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.
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