Asymptotic Solution of Systems of Linear Ordinary Differential Equations With Discontinuous Coefficients (Classic Reprint) - Softcover

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.