Books in Mathematical methods in physics

Statistical Mechanics

4th Edition
February 11, 2021
R.K. Pathria + 1 more
English
Paperback
9 7 8 0 0 8 1 0 2 6 9 2 2
eBook
9 7 8 0 0 8 1 0 2 6 9 3 9

Statistical Mechanics, Fourth Edition, explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. This valuable textbook introduces the reader to the historical context of the subject before delving deeper into chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. In the latest revision, the book's authors have updated the content throughout, including new coverage on biophysical applications, updated exercises, and computer simulations. This updated edition will be an indispensable to students and researchers of statistical mechanics, thermodynamics, and physics.

Derivative with a New Parameter

1st Edition
September 10, 2015
Abdon Atangana
English
Paperback
9 7 8 0 0 8 1 0 0 6 4 4 3
eBook
9 7 8 0 1 2 8 0 3 8 2 5 3

Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives. Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies.

Mathematical Methods for Physicists

7th Edition
December 26, 2011
George B. Arfken + 2 more
English
Hardback
9 7 8 0 1 2 3 8 4 6 5 4 9
eBook
9 7 8 0 1 2 3 8 4 6 5 5 6

Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.

Mathematical Physics with Partial Differential Equations

1st Edition
December 1, 2011
James Kirkwood
English
eBook
9 7 8 0 1 2 3 8 6 9 9 4 4

Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments. The text presents some of the most important topics and methods of mathematical physics. The premise is to study in detail the three most important partial differential equations in the field – the heat equation, the wave equation, and Laplace’s equation. The most common techniques of solving such equations are developed in this book, including Green’s functions, the Fourier transform, and the Laplace transform, which all have applications in mathematics and physics far beyond solving the above equations. The book’s focus is on both the equations and their methods of solution. Ordinary differential equations and PDEs are solved including Bessel Functions, making the book useful as a graduate level textbook. The book’s rigor supports the vital sophistication for someone wanting to continue further in areas of mathematical physics.

Harmonic Vector Fields

1st Edition
October 4, 2011
Sorin Dragomir + 1 more
English
Hardback
9 7 8 0 1 2 4 1 5 8 2 6 9
eBook
9 7 8 0 1 2 4 1 6 0 3 2 3

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ﬁelds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail.

Exploring Monte Carlo Methods

1st Edition
April 6, 2011
William L. Dunn + 1 more
English
Hardback
9 7 8 0 4 4 4 5 1 5 7 5 9
eBook
9 7 8 0 0 8 0 9 3 0 6 1 9

Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon’s needle problem" provides a unifying theme as it is repeatedly used to illustrate many features of Monte Carlo methods. This book provides the basic detail necessary to learn how to apply Monte Carlo methods and thus should be useful as a text book for undergraduate or graduate courses in numerical methods. It is written so that interested readers with only an understanding of calculus and differential equations can learn Monte Carlo on their own. Coverage of topics such as variance reduction, pseudo-random number generation, Markov chain Monte Carlo, inverse Monte Carlo, and linear operator equations will make the book useful even to experienced Monte Carlo practitioners.

Mathematica by Example

4th Edition
September 9, 2008
Martha L. Abell + 1 more
English
eBook
9 7 8 0 0 8 0 9 2 1 6 9 3

Mathematica by Example, 4e is designed to introduce the Mathematica programming language to a wide audience. This is the ideal text for all scientific students, researchers, and programmers wishing to learn or deepen their understanding of Mathematica. The program is used to help professionals, researchers, scientists, students and instructors solve complex problems in a variety of fields, including biology, physics, and engineering.

The Synchronized Dynamics of Complex Systems

1st Edition
Volume 6
February 5, 2008
Stefano Boccaletti
Albert C.J. Luo + 1 more
English
eBook
9 7 8 0 0 8 0 5 6 0 4 2 7

The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics. Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest.The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems.Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence.The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos.Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators.These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology.

Neutron Fluctuations

1st Edition
October 5, 2007
Imre Pazsit + 1 more
English
Hardback
9 7 8 0 0 8 0 4 5 0 6 4 3
eBook
9 7 8 0 0 8 0 5 5 0 4 3 5

The transport of neutrons in a multiplying system is an area of branching processes with a clear formalism. Neutron Fluctuations presents an account of the mathematical tools used in describing branching processes, which are then used to derive a large number of properties of the neutron distribution in multiplying systems with or without an external source. In the second part of the book, the theory is applied to the description of the neutron fluctuations in nuclear reactor cores as well as in small samples of fissile material. The question of how to extract information about the system under study is discussed. In particular the measurement of the reactivity of subcritical cores, driven with various Poisson and non-Poisson (pulsed) sources, and the identification of fissile material samples, is illustrated. The book gives pragmatic information for those planning and executing and evaluating experiments on such systems.

Handbook of Mathematical Fluid Dynamics

1st Edition
Volume 4
April 4, 2007
S. Friedlander + 1 more
English
eBook
9 7 8 0 0 8 0 4 7 8 3 0 2

This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.

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