M 274M - Introduction to Differential Equations

Credit(s): 4

Prerequisite(s): a grade of “B” or better in M 172 or a grade of “C” or better in M 273 or Math Department consent.
This is a first course in ordinary differential equations. Topics may include linear and non-linear first order differential equations and systems, existence and uniqueness for initial value problems, series solutions, Laplace Transformations, and linear equations of second and higher order. Applications include forced oscillation, resonance, electrical circuits, and modeling differential equations. (Spring Semester)

Course Learning Outcomes: Upon completion of the course, students will be able to

Use mathematical techniques to problem solve.
Understand the classifications of ordinary and partial differential equations, linear and nonlinear differential equations.
Determine solutions of differential equations and initial value problems, and the concepts of existence and uniqueness of a solution to an initial value problem.
Use direction fields and the method of isoclines as qualitative techniques for analyzing the asymptotic behavior of solutions of first order differential equations and/or use the phase line to characterize the asymptotic behavior of solutions for autonomous first order differential equations.
Understand methods for solving second order, linear, and constant coefficient differential equations as well as some techniques for solving second order, linear, and variable coefficient differential equations.
Use mathematical modeling applications of first and second order differential equations and understand the techniques of solutions as well as the theory underlying the methods.