Partial Differential Equations with Applications

Catalog description

A course containing the following topics: first order partial differential equations; the wave equation; the diffusion equation; the Laplace equation; d’Alembert’s solution; Duhamel’s principle; the classification of partial differential equations; elliptic, parabolic, and hyperbolic partial differential equations; Stability theory; energy conservation; Sturm-Liouville problems; Fourier series; integral transforms; Laplace transforms; Greens’s functions; and variational methods. Applications in medicine, engineering, meteorology, and industry will be discussed. Mathematical software such as ACSL, Maple, and Mathematica will be used.