An Infinite System of Linear Equations Arising in Diffraction Theory (Classic Reprint) - Hardcover

W. Magnus

Hardcover

ISBN 10: 0331024748 ISBN 13: 9780331024746

Publisher: Forgotten Books, 2017

Synopsis

A clear, practical introduction to solving a class of infinite linear equations that arise in diffraction theory.

This edition shows how Bouwkamp’s system can be used to compute the field in an aperture and the corresponding transmission coefficient, with a focus on reliable, approximate solutions.

The book frames the problem in a way that lets you follow the math from the original equations to concrete approximations. It explains why the infinite system is useful, how to replace it with finite forms for real values of the parameter a, and what that implies for the field and transmission in diffraction scenarios.

• See how an infinite matrix can be managed by solving only the first N+1 equations and letting N grow.
• Learn why the system simplifies to a diagonal form as certain parameters vary, and what that means for computations.
• Explore the kernel G(s, a) and its various representations, including integral equations and their equivalence to the original system.
• Understand existence, uniqueness, and analytic properties of the solution under different conditions on a.

Ideal for readers of diffraction theory and applied mathematics who want a rigorous, approachable path from the equations to practical results.

Edition details

• Publisher: Forgotten Books
• Publication date: 2017
• Language: English
• ISBN 10: 0331024748
• ISBN 13: 9780331024746
• Binding: Hardcover
• Number of pages: 37