Asymptotic Solution of Systems of Linear Ordinary Differential Equations With Discontinuous Coefficients (Classic Reprint) - Couverture souple
Synopsis
A practical guide to extending key formulas for large-parameter systems when coefficients jump. You’ll learn how to get accurate terms beyond the known expansion and apply them to real-world wave problems.
This book analyzes a system of first-order linear ODEs with a coefficient matrix that depends on a real parameter. It shows how asymptotic expansions in powers of the parameter behave when derivatives of the coefficient matrix have finite jump discontinuities, and it derives the next term beyond the previously known results. The work reveals that this new term is itself discontinuous, marking a meaningful difference from smoother cases. A clear treatment links these ideas to applications in one-dimensional, time-harmonic wave propagation in inhomogeneous media.
- How to construct asymptotic solutions for large parameter values when jump discontinuities occur.
- How discontinuities affect the continuity of successive terms in the expansion.
- Methods for handling diagonalization and reducing the problem to simpler components.
- Connections to the reduced wave equation and reflection behavior in varying media.
Ideal for readers of applied mathematics, physics, and engineering who want a rigorous, accessible path from theory to practical wave problems.
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Asymptotic Solution of Systems of Linear Ordinary Differential Equations With
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Paperback. Etat : New. Print on Demand. This book introduces readers to methods of deriving asymptotic solutions for systems of linear ordinary differential equations, both when the coefficients of the system depend on a small or large parameter and when the coefficients have finite jump discontinuities. The author presents a thorough introduction to the theory of these equations, discussing the Lyapunov and Floquet methods of obtaining asymptotic solutions and the key role of the monodromy matrix in applying the Floquet method. In addition, the author applies the theory of asymptotic solutions to the one-dimensional propagation of time-harmonic waves in inhomogeneous media. The book will be of particular interest to mathematicians, physicists, and engineers. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781332945535_0
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Asymptotic Solution of Systems of Linear Ordinary Differential Equations With Discontinuous Coefficients Classic Reprint
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
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PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781332945535
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Asymptotic Solution of Systems of Linear Ordinary Differential Equations With Discontinuous Coefficients Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781332945535
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Expédition depuis Royaume-Uni vers Etats-Unis
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