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The Mathematical Theory of Huygens' Principle
Bevan B. Baker and E. T. Copson
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AMS Chelsea Publishing
1987; 193 pp; hardcover
Volume: 329
Reprint/Revision History:
third edition with corrections 1987; second AMS printing 2009
ISBN-10: 0-8218-3478-9
ISBN-13: 978-0-8218-3478-7
List Price: US$38
Member Price: US$30.40
Order Code: CHEL/329.H
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The book can only be described as an indispensable reference for its thorough and transparent account of the historical development of Huygens' principle. [ ... ] The text of the book is clear and easy to read, the computations are usually elegant and transparent, methodical but not quite uniform, and the physical considerations are generally referenced, rather than fully worked out. [ ... ] The great value of the book lies in the excellent historical account, which leaves hardly a single wish unfulfilled, and recounts a whole series of mistakes that have become customary in the literature. Familiarity with "Baker-Copson" is therefore essential for anyone who works in this field or who seeks a convenient and reliable introduction.

--Zentralblatt MATH

By rigor of logical treatment and careful attention to detail the authors have produced a critical treatise which will undoubtedly become a standard reference work.

--Bulletin of the AMS

Baker and Copson originally set themselves the task of writing a definitive text on partial differential equations in mathematical physics. However, at the time, the subject was changing rapidly and greatly, particularly via the developments coming from quantum mechanics. Instead, the authors chose to focus on a particular area of the broad theory, producing a monograph complete in itself. The resulting book deals with Huygens' principle in optics and its application to the theory of diffraction. Baker and Copson concern themselves with the general theory of the solution of the PDEs governing the propagation of light. Extensive use is made of Green's method. A chapter is dedicated to Sommerfeld's theory of diffraction, including diffraction of polarized light by a perfectly reflecting half-plane and by a black half-plane. New material was added for subsequent editions, notably Rayleigh's method of integral equations to the problem of diffraction by a planar screen. Some of the simpler diffraction problems are discussed as examples. Baker and Copson's book quickly became the standard reference on the subject of Huygens' principle. It remains so today.

Table of Contents

  • The Analytical Representation of Huygens' Principle: 1 The principle of Huygens; 2 Huygens' construction as a contact-transformation; 3 The propagation of sound waves in air; 4 Huygens' principle for monochromatic phenomena; 5 Wave-motions in three dimensions; 6 Wave-motions in two dimensions; 7 Marcel Riesz's solution of the equation of cylindrical waves
  • Huygens' Principle and the Theory of Diffraction: 1 Kirchhoff's theory of diffraction; 2 Maggi's transformation; 3 Diffraction by a black half-plane; 4 Kottler's theory of diffraction by a black screen
  • Huygens' Principle for Electromagnetic Waves: 1 Huygens' principle and Maxwell's equations; 2 The failure of the Kirchhoff and the Larmor-Tedone formulæ; 3 Kottler's formulation of Huygens' principle for electromagnetic waves; 4 The diffraction of electromagnetic waves by a black screen
  • Sommerfeld's Theory of Diffraction: 1 Sommerfeld's many-valued wave-functions; 2 The diffraction of plane-polarized light by a reflecting half-plane; 3 Diffraction of plane-polarized light by a black half-plane
  • Diffraction by a Plane Screen: 1 Introduction; 2 Diffraction of sound by a plane screen; 3 Diffraction of electromagnetic waves; 4 Sommerfeld's diffraction problem; 5 Schwarzschild's diffraction problem; 6 Approximate solutions
  • Index
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