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Advanced Mathematical Methods for Scientists and Engineers I
Author: Carl M. Bender, Steven A. Orszag
Publisher: Springer Science & Business Media
ISBN: 1475730691
Pages: 593
Year: 2013-03-09
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A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Applied Analysis
Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 0486319261
Pages: 576
Year: 2013-04-22
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Classic work on analysis and design of finite processes for approximating solutions of analytical problems. Features algebraic equations, matrices, harmonic analysis, quadrature methods, and much more.
The Theory of Intermolecular Forces
Author: Anthony Stone
Publisher: OUP Oxford
ISBN: 0191652954
Pages: 352
Year: 2013-01-31
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The theory of intermolecular forces has advanced very greatly in recent years. It has become possible to carry out accurate calculations of intermolecular forces for molecules of useful size, and to apply the results to important practical applications such as understanding protein structure and function, and predicting the structures of molecular crystals. The Theory of Intermolecular Forces sets out the mathematical techniques that are needed to describe and calculate intermolecular interactions and to handle the more elaborate mathematical models. It describes the methods that are used to calculate them, including recent developments in the use of density functional theory and symmetry-adapted perturbation theory. The use of higher-rank multipole moments to describe electrostatic interactions is explained in both Cartesian and spherical tensor formalism, and methods that avoid the multipole expansion are also discussed. Modern ab initio perturbation theory methods for the calculation of intermolecular interactions are discussed in detail, and methods for calculating properties of molecular clusters and condensed matter for comparison with experiment are surveyed.
Geometric Control of Mechanical Systems
Author: Francesco Bullo, Andrew D. Lewis
Publisher: Springer Science & Business Media
ISBN: 0387221956
Pages: 727
Year: 2004-11-04
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The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
Complex Variables
Author: Mark J. Ablowitz, Athanssios S. Fokas
Publisher: Cambridge University Press
ISBN: 0521485231
Pages: 664
Year: 1997-02-13
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In addition to being mathematically elegant, complex variables provide a powerful tool for solving problems that are either very difficult or virtually impossible to solve in any other way. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, numerical methods and more. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems. The authors also provide an extensive array of applications, illustrative examples and homework exercises. This book is ideal for use in introductory undergraduate and graduate level courses in complex variables.
A Random Walk in Science,
Author: Robert L. Weber
Publisher: CRC Press
ISBN: 085498027X
Pages: 206
Year: 1973-01-01
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This anthology provides an insight into the wit and intellect of the scientific mind through a blend of amusing and serious contributions written by and about scientists. The contributions record changing attitudes within science and mirror the interactions of science with society.
Black Bodies and Quantum Cats
Author: Jennifer Ouellette
Publisher: Penguin
ISBN: 1101221402
Pages: 336
Year: 2005-12-01
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Physics, once known as "natural philosophy," is the most basic science, explaining the world we live in, from the largest scale down to the very, very, very smallest, and our understanding of it has changed over many centuries. In Black Bodies and Quantum Cats, science writer Jennifer Ouellette traces key developments in the field, setting descriptions of the fundamentals of physics in their historical context as well as against a broad cultural backdrop. Newton’s laws are illustrated via the film Addams Family Values, while Back to the Future demonstrates the finer points of special relativity. Poe’s "The Purloined Letter" serves to illuminate the mysterious nature of neutrinos, and Jeanette Winterson’s novel Gut Symmetries provides an elegant metaphorical framework for string theory. An enchanting and edifying read, Black Bodies and Quantum Cats shows that physics is not an arcane field of study but a profoundly human endeavor—and a fundamental part of our everyday world.
Modern Aspects of Random Matrix Theory
Author: Van H. Vu
Publisher: American Mathematical Society
ISBN: 0821894714
Pages: 176
Year: 2014-07-16
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The theory of random matrices is an amazingly rich topic in mathematics. Random matrices play a fundamental role in various areas such as statistics, mathematical physics, combinatorics, theoretical computer science, number theory and numerical analysis. This volume is based on lectures delivered at the 2013 AMS Short Course on Random Matrices, held January 6-7, 2013 in San Diego, California. Included are surveys by leading researchers in the field, written in introductory style, aiming to provide the reader a quick and intuitive overview of this fascinating and rapidly developing topic. These surveys contain many major recent developments, such as progress on universality conjectures, connections between random matrices and free probability, numerical algebra, combinatorics and high-dimensional geometry, together with several novel methods and a variety of open questions.
