003. 
Description  VIII, 195 p : online resource 
Abstract Note  Dynamical systems theory is especially wellsuited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations. In this book we discuss cosmological models as dynamical systems, with particular emphasis on applications in the early Universe. We point out the important role of selfsimilar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss the dynamical properties of cosmological models derived from the string effective action. This book is a valuable source for all graduate students and professional astronomers who are interested in modern developments in cosmology 
ISBN,Price  9789401703277 
Keyword(s)  1. Applications of Mathematics
2. APPLIED MATHEMATICS
3. Astronomy, Observations and Techniques
4. Astronomy???Observations
5. Classical and Quantum Gravitation, Relativity Theory
6. COSMOLOGY
7. DIFFERENTIAL EQUATIONS
8. EBOOK
9. EBOOK  SPRINGER
10. ENGINEERING MATHEMATICS
11. GRAVITATION
12. MATHEMATICAL PHYSICS
13. Observations, Astronomical
14. ORDINARY DIFFERENTIAL EQUATIONS
15. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I11465 


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8.


Title  Order and Chaos in Dynamical Astronomy 
Author(s)  Contopoulos, George 
Publication  Berlin, Heidelberg, Springer Berlin Heidelberg, 2002. 
Description  XIII, 624 p : online resource 
Abstract Note  The study of orbits in dynamical systems and the theory of order and chaos has progressed enormously over the last few decades. It thus became an essential tool in dynamical astronomy. The book is the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology. This book, addressing especially the astrophysics, is also written as a textbook on dynamical systems for students in physics 
ISBN,Price  9783662049174 
Keyword(s)  1. ASTRONOMY
2. Astronomy, Astrophysics and Cosmology
3. ASTROPHYSICS
4. Astrophysics and Astroparticles
5. COMPLEX SYSTEMS
6. DIFFERENTIAL EQUATIONS
7. DYNAMICAL SYSTEMS
8. Dynamical Systems and Ergodic Theory
9. DYNAMICS
10. EBOOK
11. EBOOK  SPRINGER
12. ERGODIC THEORY
13. MATHEMATICAL PHYSICS
14. ORDINARY DIFFERENTIAL EQUATIONS
15. STATISTICAL PHYSICS
16. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I11280 


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9.


Title  Normal Modes and Localization in Nonlinear Systems 
Author(s)  Vakakis, Alexander F 
Publication  Dordrecht, Springer Netherlands, 2001. 
Description  VI, 294 p : online resource 
Abstract Note  The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integralpartial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin?? earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a singlemode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the singlemode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape ??n, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape ??n. Therefore, in the case of largeamplitude oscillations, the singlemode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996 
ISBN,Price  9789401724524 
Keyword(s)  1. CLASSICAL MECHANICS
2. DIFFERENTIAL EQUATIONS
3. DYNAMICAL SYSTEMS
4. DYNAMICS
5. EBOOK
6. EBOOK  SPRINGER
7. MECHANICS
8. ORDINARY DIFFERENTIAL EQUATIONS
9. PARTIAL DIFFERENTIAL EQUATIONS
10. VIBRATION
11. Vibration, Dynamical Systems, Control

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Call#  Status  Issued To  Return Due On  Physical Location 
I10997 


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10.
 
Title  Dynamical Systems with Applications using MAPLE 
Author(s)  Lynch, Stephen 
Publication  Boston, MA, 1. Birkh??user Boston
2. Imprint: Birkh??user, 2001. 
Description  XIII, 399 p. 83 illus : online resource 
Abstract Note  "The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple." ???UK Nonlinear News (Review of First Edition) "The book will be useful for all kinds of dynamical systems courses???. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. ??? [It] is well written and a pleasure to read, which is helped by its attention to historical background." ???Mathematical Reviews (Review of First Edition) Since the first edition of this book was published in 2001, Maple??? has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gr??bner bases, and chaos synchronization. The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters. The book has a handson approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author???s website. Additional applications and further links of interest may be found at Maplesoft???s Application Center. Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering. ISBN 9780817643898 ?? Also by the author: Dynamical Systems with Applications using MATLAB??, ISBN 9780817643218 Dynamical Systems with Applications using Mathematica??, ISBN 9780817644826 
ISBN,Price  9781489928498 
Keyword(s)  1. Applications of Mathematics
2. APPLIED MATHEMATICS
3. COMPLEXITY
4. COMPUTATIONAL COMPLEXITY
5. Computational Mathematics and Numerical Analysis
6. Computer mathematics
7. DIFFERENTIAL EQUATIONS
8. EBOOK
9. EBOOK  SPRINGER
10. ENGINEERING MATHEMATICS
11. Mathematical Modeling and Industrial Mathematics
12. MATHEMATICAL MODELS
13. MATHEMATICAL PHYSICS
14. ORDINARY DIFFERENTIAL EQUATIONS
15. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I10751 


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