Book Description
This book deals with the derivation of the Fokker-Planck equation, methods of solving it and some of its applications. Various methods such as the simulation method, the eigenfunction expansion, numerical integration, the variational method, and the matrix continued-fraction method are discussed. This is the first time that this last method, which is very effective in dealing with simple Fokker-Planck equations having two variables, appears in a textbook. The methods of solution are applied to the statistics of a simple laser model and to Brownian motion in potentials. It is shown that the solution of the equation for Brownian motion in a variety of potentials can be expressed in terms suitable for evaluation on a computer. A supplement is included, containing a short review of new material together with some recent references. The book should be very useful to graduate students in physics, chemical physics, and electrical engineering, and also to research workers in these fields.
Customer Reviews:
Rigorous book .......2006-12-28
This book is a classical reference in the subject of stochastic dynamics. It is a graduate level book written in clear and concise language. It covers all the basics about Langevin and Fokker-Planck equations (Chapters 3 and 4). In these chapters, Moyal expansion, Ito and Stratonovich interpretation of stochastic processes is presented carefully. Then they move on to study various methods of solving FP equation in the next 7 chapters. In the final chapter, FP equation and its application to Laser is discussed.
I recommend reading this book along with Gardiner's book (Handbook of Stochastic Methods) to anyone who wants to learn about stochastic dynamics seriously.
A good book on a difficult subject........2004-03-15
I got the impression that there are very few good textbooks on the subject of random processes in continuous time and the Fokker-Planck equation, which are accessible for physicists. In this book the subject presented in a manner that I thought to be a good compromise between mathematical rigor and physical intuition. For example to the spirit of the book, white noise is introduced both from the point of view of a physicist (it has a very short correlation time etc) and from the point of view of a mathematician (as the "derivative" of a Wiener process). While I found the book not very friendly or easy to read, it was one of my main sources for self-learning this subject during my Ph. D. work. I found the book three years ago, own it for two years and keep learning from it until today. I recommend the book very much.
Amazon.com
E=mc2. Just about everyone has at least heard of Albert Einstein's formulation of 1905, which came into the world as something of an afterthought. But far fewer can explain his insightful linkage of energy to mass. David Bodanis offers an easily grasped gloss on the equation. Mass, he writes, "is simply the ultimate type of condensed or concentrated energy," whereas energy "is what billows out as an alternate form of mass under the right circumstances."
Just what those circumstances are occupies much of Bodanis's book, which pays homage to Einstein and, just as important, to predecessors such as Maxwell, Faraday, and Lavoisier, who are not as well known as Einstein today. Balancing writerly energy and scholarly weight, Bodanis offers a primer in modern physics and cosmology, explaining that the universe today is an expression of mass that will, in some vastly distant future, one day slide back to the energy side of the equation, replacing the "dominion of matter" with "a great stillness"--a vision that is at once lovely and profoundly frightening.
Without sliding into easy psychobiography, Bodanis explores other circumstances as well; namely, Einstein's background and character, which combined with a sterling intelligence to afford him an idiosyncratic view of the way things work--a view that would change the world. --Gregory McNamee
Book Description
Already climbing the bestseller lists-and garnering rave reviews-this "little masterpiece"* sheds brilliant light on the equation that changed the world.
