![]() WAVEFRONTS AND RAYS
As Characteristics and Asymptotics
by Andrej Bóna (Curtin University, Australia) & Michael
A Slawinski (Memorial University, Canada)
300pp (approx.)
978-981-4295-51-2: US$90 / £62 US$63 /
£43.40
"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
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.
Contents:
- Characteristic Equations of First-Order Linear
Partial Differential Equations
- Characteristic Equations of Second-Order Linear
Partial Differential Equations
- Characteristic Equations of First-Order
Nonlinear Partial Differential Equations
- Propagation of Discontinuities
- Caustics
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