Download or read book The Basic Theory of Power Series written by Jesús M. Ruiz and published by Vieweg+Teubner Verlag. This book was released on 1993-01-01 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these branches. In particular it presents Rückert's complex nullstellensatz, Risler's real nullstellensatz, Tougerons' implicit function theorem, and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. The present book opens another path: One gets acquaintance with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, and also some others.
Download or read book The Basic Theory of Power Series written by Jesús M. Ruiz and published by Vieweg+Teubner Verlag. This book was released on 1993-03-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these branches. In particular it presents Rückert's complex nullstellensatz, Risler's real nullstellensatz, Tougerons' implicit function theorem, and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. The present book opens another path: One gets acquaintance with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, and also some others.
Download or read book From Divergent Power Series to Analytic Functions written by Werner Balser and published by Springer. This book was released on 2006-11-15 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
Download or read book Basic Theory of Ordinary Differential Equations written by Po-Fang Hsieh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.
Download or read book Theory of Infinite Sequences and Series written by Ludmila Bourchtein and published by Springer Nature. This book was released on 2021-11-13 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.
Download or read book Transcendence in Algebra Combinatorics Geometry and Number Theory written by Alin Bostan and published by Springer Nature. This book was released on 2021-11-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Download or read book Field Theory and Its Classical Problems written by Charles Robert Hadlock and published by American Mathematical Soc.. This book was released on 2018-12-05 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular n-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of algebra is assumed. Notable topics treated along this route include the transcendence of e and π , cyclotomic polynomials, polynomials over the integers, Hilbert's irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems.
Download or read book Lattices and Codes written by Wolfgang Ebeling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory.Das Ziel der Codierungstheorie ist der Entwurf eines effektiven Transformierungssystems für Informationen. Die mathematische Behandlung führt zu bestimmten endlichen Strukturen: fehlerkorrigierende Codes. Überraschenderweise stellt sich heraus, daß Zusammenhänge, die für den Entwurf solcher Codes interessant sind, eng mit Problemen, die zuvor und unabhängig davon in der Reinen Mathematik studiert wurden, verwandt sind. Dieses Buch handelt von einem Beispiel für eine solche Verwandtschaft: die von Codes und Gittern. Gitter werden in der Zahlentheorie und in der Zahlengeometrie studiert. Viele Probleme in bezug auf Codes haben ihr Gegenstück in Gittern und Kugelpackungen.
Download or read book Formal Analysis written by Xiao-Xiong Gan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-06-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal analysis is the study of formal power series, formal Laurent series, formal root series, and other formal series or formal functionals. This book is the first comprehensive presentation of the topic that systematically introduces formal analysis, including its algebraic, analytic, and topological structure, along with various applications.
Download or read book Basic Theory in Reflection Seismology written by J.K. Costain and published by Elsevier. This book was released on 2004-10-27 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material in this volume provides the basic theory necessary to understand the principles behind imaging the subsurface of the Earth using reflection and refraction seismology. For reflection seismology, the end product is a "record section" from a collection of "wiggly traces" that are recorded in the field from which information about the properties of subsurface structure and rock can be derived. For the most part, the principles of imaging are the same regardless of the depth to the target; the same mathematical background is necessary for targeting a shallow water table as for investigating the base of the earth's continental "crust" at a depth of 30-50 km.
Download or read book Complex Function Theory written by Donald Sarason and published by American Mathematical Society. This book was released on 2021-02-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.
Download or read book Algebraic Structures written by George R. Kempf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.
Download or read book A Computational Introduction to Number Theory and Algebra written by Victor Shoup and published by Cambridge University Press. This book was released on 2009 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory graduate-level text emphasizing algorithms and applications. This second edition includes over 200 new exercises and examples.
Download or read book Algebraic Combinatorics written by Chris Godsil and published by Routledge. This book was released on 2017-10-19 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.
Download or read book Spline Functions Basic Theory written by Larry Schumaker and published by Cambridge University Press. This book was released on 2007-08-16 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.
Download or read book Hybrid Systems Computation and Control written by Alberto Bemporad and published by Springer. This book was released on 2007-05-31 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007, held in Pisa, Italy in April 2007. Among the topics addressed are models of heterogeneous systems, computability and complexity issues, real-time computing and control, embedded and resource-aware control, control and estimation over wireless networks, and programming languages support and implementation.
Download or read book Inductive Powering written by Koenraad van Schuylenbergh and published by Springer Science & Business Media. This book was released on 2009-05-31 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inductive powering has been a reliable and simple method for many years to wirelessly power devices over relatively short distances, from a few centimetres to a few feet. Examples are found in biomedical applications, such as cochlear implants; in RFID, such as smart cards for building access control; and in consumer devices, such as electrical toothbrushes. Device sizes shrunk considerably the past decades, demanding accurate design tools to obtain reliable link operation in demanding environments. With smaller coil sizes, the link efficiency drops dramatically to a point where the commonly used calculation methods become invalid. Inductive Powering: Basic Theory and Application to Biomedical Systems lists all design equations and topology alternatives to successfully build an inductive power and data link for your specific application. It also contains practical guidelines to expand the external driver with a servomechanism that automatically tunes itself to varying coupling and load conditions.