"This is not a physics book. It is a history of where the equation [E=mc2] came from and how it has changed the world. After a short chapter on the equation's birth, Bodanis presents its five symbolic ancestors in sequence, each with its own chapter and each with rich human stories of achievement and failure, encouragement and duplicity, love and rivalry, politics and revenge. Readers meet not only famous scientists at their best and worst but also such famous and infamous characters as Voltaire and Marat...Bodanis includes detailed, lively and fascinating back matter...His acknowledgements end, 'I loved writing this book.' It shows." (The Cleveland Plain Dealer)
"E=mc2, focusing on the 1905 theory of special relativity, is just what its subtitle says it is: a biography of the world's most famous equation, and it succeeds beautifully. For the first time, I really feel that I understand the meaning and implications of that equation, as Bodanis takes us through each symbol separately, including the = sign...there is a great 'aha!' awaiting the lay reader." (St. Louis Post-Dispatch)
"'The equation that changed everything' is familiar to even the most physics-challenged, but it remains a fuzzy abstraction to most. Science writer Bodanis makes it a lot more clear." (Discover)
"Excellent...With wit and style, he explains every factor in the world's most famous and least understood equation....Every page is rich with surprising anecdotes about everything from Einstein's youth to the behind-the-scenes workings of the Roosevelt administration. Here's a prediction: E=mc2 is one of those odd, original, and handsomely written books that will prove more popular than even its publisher suspects." (Nashville Scene)
"You'll learn more in these 300 pages about folks like Faraday, Lavoisier, Davy and Rutherford than you will in many a science course...a clearly written, astonishingly understandable book that celebrates human achievement and provides some idea of the underlying scientific orderliness and logic that guides the stars and rules the universe." (Parade )
"Bodanis truly has a gift for bringing his subject matter to life." (Library Journal [starred review] )
"Entertaining...With anecdotes and illustrations, Bodanis effectively opens up E=mc2 to the widest audience." (Booklist )
"Accessible...he seeks, and deserves, many readers who know no physics. They'll learn a handful-more important, they'll enjoy it, and pick up a load of biographical and cultural curios along the way." (Publishers Weekly)
Customer Reviews:
Interesting History of Science.......2007-09-21
This is not a book for people who are looking to learn science. It is a book for people who want to learn about scientists. Bodanis includes lots of fascinating biographical snippets, some about people, such as Emilie du Châtelet, who are entirely overlooked in most textbook histories. His book is a great introduction for those who want to fill in some of the gaps in their knowledge about the people who created modern civilization.
Simple equation, enormous implications.......2007-09-13
A well written story about this famous equation, its history, and perhaps it's future. I STILL don't fully understand it all, but hey, the author tried.
Another masterpiece by Bodanis.......2007-07-20
David Bodanis as a way of writing that one can enjoy. I love all his work and this book was no disappointment. A masterful mix of history and physics that makes science come alive. I can recommend all Bodanis's books.
Even more undrstanding.......2007-04-14
This was a splendid documenation of the actions and thoughts of the individuals involved in the revelations of the most important discoveries in physics ever made. It was told in an exceptionally clear manner by the author. It was very obvious that his research was thorough. He also documented all his discoveries so that the reader could easily do more research.
Personally, I had a hard time putting it down even though I have read other books on the subject. It is the best technical writing I can remember.
Havent read it yet.......2007-03-22
Really havent read it yet, I just bought it for a class, but it looks boring.
Average customer rating:
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Stability and Transition: Theory and Application: Efficient Numerical Methods with Computer Programs
Tuncer Cebeci
Manufacturer: Springer
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ASIN: 3540201602 |
Book Description
Cebeci addresses transition from laminar to turbulent flows and considers solutions, mainly with the help of the linear stability theory and the ways in which it can be implemented accurately by numerical procedures. The main concern is transition of wall boundary layers, although one chapter is devoted to an approach based on the Navier-Stokes equations. The first three chapters summarize physical knowledge of the transition process, consider the stability equations and methods for predicting transition by linear stability theory, and describe efficient and accurate numerical methods for the solution of stability equations. Chapters 4 to 7 describe computer programs based on stability-theory approach to identify the location of transition in two- and three-dimensional incompressible and compressible flows, respectively, and Chapter 7 describes a computer program within the framework of parabolized stability equations. These programs are provided on an accompanying CD-ROM.
Book Description
Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988. The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The first half of the book provides the algorithmic details of orthogonal expansions, transform methods, spectral discretization of differential equations plus their boundary conditions, and solution of the discretized equations by direct and iterative methods. The second half furnishes a comprehensive discussion of the mathematical theory of spectral methods on single domains, including approximation theory, stability and convergence, and illustrative applications of the theory to model boundary-value problems. Both the algorithmic and theoretical discussions cover spectral methods on tensor-product domains, triangles and tetrahedra. All chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is greatly expanded as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms.
