Book Description
Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In this book, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, with references provided. Asymptotic Approximations of Integrals contains the distributional method, not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as exponential asymptotics. Expositions of these new theories are available in papers published in various journals, but not yet in book form. ... Read more

Customer Reviews (1)

This book is very important to my study in guraduate school.
I am studying "Asyptotic Expantions" in graduate school. To study this field, this book is veryimportant reference one of them. ... Read more

Book Description
This book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple and a few complicated settings, along with numerical, as well as asymptotic assessments of their accuracy. Variants on these expansions, including much of modern likelihood theory, are discussed and applications to lattice distributions are extensively treated. This book is intended primarily for advanced graduate students and researchers in the field needing a collection of core results in a uniform notation, with bibliographical references to further examples and applications. It assumes familiarity with real analysis, vector calculus, and complex analysis. This third edition features an expansion of the material on the Blackwell approximation and an expansion of the discussions on saddlepoint approximation. ... Read more

Book Description
A long-awaited revision of one of the most respected primers on applied mathematics

Principles of Applied Mathematics provides a comprehensive look at how classical methods are used in many fields and contexts. Updated to reflect developments of the last twenty years, it shows how two areas of classical applied mathematics-spectral theory of operators and asymptotic analysis-are useful for solving a wide range of applied science problems. Topics such as asymptotic expansions, inverse scattering theory, and perturbation methods are combined in a unified way with classical theory of linear operators. Several new topics, including wavelet analysis, multigrid methods, and homogenization theory, are blended into this mix to amplify this theme.

This book is ideal as a survey course for graduate students in applied mathematics and theoretically oriented engineering and science students. ... Read more

Customer Reviews (4)

Broad, shallow and uneven
When an author invites a reader to purchase and read his book the assumption one makes is that the book provides a new or a different insight to a familiar or difficult subject that opens new vistas and level of comprehension into the subject matter. First, writing a book on advanced applied mathematics is quite an endeavor and thus, I applaud the author for such an effort.However, the book overall provides panorama but very little detail and new vistas in critical areas. Thus there does not seem to be a significant reason for this book to have been published because most of the topics have been adequately covered in other sources. Clearly the author set out with a lofty and challenging goal; to present the theory for a very broad range of mathematical tools, topics that in fairness needed a fuller and more coherent development that are not present in the book.However, there are some bright spots for which the book deserves at least two stars. The best written chapters, albeit too short, are Chapters 1-3 and Chapters 6 on Complex variables. But the treatment is neither compelling or original.In chapter 6 the author introduces the reader to orthogonal polynomials and special functions but leaves the reader with such a limited view of these topics as to make the effort at teasing the reader's curiosity quite frustrating.The book is generous with bibliography at the end of each chapter and a great source for further research. Nevertheless, it would an improvement in future editions, if the author points out to the reader which pages of the suggested readings the reader should be focused on for the chapter in which it is being cited as a reference. The author engages in serial titillation by introducing the reader to exotic topics such as Sobolev spaces but quickly retreats stating that many of the operators in Sobolev space lack "self-adjointness" and thus of not much practical use for applied mathematics. (See page 66-67). Similarly, he also introduces the reader to Mellin and Hankel transforms but does not explain where and how they are used and when one these particular transforms arebetter suited than Laplace and Fourier Transforms. So what is the point here?The treatment of Green functions is too compressed beyond belieffor it to be of any significant value. The same goes for the discution of Sturm-Liouville systems.The physical examples are too compressed and for the most part difficult to follow and relate to the theory the author just discussed that ostensibly equips the reader to understand the example.

The discussion of Laplace and in particular Fourier transforms seems not to logically and seamlessly emerge from the previous discussion of the theory of operators.A word on proofs.Some of the proofs are so abbreviated with little explanation following that it is frustrating experience to attempt to follow.

In sum, I commend the author to either expand the length of chapters or consider choosing less topics and develop them more fully and coherently so the book attains depth and eminence.

Every chapter can be a book
This is a book with very broad coverage, which is also its strength. It happens to be my textbook for a graduate course when I worked toward my phd degree in engineering. I had a hard time through it, although I had a high grade in this course. Even though, I don't think this book is well written.

