It is not easy to master the theory of partial

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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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