A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries.
Book Description
The theory of distributions is an extension of classical analysis, an area of particular importance in the field of linear partial differential equations. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without a knowledge of this. The material in this book, based on graduate lectures given over a number of years requires few prerequisites but the treatment is rigorous throughout. From the outset, the theory is developed in several variables. It is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces. In this second edition, the notion of the wavefront set of a distribution is introduced. It allows many operations on distributions to be extended to larger classes and gives much more precise understanding of the nature of the singularities of a distribution. This is done in an elementary fashion without using any involved theories. This account will be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics.
Customer Reviews:
An Excellent Introduction.......2000-11-02
Every physicist and mathematician uses distributions (sometimes called generalized functions), albeit often unknowingly. From its origins in the Dirac delta `function', distribution theory continues to influence many research areas from quantum mechanics to partial differential equations, but has also grown into an important field in its own right. For anyone interested in learning about the field, this is clearly the first port of call. It presents a balanced introduction to the subject on a level suitable for anyone with a basic grounding in analysis (no knowledge of functional analysis is required).
The book begins by defining the two building blocks of the theory---test functions and distributions. It then quickly expands, filling in the important details of differentiation, multiplication, tensor products and convolution. All of this is written with sufficient mathematical rigor, but never too much that it interferes with the basic understanding of the subject, and is supported throughout by useful exercises. The book then builds up the theory of Fourier and Laplace transforms of distributions, which has important applications in the study of linear partial differential equations. The second edition contains an indispensable new chapter on the calculus of wavefront sets, which, among its uses, allows the propagation of singularities of solutions to partial differential equations to be properly treated. All in all, while the book is not for the common man, and does require a certain level of mathematical maturity, it does present an excellent introduction to an important, and often poorly understood, area of mathematics.
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Inverse Problems in Atmospheric Constituent Transport
I. G. Enting
Manufacturer: Cambridge University Press
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ASIN: 0521812100 |
Book Description
This book describes mathematical techniques for interpreting measurements of greenhouse gases in order to learn about their sources and sinks. The majority of the book gives general descriptions of techniques, but the last third covers the applications to carbon dioxide, methane, chlorofluorocarbons and other gases implicated in global change.
Download Description
The critical role of trace gases in global atmospheric change makes an improved understanding of these gases imperative. Measurements of the distributions of these gases in space and time provide important information, but the interpretation of this information often involves ill-conditioned model inversions. A variety of techniques have therefore been developed to analyze these problems. Inverse Problems in Atmospheric Constituent Transport is the first book to give comprehensive coverage of work on this topic. The trace gas inversion problem is presented in general terms and the various different approaches are unified by treating the inversion problem as one of statistical estimation. Later chapters demonstrate the application of these methods to studies of carbon dioxide, methane, halocarbons and other gases implicated in global climate change. This book is aimed at graduate students and researchers embarking upon studies of global atmospheric change, biogeochemical cycles and Earth systems science.
Book Description
One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.
Key features include:
* Applications to a wide variety of physical problems in numerous interdisciplinary areas
* Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry
* Historical comments on partial differential equations
* Solutions and hints to selected exercises
* A comprehensive bibliography—comprised of many standard texts and reference books, as well as a set of selected classic and recent papers—for readers interested in learning more about the modern treatment of the subject
Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields.
Also by L. Debnath:
Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.
Customer Reviews:
Aimed at the Person who needs to do Real Work.......2007-04-05
Partial Differential equations are really the first time that the science or entineering student begins to see that math can really represent real life situations that are more complex than the almost trivial examples he has studied up until now.
This book, now in its fourth edition reflects comments made by users: students, faculty and researchers as well as covering the major new discoveries of methods for the solution of partial differential equations in the years since the last edition. The book is aimed at the advanced undergraduate or beginning graduate student, and it should be useful as a research reference for professionals in mathematics, science, engineering and the other applied sciences. In addition other fields of study from the social sciented to financial analysis have begin to use more advanced mathematics in their calculations.
