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The Asymptotic Solutions Of An Ordinary Differential Equation In Which The Coefficient Of The Parameter Is Singular
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Book Synopsis Asymptotic Expansions for Ordinary Differential Equations by : Wolfgang Wasow
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Book Synopsis Perturbation Methods by : Ali H. Nayfeh
Download or read book Perturbation Methods written by Ali H. Nayfeh and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1956 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics (set) by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics (set) written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1994-02-28 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient by :
Download or read book Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient written by and published by Elsevier. This book was released on 1975-01-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient
Book Synopsis Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems by : George David Birkhoff
Download or read book Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems written by George David Birkhoff and published by . This book was released on 1908 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Differential Equations in Theory and Practice by : Robert Mattheij
Download or read book Ordinary Differential Equations in Theory and Practice written by Robert Mattheij and published by SIAM. This book was released on 1996-01-01 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained. Audience: the book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.
Book Synopsis Applications of Group-Theoretical Methods in Hydrodynamics by : V.K. Andreev
Download or read book Applications of Group-Theoretical Methods in Hydrodynamics written by V.K. Andreev and published by Springer Science & Business Media. This book was released on 1998-10-31 with total page 966 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics.
Book Synopsis Asymptotics and Special Functions by : F. W. J. Olver
Download or read book Asymptotics and Special Functions written by F. W. J. Olver and published by Academic Press. This book was released on 2014-05-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
Book Synopsis Mathematical Analysis by : R. V. Gamkrelidze
Download or read book Mathematical Analysis written by R. V. Gamkrelidze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains three articles: "Asymptotic methods in the theory of ordinary differential equations" b'y V. F. Butuzov, A. B. Vasil'eva, and M. V. Fedoryuk, "The theory of best ap proximation in Dormed linear spaces" by A. L. Garkavi, and "Dy namical systems with invariant measure" by A. 'VI. Vershik and S. A. Yuzvinskii. The first article surveys the literature on linear and non linear singular asymptotic problems, in particular, differential equations with a small parameter. The period covered by the survey is primarily 1962-1967. The second article is devoted to the problem of existence, characterization, and uniqueness of best approximations in Banach spaces. One of the chapters also deals with the problem of the convergence of positive operators, inasmuch as the ideas and methods of this theory are close to those of the theory of best ap proximation. The survey covers the literature of the decade 1958-1967. The third article is devoted to a comparatively new and rapid ly growing branch of mathematics which is closely related to many classical and modern mathematical disciplines. A survey is given of results in entropy theory, classical dynamic systems, ergodic theorems, etc. The results surveyed were primarily published during the period 1956-1967.
Book Synopsis Lectures on Ordinary Differential Equations by : Robert W. McKelvey
Download or read book Lectures on Ordinary Differential Equations written by Robert W. McKelvey and published by . This book was released on 1970 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Differential Operators by : Aiping Wang
Download or read book Ordinary Differential Operators written by Aiping Wang and published by American Mathematical Soc.. This book was released on 2019-11-08 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
Book Synopsis Linear Turning Point Theory by : Wolfgang Wasow
Download or read book Linear Turning Point Theory written by Wolfgang Wasow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing. Instead of undertaking such a task, I have concentrated, in this exposi tion, on the aspects of the asymptotic theory with which I have been particularly concerned during those 20 years, which is the nature and structure of turning points. As in Chapter VIII of my previous book, only linear analytic differential equations are considered, but the inclusion of important new ideas and results, as well as the development of the neces sary background material have made this an exposition of book length. The formal theory of linear analytic differential equations without a parameter near singularities with respect to the independent variable has, in recent years, been greatly deepened by bringing to it methods of modern algebra and topology. It is very probable that many of these ideas could also be applied to the problems concerning singularities with respect to a parameter, and I hope that this will be done in the near future. It is less likely, however, that the analytic, as opposed to the formal, aspects of turning point theory will greatly benefit from such an algebraization.
Book Synopsis Equations of Mathematical Physics by : A. S. Demidov
Download or read book Equations of Mathematical Physics written by A. S. Demidov and published by Springer Nature. This book was released on 2023-06-27 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise volume presents an overview of equations of mathematical physics and generalized functions. While intended for advanced readers, the accessible introduction and text structure allows beginners to study at their own pace as the material gradually increases in difficulty. The text introduces the concept of generalized Sobolev functions and L. Schwartz distributions briefly in the opening section, gradually approaching a more in-depth study of the “generalized” differential equation (also known as integral equality). In contrast to the traditional presentation of generalized Sobolev functions and L. Schwartz distributions, this volume derives the topology from two natural requirements (which are equivalent to it). The text applies the same approach to the theory of the canonical Maslov operator. It also features illustrative drawings and helpful supplementary reading in the footnotes concerning historical and bibliographic information related to the subject of the book. Additionally, the book devotes a special chapter to the application of the theory of pseudodifferential operators and Sobolev spaces to the inverse magneto/electroencephalography problem. Explicit numerically realizable formulas related to the Cauchy problem for elliptic equations (including quasilinear ones) and also to the Poincaré--Steklov operators are presented. The book is completed by three additions, which were written by famous mathematicians Yu. V. Egorov, A. B. Antonevich, and S. N. Samborski.
Download or read book Pacific Journal of Mathematics written by and published by . This book was released on 1951-03 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
