# Math 238 syllabus

Differential Equations

Course Description: This course provides an introduction to ordinary differential equations. Topics include first order differential equations, higher order linear differential equations, systems of first order linear differential equations, Laplace transforms, methods for approximating solutions to first order differential equations, applications. Students should have taken or be taking MA 227. Core Course.
Prerequisites: MA 227 Minimum Grade of D or concurrent enrollment in  MA 227

Textbook:   Fundamentals of Differential Equations and Boundary Value Problems, 7th Edition,   R. Kent Nagle, Edward B. Saff, Arthur David Snider, Pearson, 2018

Coverage: Chapter 1 (1.1-1.3), Chapter 2 (2.1-2.4, 2.6), Chapter 3 (3.1-3.5), Chapter 4  (4.1-4.6), Chapter 5 (5.1, 5.2), Chapter 6 (6.1-6.4), Chapter 7 (7.1-7.10)

Learning outcomes: Upon the successful completion of the course a student will:
Understand the introductory concepts such as distinguishing ODEs from PDEs,  the definition of an ODE, the meaning of a solution of an ODE, the mathematical modelling process
Characterize and solve first order ODEs : separable equations  linear first order ODEs, ODEs reducible to separable or linear form through substitution
Understand existence and uniqueness of solutions theorem for first order ODEs
Solve applications involving first order ODEs such as population models, heating and cooling of objects and buildings, acceleration-velocity models, motion in a resisting medium, mixing problems, modeling electric circuits
Solve higher order linear constant coefficient ODEs: homogeneous equations with constant coefficients (general solutions), non-homogeneous equations (particular solutions using methods undetermined  coefficients and variation of parameters)
Solve applications involving higher order linear ODEs: Spring-Mass oscillators, Equations of Motion
Solve simple First-order linear systems of ODEs using elimination
Use the Laplace Transform (use of Transform Tables) to solve ODEs