The H-Function
Author: A.M. Mathai, Ram Kishore Saxena, Hans J. Haubold
Publisher: Springer Science & Business Media
ISBN: 1441909168
Pages: 268
Year: 2009-10-10
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TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
On Three Levels
Author: Mark Fannes, Christan Maes, Andre Verbeure
Publisher: Springer Science & Business Media
ISBN: 1461524601
Pages: 485
Year: 2012-12-06
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This volume contains the proceedings of a five-day NATO Advanced Research Workshop "On Three Levels, the mathematical physics of micro-, meso-, and macro phenomena," conducted from July 19 to 23 in Leuven, Belgium. The main purpose of the workshop was to bring together and to confront where relevant, classical and quantum approaches in the rigorous study of the relation between the various levels of physical description. The reader will find here discussions on a variety of topics involving a broad range of scales. For the micro-level, contributions are presented on models of reaction-diffusion pro cesses, quantum groups and quantum spin systems. The reports on quantum disorder, the quantum Hall effect, semi-classical approaches of wave mechanics and the random Schrodinger equation can be situated on the meso-level. Discussions on macroscopic quantum effects and large scale fluctuations are dealing with the macroscopic level of description. These three levels are however not independent and emphasis is put on relating these scales of description. This is especially the case for the contributions on kinetic and hydrodynamicallimits, the discussions on large deviations and the strong and weak coupling limits. The advisory board was composed of J.L. Lebowitz, J.T. Lewis and E.H. Lieb. The organizing committee was formed by Ph.A. Martin, G.L. Sewell, E.R. Speer and A.
Sources of Quantum Mechanics
Author: B. L. Van Der Waerden
Publisher: Courier Corporation
ISBN: 048645892X
Pages: 430
Year: 2007
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Originally published: Amsterdam: North-Holland Pub. Co., 1967.
Networks on Networks
Author: Allen G. Hunt, Stefano Manzoni
Publisher: Morgan & Claypool Publishers
ISBN: 1681741598
Pages: 177
Year: 2016-01-01
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Order from chaos is simultaneously a mantra of physics and a reality in biology. Physicist Norman Packard suggested that life developed and thrives at the edge of chaos. Questions remain, however, as to how much practical knowledge of biology can be traced to existing physical principles, and how much physics has to change in order to address the complexity of biology. Phil Anderson, a physics Nobel laureate, contributed to popularizing a new notion of the end of “reductionism.” In this view, it is necessary to abandon the quest of reducing complex behavior to known physical results, and to identify emergent behaviors and principles. In the present book, however, we have sought physical rules that can underlie the behavior of biota as well as the geochemistry of soil development. We looked for fundamental principles, such as the dominance of water flow paths with the least cumulative resistance, that could maintain their relevance across a wide range of spatial and temporal scales, together with the appropriate description of solute transport associated with such flow paths. Thus, ultimately, we address both nutrient and water transport limitations of processes from chemical weathering to vascular plant growth. The physical principles guiding our effort are established in different, but related concepts and fields of research, so that in fact our book applies reductionist techniques guided by analogy. The fact that fundamental traits extend across biotic and abiotic processes, i.e., the same fluid flow rate is relevant to both, but that distinctions in topology of the connected paths lead to dramatic differences in growth rates, helps unite the study of these nominally different disciplines of geochemistry and geobiology within the same framework. It has been our goal in writing this book to share the excitement of learning, and one of the most exciting portions to us has been the ability to bring some order to the question of the extent to which soils can facilitate plant growth, and what limitations on plant sizes, metabolism, occurrence, and correlations can be formulated thereby. While we bring order to the soil constraints on growth , we also generate some uncertainties in the scaling relationships of plant growth and metabolism. Although we have made an first attempt to incorporate edaphic constraints into allometric scaling, this is but an initial foray into the forest.
Quantum Electrodynamics
Author: Richard P. Feynman
Publisher: CRC Press
ISBN: 0429972873
Pages: 212
Year: 2018-02-19
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This classic work presents the main results and calculational procedures of quantum electrodynamics in a simple and straightforward way. Designed for the student of experimental physics who does not intend to take more advanced graduate courses in theoretical physics, the material consists of notes on the third of a three-semester course given at the California Institute of Technology.
Differential Geometrical Theory of Statistics
Author: Frédéric Barbaresco, Frank Nielsen
Publisher: MDPI
ISBN: 3038424242
Pages: 472
Year: 2018-04-06
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This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy
Fundamentals of Semiconductors
Author: Peter YU, Manuel Cardona
Publisher: Springer Science & Business Media
ISBN: 3642007104
Pages: 778
Year: 2010-04-07
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Excellent bridge between general solid-state physics textbook and research articles packed with providing detailed explanations of the electronic, vibrational, transport, and optical properties of semiconductors "The most striking feature of the book is its modern outlook ... provides a wonderful foundation. The most wonderful feature is its efficient style of exposition ... an excellent book." Physics Today "Presents the theoretical derivations carefully and in detail and gives thorough discussions of the experimental results it presents. This makes it an excellent textbook both for learners and for more experienced researchers wishing to check facts. I have enjoyed reading it and strongly recommend it as a text for anyone working with semiconductors ... I know of no better text ... I am sure most semiconductor physicists will find this book useful and I recommend it to them." Contemporary Physics Offers much new material: an extensive appendix about the important and by now well-established, deep center known as the DX center, additional problems and the solutions to over fifty of the problems at the end of the various chapters.