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Unformatted text preview: ectors and matrices with real or complex entries.
(This topic will be reviewed in the second chapter.) Familiarity is also needed
with the basics of vector calculus, including the gradient, divergence and curl,
and the integral theorems which relate them to each other. Finally, one needs
ability to carry out lengthy calculations with conﬁdence. Needless to say, all
of these skills are necessary for a thorough understanding of the mathematical i language that is an essential foundation for the sciences and engineering.
Moreover, the subject of partial diﬀerential equations should not be studied
in isolation, because much intuition comes from a thorough understanding of
applications. The individual branches of the subject are concerned with the
special types of partial diﬀerential equations which which are needed to model
diﬀusion, wave motion, equilibria of membranes and so forth. The behavior
of physical systems often suggest theorems which can be proven via rigorous
mathematics. (This last point, and the book itself, can be best appreciated by
those who have taken a course in rigorous mathematical proof, such as a course
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- Winter '14