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Author  Title  Accn#  Year  Item Type  Claims 
1 
Levi, Decio 
Symmetries and Integrability of Difference Equations 
I10153 
2017 
eBook 

2 
Maximon, Leonard C 
Differential and Difference Equations 
I09655 
2016 
eBook 

3 
Akhmet, Marat 
Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities 
I08930 
2017 
eBook 

4 
Akhmet, Marat 
Replication of Chaos in Neural Networks, Economics and Physics 
I08638 
2016 
eBook 

5 
Orlandi, Paolo 
Fluid Flow Phenomena 
I11112 
2000 
eBook 

6 
Luo, Albert C. J 
Discretization and Implicit Mapping Dynamics 
I07463 
2015 
eBook 

7 
Dong, ShiHai 
Wave Equations in Higher Dimensions 
I07415 
2011 
eBook 


1.


Title  Symmetries and Integrability of Difference Equations : Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016 
Author(s)  Levi, Decio;Rebelo, Rapha??l;Winternitz, Pavel 
Publication  Cham, 1. Imprint: Springer
2. Springer International Publishing, 2017. 
Description  X, 435 p. 67 illus., 26 illus. in color : online resource 
Abstract Note  This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, spacetime may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peerreviewed chapters in this volume serves as a selfcontained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers 
ISBN,Price  9783319566665 
Keyword(s)  1. ALGEBRA
2. Difference and Functional Equations
3. DIFFERENCE EQUATIONS
4. EBOOK
5. EBOOK  SPRINGER
6. Field theory (Physics)
7. Field Theory and Polynomials
8. FUNCTIONAL EQUATIONS
9. Numerical and Computational Physics, Simulation
10. PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I10153 


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2.


Title  Differential and Difference Equations : A Comparison of Methods of Solution 
Author(s)  Maximon, Leonard C 
Publication  Cham, 1. Imprint: Springer
2. 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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3.


Title  Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities 
Author(s)  Akhmet, Marat;Kashkynbayev, Ardak 
Publication  Singapore, 1. Imprint: Springer
2. 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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4.


Title  Replication of Chaos in Neural Networks, Economics and Physics 
Author(s)  Akhmet, Marat;Fen, Mehmet Onur 
Publication  Berlin, Heidelberg, 1. Imprint: Springer
2. Springer Berlin Heidelberg, 2016. 
Description  XV, 457 p. 141 illus., 133 illus. in color : online resource 
Abstract Note  This book presents detailed descriptions of chaos for continuoustime systems. It is the firstever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the indepth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics 
ISBN,Price  9783662475003 
Keyword(s)  1. Applications of Nonlinear Dynamics and Chaos Theory
2. BIOMATHEMATICS
3. Difference and Functional Equations
4. DIFFERENCE EQUATIONS
5. EBOOK
6. EBOOK  SPRINGER
7. ECONOMIC THEORY
8. Economic Theory/Quantitative Economics/Mathematical Methods
9. FUNCTIONAL EQUATIONS
10. Mathematical and Computational Biology
11. MECHANICS
12. Mechanics, Applied
13. STATISTICAL PHYSICS
14. Theoretical and Applied Mechanics

Item Type  eBook 
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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I08638 


On Shelf 




5.


Title  Fluid Flow Phenomena : A Numerical Toolkit 
Author(s)  Orlandi, Paolo 
Publication  Dordrecht, 1. Imprint: Springer
2. Springer Netherlands, 2000. 
Description  XII, 356 p. 10 illus : online resource 
Abstract Note  This book deals with the simulation of the incompressible NavierStokes equations for laminar and turbulent flows. The book is limited to explaining and employing the finite difference method. It furnishes a large number of source codes which permit to play with the NavierStokes equations and to understand the complex physics related to fluid mechanics. Numerical simulations are useful tools to understand the complexity of the flows, which often is difficult to derive from laboratory experiments. This book, then, can be very useful to scholars doing laboratory experiments, since they often do not have extra time to study the large variety of numerical methods; furthermore they cannot spend more time in transferring one of the methods into a computer language. By means of numerical simulations, for example, insights into the vorticity field can be obtained which are difficult to obtain by measurements. This book can be used by graduate as well as undergraduate students while reading books on theoretical fluid mechanics; it teaches how to simulate the dynamics of flow fields on personal computers. This will provide a better way of understanding the theory. Two chapters on Large Eddy Simulations have been included, since this is a methodology that in the near future will allow more universal turbulence models for practical applications. The direct simulation of the NavierStokes equations (DNS) is simple by finitedifferences, that are satisfactory to reproduce the dynamics of turbulent flows. A large part of the book is devoted to the study of homogeneous and wall turbulent flows. In the second chapter the elementary concept of finite difference is given to solve parabolic and elliptical partial differential equations. In successive chapters the 1D, 2D, and 3D NavierStokes equations are solved in Cartesian and cylindrical coordinates. Finally, Large Eddy Simulations are performed to check the importance of the subgrid scale models. Results for turbulent and laminar flows are discussed, with particular emphasis on vortex dynamics. This volume will be of interest to graduate students and researchers wanting to compare experiments and numerical simulations, and to workers in the mechanical and aeronautic industries 
ISBN,Price  9789401142816 
Keyword(s)  1. Classical and Continuum Physics
2. CLASSICAL MECHANICS
3. Continuum physics
4. Difference and Functional Equations
5. DIFFERENCE EQUATIONS
6. EBOOK
7. EBOOK  SPRINGER
8. FUNCTIONAL EQUATIONS
9. MATHEMATICAL PHYSICS
10. MECHANICS
11. Theoretical, Mathematical and Computational Physics

Item Type  eBook 
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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I11112 


On Shelf 




6.


Title  Discretization and Implicit Mapping Dynamics 
Author(s)  Luo, Albert C. J 
Publication  Berlin, Heidelberg, 1. Imprint: Springer
2. Springer Berlin Heidelberg, 2015. 
Description  X, 310 p. 46 illus., 26 illus. in color : online resource 
Abstract Note  This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the singlestep and multistep discretizations. The implicit dynamics of periodm solutions in discrete nonlinear systems are discussed. The book also offers a generalized??approach to finding??analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without timedelay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering 
ISBN,Price  9783662472750 
Keyword(s)  1. Applications of Nonlinear Dynamics and Chaos Theory
2. Difference and Functional Equations
3. DIFFERENCE EQUATIONS
4. DYNAMICAL SYSTEMS
5. DYNAMICS
6. EBOOK
7. EBOOK  SPRINGER
8. FUNCTIONAL EQUATIONS
9. STATISTICAL PHYSICS
10. VIBRATION
11. Vibration, Dynamical Systems, Control

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Call#  Status  Issued To  Return Due On  Physical Location 
I07463 


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7.
 
Title  Wave Equations in Higher Dimensions 
Author(s)  Dong, ShiHai 
Publication  Dordrecht, 1. Imprint: Springer
2. Springer Netherlands, 2011. 
Description  XXV, 295 p : online resource 
Abstract Note  Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader???s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of nonrelativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schr??dinger equation with positiondependent mass and the KaluzaKlein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography 
ISBN,Price  9789400719170 
Keyword(s)  1. Classical and Quantum Gravitation, Relativity Theory
2. Difference and Functional Equations
3. DIFFERENCE EQUATIONS
4. EBOOK
5. EBOOK  SPRINGER
6. FUNCTIONAL EQUATIONS
7. GRAVITATION
8. QUANTUM PHYSICS

Item Type  eBook 
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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I07415 


On Shelf 



 