# MSUB Mathematics Department

### M 274 Introduction to Differential Equations

Course Description

4 credits
Prerequisite: M 172 and either M 110 or EGEN 105
Presents methods for the solution of first and higher-order differential equations including variation of parameters, undetermined coefficients, the Laplace transform, and power series expansions.  Introduces phase plane methods.

Learning Outcomes

• Classifications of ordinary and partial differential equations, linear and nonlinear differential equations.
• Solutions of differential equations and initial value problems, and the concepts of existence and uniqueness of a solution to an initial value problem.
• Using direction fields and the method of isoclines as qualitative techniques for analyzing the asymptotic behavior of solutions of first order differential equations.
• Using the phase line to characterize the asymptotic behavior of solutions for autonomous first order differential equations.
• Classification of the stability properties of equilibrium solutions of autonomous first order differential equations.
• Separable, linear and exact first order differential equations.
• Substitution and transformation techniques for first order linear differential equations of special forms. These include Bernoulli and homogeneous equations.
• Mathematical modeling applications of first and second order differential equations.
• Methods for solving second order, linear, constant coefficient differential equations. (includes both homogeneous and nonhomogeneous equations)
• Some techniques for solving second order, linear, variable coefficient differential equations. (includes Variation of Parameters, Reduction of Order and Variable Substitutions for Euler equations).
• Basic theory of nth order linear, constant coefficient ordinary differential equations.
• The method of Laplace Transforms for solving first and second order, linear ordinary differential equations.
• Using Unit Step (Heaviside) and Dirac Delta functions to model discontinuous, periodic and impulse forcing functions for first and second order, linear ordinary differential equations.
• Using Laplace Transforms to solve linear differential equations containing Unit Step (Heaviside) and Dirac Delta functions.
• Basic matrix and phase-plane methods for systems of ordinary differential equations.
• Existence and uniqueness of solutions for initial value problems taking the form of linear systems of ordinary differential equations and corresponding initial conditions.

Course Documents