As my title said, every chapter in this book can be written as a book. I am not exaggerating. It's true. Since the author condenses so much material into a small book, there is sacrifice certainly. For example, the coverage is not thorough for a specific topic, the proof is too short or even not given...etc. To overcome this, usually you need to consult other books to get a more clear understanding. In addition, I had a bad experience that some examples have nothing to do with what he has just said above. That drove me crazy. The author mentions in the preface that he intends to seek a balance on application and theory in this book. I don't think he gets the job done.

In spite of so many drawbacks, there are still bright sides. For example, the broad coverage is good for me to get into or acquainted with some topics. When you are not understanding what he said, try to find a reference book. That usually helps. In addition, the motivation part is good. He tells you why you need this, why that way doesn't work...etc.

Simply speaking, this book is kind of opening a door for you and then you need to work out the rest not depending on it but by yourself.

If you need a book for self study, this is not the one. If not for that course, I wouldn't force myself reading through it. I think Logan's "Applied Mathematics" is much better for self study at the expense of narrower coverage than this one. This one is better for course use accompanying instructor's good supplement.

Excellently organized book.
This book presents various mathematical principles in an organization I have not seen before.It starts with the idea of a transformation, then goes on to relate eigenvalues and eigenvectors to general spectral theory,explain how the need for closed function spaces naturally leads to Lebesgueintegration (I know about Lebesgue integration before but I didn't know whyit was needed), and show how the definition of certain inverse operatorsleads to distribution theory.This is a very natural way of organizingthese principles.While other books, such as Strang's Intro to AppliedMathematics and Rudin's Real & Complex Analysis, provide you with onemathematical "toy" after another (Fourier series, Lebesgueintegration, etc.), Keener's book tells you why you need the toy beforegiving it to you.

Am I stupid or this book is too advance???
This book doesn't clearify anything for you. No examples, No further explanation. It only keeps introduce various theories to you. It can compact theories that other books take 2-3 pages to explain it into 5lines! I think you can imagine. Obviously, this book is not suitable to beyour first book (not the second also). Buy it if you are sure that you aresmart enough to understand it! ... Read more

Book Description

The well known transport laws of Navier-Stokes and Fourier fail for the simulation of processes on lengthscales in the order of the mean free path of a particle that is when the Knudsen number is not small enough. Thus, the proper simulation of flows in rarefied gases requires a more detailed description.

Book Description

Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical analysis, approximation theory, partial differential equations, integral equations, harmonic analysis, etc. In this work the exposition focuses primarily on a powerful tool that has become especially important in our computerized age, namely, dimensionality reducing expansion (DRE). The method of DRE is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. To date, there is no comprehensive treatment of this subject in monograph or textbook form.

Book Description
This digital document is a journal article from Journal of Econometrics, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The finite sample behavior is analyzed of particular least squares (LS) and a range of (generalized) method of moments (MM) estimators in panel data models with individual effects and both a lagged dependent variable regressor and another explanatory variable. The latter may be affected by lagged feedbacks from the dependent variable too. Asymptotic expansions indicate how the order of magnitude of bias of MM estimators tends to increase with the number of moment conditions exploited. They also provide analytic evidence on how the bias of the various estimators depends on the feedbacks and on other model characteristics such as prominence of individual effects and correlation between observed and unobserved heterogeneity. Simulation results corroborate the theoretical findings and reveal that in small samples of models with dynamic feedbacks none of the techniques examined dominates regarding bias and mean squared error over all parametrizations examined. ... Read more

Book Description
This digital document is a journal article from Journal of Econometrics, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The finite sample behavior is analyzed of particular least squares (LS) and a range of (generalized) method of moments (MM) estimators in panel data models with individual effects and both a lagged dependent variable regressor and another explanatory variable. The latter may be affected by lagged feedbacks from the dependent variable too. Asymptotic expansions indicate how the order of magnitude of bias of MM estimators tends to increase with the number of moment conditions exploited. They also provide analytic evidence on how the bias of the various estimators depends on the feedbacks and on other model characteristics such as prominence of individual effects and correlation between observed and unobserved heterogeneity. Simulation results corroborate the theoretical findings and reveal that in small samples of models with dynamic feedbacks none of the techniques examined dominates regarding bias and mean squared error over all parametrizations examined. ... Read more