Author: Wilhelm MagnusPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Infinite Determinants Associated with Hill's Equation
Author: Wilhelm MagnusInfinite Determinants Associated with Hill's Equation
Author: Wilhelm MagnusInfinite Determinants Associated with Hill's Equation (Classic Reprint)
Author: Wilhelm MagnusPublisher: Forgotten Books
ISBN: 9780331469875
Category : Mathematics
Languages : en
Pages : 28
Book Description
Excerpt from Infinite Determinants Associated With Hill's Equation Hill's equation plays a role in many problems of electromagnetic theory. Its simplest form, Mathieu's equation arises in the problem of the diffraction by an elliptic cylinder. Generally Speaking, Hill's equation is the differ ential equation for a one-dimensional linear oscillator with a periodic potential. In most applications, the question of the existence of a periodic solution arises. The main purpose of this investigation is to examine the analytic character of the transcendental function whose zeros determine the periodic solutions. 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.
Infinite Determinants in the Theory of Mathieu's and Hill's Equations (Classic Reprint)
Author: Wilhelm MagnusPublisher:
ISBN: 9781332795109
Category : Mathematics
Languages : en
Pages : 50
Book Description
Excerpt from Infinite Determinants in the Theory of Mathieu's and Hill's Equations The existence of even or odd solutions of Mathieu's equation with period n or 2n depends on the vanishing of certain infinite determinants. It is shown that these determinants can be expressed in terms of the values of the even or odd solutions at x n/z, where x is the independent variabhe. The corresponding result for Hill's determinant (which can be expressed in terms of the values of certain solutions at x a n) has long since been found. The method applied in the present report uses theorems about the order of growth of the solutions both with respect to x and the parameters. A rapra sentation of the solutions as a finite Fourier integral can also be derived by this method. We indicate how far the results can be extended to the case of more general equations of Hill's type. The periodic solutions of the inhomo goueoua Mathieu equations are constructed by using an inversion formula for. 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.
Infinite Determinants in the Theory of Mathieu's and Hill's Equations
Author: Wilhelm MagnusPublisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 86
Book Description
Hill's Equation
Author: Wilhelm MagnusPublisher:
ISBN:
Category : Hill's equation
Languages : en
Pages : 48
Book Description
The Discriminant of Hill's Equation
Author: Wilhelm MagnusPublisher:
ISBN:
Category : Hill's equation
Languages : en
Pages : 52
Book Description
Hill's Equation
Author: Wilhelm MagnusPublisher: Courier Corporation
ISBN: 0486150291
Category : Mathematics
Languages : en
Pages : 148
Book Description
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.
Indefinite Determinants Associated with Hill's Equation
Author: Wilhelm MagnusPublisher:
ISBN:
Category : Hill's equation
Languages : en
Pages : 0
Book Description
Determinants and Their Applications in Mathematical Physics
Author: Robert VeinPublisher: Springer Science & Business Media
ISBN: 0387227741
Category : Mathematics
Languages : en
Pages : 392
Book Description
A unique and detailed account of all important relations in the analytic theory of determinants, from the classical work of Laplace, Cauchy and Jacobi to the latest 20th century developments. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. The solutions are verified by applying theorems established in earlier chapters, and the book ends with an extensive bibliography and index. Several contributions have never been published before. Indispensable for mathematicians, physicists and engineers wishing to become acquainted with this topic.