On an Integral Equation Arising in Inverse Scattering (Classic Reprint) - Hardcover

Chao-Hui Yang

9780656135998: On an Integral Equation Arising in Inverse Scattering (Classic Reprint)

Hardcover

ISBN 10: 0656135999 ISBN 13: 9780656135998

Publisher: Forgotten Books, 2018

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Unlock the math behind inverse scattering with a clear, methodical approach.

This edition presents a focused study of an integral equation that arises in physical problems, offering a step-by-step path from problem setup to solution.

Readers will follow how a given reflection coefficient leads to a kernel, a potential function, and ultimately the ionization density. The text unfolds with key ideas from Fourier transforms, analytic continuation, and Fredholm theory, while keeping the emphasis on practical computation and the structure of the solution.

The material is technical but organized, guiding you through recursion formulas and conditions that ensure solvability. It highlights how different cases for the kernel K(x,y) affect the solution and what that means for real-world applications in scattering theory.

How to derive and interpret the kernel from the integral equation
Techniques for solving with Fourier transforms and analytic methods
Recursive procedures that build up the solution term by term
Conditions that guarantee existence and how they shape the final result

Ideal for readers with a background in applied mathematics or theoretical physics who want a rigorous, applied treatment of inverse scattering mathematics.

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