Differential Equations and Mathematical Modeling

Catalog description

Differential equations play a vital role in modeling nearly every physical, chemical, and biological process. Understanding how to create and interpret mathematical models, as well as how to solve and characterize solutions of differential equations, is of fundamental importance to applied mathematics, contemporary science, and engineering. This course provides a first introduction to this ubiquitous field of analysis with a heavy emphasis on the development, refinement, and interpretation of mathematical models using differential equations. The first portion of the course examines the various analytical, qualitative and numerical techniques available for analyzing the solutions of linear and nonlinear first-order differential equations (topics include separable equations, linear equations, transformation of variables, series methods, integral transforms, slope fields, equilibria, Euler's Method, and bifurcations). The second portion of the course focuses on techniques for studying systems of first-order differential equations (topics include direction fields, phase planes, Euler's Method for systems, homogeneous and nonhomogeneous linear systems, and the linearization of nonlinear systems). Students will not be able to get credit for both MTH 303 and MTH 304 .