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