Airy Functions And Applications To Physics

"This small (nearly 200 pages) monograph on the Airy functions is an important addition to the literature on special functions. It is competently written, with mathematical equations nicely embedded in the text and with many beautiful figures, which help in following the discussed subject. I strongly recommend this book, not only to people who like analytical solutions and the beauty and elegance of special functions, but also to the large group of mathematicians, researchers and graduate students involved in solving applied problems in physics, chemistry and technology." Professor Alexander Apelblat Ben Gurion University of the Negev, Israel "These authors have collected a great deal of useful material that will be unfamiliar to most scientists. I am especially enthusiastic about the large collection of integrals; I was already aware of the integral (2.152) relating an Airy function to its square, and the Fourier generalization (3.94-5) of this, but most of the others were new to me -- in particular the Airy transform which is remarkable." Professor Michael Berry University of Bristol, UK "The text by Vallee and Soares provides a relatively compact discussion of these functions and their applications to both classical and quantum problems. The book takes a tutorial approach and the mathematical presentations are logical ... The text will make a good reference source." Barrie S H Royce Professor of Mechanical and Aerospace Engineering Princeton University "In conclusion, I am very enthusiastic that this book exists. It fills a long-standing gap in a very special but essential segment of applied mathematics, or mathematics for applications. I am aware of no other text that would rival it for the coverage of this subject. It will be a highly useful reference work for a broad community, from mathematicians to engineers, as it collates thorough, up-to-date and almost encyclopaedic data inside a reasonable size (below 200 pages) and price." Andre Voros CEA-Service de Physique Theorique de Saclay "In spite of the book's flaws, I did enjoy reading it for the many beautiful formulas it contains. Certain integrals involving Airy functions are surprisingly easy because of the simplicity of the differential equation, and there is an excellent list of these on pages 43-45 that was great fun to go through." MAA Online Book Review "This book may serve as a comprehensive collection of formulas as well as a textbook in a course on mathematical techniuqes in physics." Mathematical Reviews