Download or read book Hill s Equation Part I General Theory written by W. Magnus and published by Hardpress Publishing. This book was released on 2013-12 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Download or read book Hill s Equation Part I General Theory written by W Magnus and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive guide to Hill's equation, a fundamental concept in the study of ordinary differential equations. The authors present the general theory of Hill's equation, along with its applications in various fields of mathematics and physics. This book is a must-read for anyone interested in the theory of ordinary differential equations and its applications. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Hill s Equation written by Wilhelm Magnus and published by . This book was released on 1957 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hill s equation 1 General theory written by Wilhelm Magnus and published by . This book was released on 1957 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hill s Equation written by Wilhelm Magnus and published by . This book was released on 1957 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hill s Equation written by Wilhelm Magnus and published by Courier Corporation. This book was released on 2013-10-29 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Download or read book Hill s Equation Vol 1 written by Wilhelm Magnus and published by Forgotten Books. This book was released on 2017-11-15 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Hill's Equation, Vol. 1: General Theory Any homogeneous linear differential equation of second order with real periodic coefficients can be reduced to an equation of Hill's type. The specific question which arises in the theory of Hill's equation is the problem of the existence of periodic solutions. This problem has many features in common with the ordinary sturm-liouville problems, and in certain cases it canjin fact, be reduced to ordinary boundary value problems of the sturm-liouville type, (see Section However, in general such a reduction is not possible, and imposing the periodicity requirements on a solution of the differential equation leads to phenomena different from those resulting from the imposition of a homogeneous boundary condition of the sturm-liouville type. Thus, the differential equation can have two linearly independent periodic solutions but it cannot have two linearly independent solutions satisfying the same homogeneous boundary conditions. Futhermore, the value of the period of the solution (which is a multiple of the period p of the coefficients) plays an important role in the discussion of periodic solutions. In a certain sense, only the solutions of period p and 2 p are of interest. 'we shall now proceed with a detailed presentation of some basic theorems and their proofs. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book The Discriminant of Hill s Equation written by Wilhelm Magnus and published by . This book was released on 1959 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Special Hill s Equation with Discontinuous Coefficients written by Harry Hochstadt and published by . This book was released on 1960 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basic Mathematical Research for Electromagnetic Theory written by Morris Kline and published by . This book was released on 1958 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of the research under this contract was to explore mathematical problems which arise in the field of theoretical electromagnetics, or to anticipate mathematical needs or methodology for electromagnetic problems. The Division of Electromagnetic Research has been tackling electromagnetic problems for a number of years and has found that many investigations have been hampered by the lack of available mathematical information or of methods.
Download or read book Maximum Principles for the Hill s Equation written by Alberto Cabada and published by Academic Press. This book was released on 2017-10-27 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,...) and for problems with parametric dependence. The authors discuss the properties of the related Green's functions coupled with different boundary value conditions. In addition, they establish the equations' relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included. - Evaluates classical topics in the Hill's equation that are crucial for understanding modern physical models and non-linear applications - Describes explicit and effective conditions on maximum and anti-maximum principles - Collates information from disparate sources in one self-contained volume, with extensive referencing throughout
Download or read book Hill s Equation Part Ii Transformations Approximation Examples written by W. Magnus and published by . This book was released on 1961 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the purpose of this report on Hill's equation to provide the reader with a few ready made transformation and approximation formulas which may be useful to anyone working on a particular problem. Some examples are discussed in detail, partly because they illustrate the general theory and partly because they appear frequently in applications. The section on the coexistence problem contains a little more than mere examples. It may be considered as a complete discussion of those results which can be obtained from the investigation of three term recurrence relations. A third part of this report will contain applications of the theory to problems of physics and engineering.
Download or read book Periodic Differential Equations written by F. M. Arscott and published by Elsevier. This book was released on 2014-05-16 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal wave equation. This book starts with a survey of the main problems related to the formation of periodic differential equations. The subsequent chapters deal with the general theory of Mathieu's equation, Mathieu functions of integral order, and the principles of asymptotic expansions. These topics are followed by discussions of the stable and unstable solutions of Mathieu's general equation; general properties and characteristic exponent of Hill's equation; and the general nature and solutions of the spheroidal wave equation. The concluding chapters explore the polynomials, orthogonality properties, and integral relations of Lamé's equation. These chapters also describe the wave functions and solutions of the ellipsoidal wave equation. This book will prove useful to pure and applied mathematicians and functional analysis.
Download or read book Hill s Equation II Vol 2 written by W. Magnus and published by Forgotten Books. This book was released on 2015-06-16 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Hill's Equation, II, Vol. 2: Transformations, Approximation, Examples It is the purpose of the present, second, report on Hill's equation to provide the reader with a few ready made transformation and approximation formulas which may be useful to anyone working on a particular problem. Also; we shall discuss some examples in detail, partly because they illustrate the general theory and partly because they appear frequently in applications. This section on the coexistence problem contains a little more than mere examples. It may be considered as a complete discussion of those results which can be obtained from the investigation of three term recurrence relations. A third part of this report will contain applications of the theory to problems of physics and engineering. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book AFOSR written by United States. Air Force. Office of Scientific Research and published by . This book was released on 1957 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hill s Equation Vol 2 written by W. Magnus and published by Forgotten Books. This book was released on 2017-10-12 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Hill's Equation, Vol. 2: Transformations, Approximation, Examples A particular problem. Also, we shall discuss some examples in detail, partly because they illustrate the general theory and partly because they appear frequently in applications. The section on the coexistence problem contains a little more than mere examples. It may be considered as a complete discussion of those results which can be. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book General Theory of Algebraic Equations written by Etienne Bézout and published by Princeton University Press. This book was released on 2009-01-10 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.
