Symbolic Asymptotics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symbolic Asymptotics write by John R. Shackell. This book was released on 2013-03-09. Symbolic Asymptotics available in PDF, EPUB and Kindle. Accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints.
Asymptotic Differential Algebra and Model Theory of Transseries
Asymptotic Differential Algebra and Model Theory of Transseries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotic Differential Algebra and Model Theory of Transseries write by Matthias Aschenbrenner. This book was released on 2017-06-06. Asymptotic Differential Algebra and Model Theory of Transseries available in PDF, EPUB and Kindle. Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Applied Asymptotics
Applied Asymptotics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applied Asymptotics write by A. R. Brazzale. This book was released on 2007-05-31. Applied Asymptotics available in PDF, EPUB and Kindle. First practical treatment of small-sample asymptotics, enabling practitioners to apply new methods with confidence.
Symbolic Asymptotics: Functions of Two Variables, Implicit Functions
Symbolic Asymptotics: Functions of Two Variables, Implicit Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symbolic Asymptotics: Functions of Two Variables, Implicit Functions write by B. Salvy. This book was released on 1996. Symbolic Asymptotics: Functions of Two Variables, Implicit Functions available in PDF, EPUB and Kindle.
A Distributional Approach to Asymptotics
A Distributional Approach to Asymptotics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Distributional Approach to Asymptotics write by Ricardo Estrada. This book was released on 2012-09-08. A Distributional Approach to Asymptotics available in PDF, EPUB and Kindle. "...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic
