Wavefronts and Rays: As Characteristics and Asymptotics [Hardcover]

Andrej Bona (Author), Michael A Slawinski (Author)

Book Description

ISBN-10: 9814295515 | ISBN-13: 978-9814295512 | Publication Date: May 9, 2011 | Edition: 1

This textbook -- incorporated with many illuminating examples and exercises -- is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation -- by a pure mathematician's standards -- is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and the phenomena such as caustics.

Editorial Reviews

Review

"I thought I knew everything I needed to know about characteristics and their role in the solution of partial differential equations. After reading this book, I discovered that I was wrong. The authors draw us along on an incredible mathematical journey by starting from simple examples and moving on to progressively more sophisticated examples. Thus, the authors provide the community interested in wave propagation with a new set of insights and tools to carry on with their research." --Norman Bleistein, Center for Wave Phenomena, Colorado School of Mines

"The authors' emphasis of presenting the characteristics as hypersurfaces on which the side conditions cannot be arbitrarily fixed -- due to constrains of the differential equations -- is extremely important. Notably, it sheds new light on the eikonal equation. Also, the authors explain why the characteristics depend only on the highest derivatives of the differential equation, from where the similarity between the characteristics of elastodynamics and electromagnetism becomes apparent. This is an extremely good presentation of the theory of characteristics." --Albert Tarantola, Institut de Physique du Globe de Paris

Product Details

• Hardcover: 296 pages
• Publisher: World Scientific Publishing Company; 1 edition (May 9, 2011)
• Language: English
• ISBN-10: 9814295515
• ISBN-13: 978-9814295512
• Product Dimensions: 9 x 6.3 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #1,807,018 in Books (See Top 100 in Books)