On Systems of Linear Ordinary Differential Equations (Classic Reprint) - Hardcover

Herbert B. Keller

9780366500758: On Systems of Linear Ordinary Differential Equations (Classic Reprint)

Hardcover

ISBN 10: 0366500759 ISBN 13: 9780366500758

Publisher: Forgotten Books, 2018

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Explore a rigorous approach to solving complex differential systems with exponential-type solutions.

This book presents a new way to obtain rapidly convergent representations by transforming the Peano–Baker matrizant into a form that reveals the solution as a sum of exponentials with variable coefficients. It links classical ideas like the WKB method to modern matrix techniques, offering a unified view of higher-order systems and turning points.

The text develops the theory step by step, showing how to construct, transform, and connect solutions across regions with and without turning points. It explains when and how the leading terms align with familiar approximations and how to interpret exponential terms as waves or oscillations. The treatment includes asymptotic expansions, scattering matrices, and practical procedures for computing connection data across complex domains.

Learn how to represent solutions as exponential sums with adjustable coefficients, and why this improves convergence.
See how the matrix machinery generalizes the WKB method to higher-order systems and to cases with parameters.
Understand turning points, connection formulas, and how to connect solutions across different regions.
Explore the interpretation of exponential terms as waves and how continuous reflections shape the overall solution.

Ideal for readers of advanced applied mathematics and theoretical physics who want a rigorous, constructive framework for exponential-type solutions.

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