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Unformatted text preview: calculus course.
It is not easy to master the theory of partial diﬀerential equations. Unlike
the theory of ordinary diﬀerential equations, which relies on the “fundamental
existence and uniqueness theorem,” there is no single theorem which is central
to the subject. Instead, there are separate theories used for each of the major
types of partial diﬀerential equations that commonly arise.
However, there are several basic skills which are essential for studying all
types of partial diﬀerential equations. Before reading these notes, students
should understand how to solve the simplest ordinary diﬀerential equations,
such as the equation of exponential growth dy/dx = ky and the equation of
simple harmonic motion d2 y/dx2 + ωy = 0, and how these equations arise in
modeling population growth and the motion of a weight attached to the ceiling
by means of a spring. It is remarkable how frequently these basic equations
arise in applications. Students should also understand how to solve ﬁrst-order
linear systems of diﬀerential equations with constant coeﬃcients in an arbitrary
number of unknowns using v...
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- Winter '14