The intent in this book is to provide the working physicist/engineer or whatever with the tools he needs to perform his work. In a few places this has meant a slight slacking of the rigor normally required by the pure mathematician in favor of producing solutions that give the user the answers he needs.
Average customer rating:
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Finite Element Methods for Maxwell's Equations (Numerical Analysis and Scientific Computation Series)
Peter Monk
Manufacturer: Oxford University Press, USA
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The Finite Element Method in Electromagnetics
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Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences)
ASIN: 0198508883 |
Book Description
Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.
Book Description
Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Throughout the book, emphasis is placed on concrete examples, often geometrical in nature, so that finite rotation groups and the 17 wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using groups actions on trees. There are more than 300 exercises and approximately 60 illustrations to help develop the student's intuition.
Customer Reviews:
Excellent introduction to abstract algebra through group theory.......2005-09-14
This was the textbook for my first course in abstract algebra and the first "yellow book" that I read. I found it an excellent book: rather than starting with axioms and dryly deriving everything, it gets one to contemplate the meaning and motivation behind the axioms. This book will encourage you to play around with mathematics on paper and in your mind, helping you to get a concrete feel for a subject that many people view as painfully abstract.
The prose is clear and well-written: there is just the right amount of discussion to elucidate necessary points, while allowing the book to remain fairly compact. Exercises are fun but difficult and many require genuine creativity.
I also really like the choice of topics: although this book is introductory (with respect to abstract algebra, it presupposes some knowledge of linear algebra), because it focuses only on groups (as opposed to also trying to handle rings & fields) it is able to get into some more advanced and very interesting topics and applications in later chapters. This book will give you a lot more than can be covered in a single semester undergrad course, and while it doesn't exactly make the best reference text, it will be a book you will want to keep coming back to, if only to study some of the more advanced material.
There are differing perspectives on the teaching of abstract algebra: some people like to start with group theory exclusively in a first course, and treat rings, fields, and other structures in later courses. Other people recommend more integrated approaches, or approaches starting from rings. While I can't say that either approach is better, I can say that this book takes the first approach, focusing exclusively on groups and assuming little prior background..and for a first course in abstract algebra, this book is an excellent choice.
Excellent introduction to group theory.......2004-11-02
Please note that the other reviews here are obviously for some other book. This is not an advanced text on bifurcations and stability. It is an introductory book on group theory. I have been using this book for self study. It is well suited to this purpose. The book uses symmetry to unify and motivate the study of groups. The discussion of the symmetry groups of Platonic solids is both enjoyable in itself and useful for visualizing groups. The chapters are very short. The exercises are well suited to gaining insight into the material.
interesting format.......2000-04-01
The book consists solely of exercises and hints for every exercise, which he curiously calls "answers". This book is perfect if you are looking to review geometrically-tinged algebraic structures like matrix groups, symmetry groups, and wallpaper groups. There is also some basic pure algebra in here. I don't think this book would work all that well for a student new to algebra, although someone with some backgroud in algebra can definitely get something out of the geometric chapters.
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Equations of mathematical physics
V. S Vladimirov
Manufacturer: Mir
ProductGroup: Book
Binding: Hardcover
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ASIN: B0006EJCYU |
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- The History of Mathematics: An Introduction
- The Intention Experiment: Using Your Thoughts to Change Your Life and the World
- The Intention Experiment: Using Your Thoughts to Change Your Life and the World
- The Language of God: A Scientist Presents Evidence for Belief
- The Life of Isaac Newton (Canto original series)
- The Principia : Mathematical Principles of Natural Philosophy
- The Road to Reality: A Complete Guide to the Laws of the Universe
- The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next
- The Variational Principles of Mechanics (Dover Books on Physics and Chemistry)
- Thin Film Solar Cells: Fabrication, Characterization and Applications (Wiley Series in Materials for Electronic & Optoelectronic Applications)
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