Module Code - Title:
MS4403
-
ORDINARY DIFFERENTIAL EQUATIONS
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
MS4022
Rationale and Purpose of the Module:
To introduce and consolidate the concepts and techniques necessary for solving ordinary differential equations(including non-linear ordinary differential equations and phase plane techniques).
Syllabus:
Classification, initial and boundary value problems.
Review of first order equations: separable equations, linear and nonlinear equations, integrating factors, exact equations, homogeneous equations; existence and uniqueness; applications e.g., in mechanics, population dynamics.
Second order linear equations, homogeneous with constant coefficients, linear independence and Wronskian, inhomogeneous equations, variation of parameters, applications in oscillators, higher order linear equations, systems of equations.
Series solution of second order linear equations, regular and singular points, BesselÆs equation.
Sturm-Liouville theory
Nonlinear ODEs: ad-hoc solution techniques, introduction to the concepts of stability and phase plane techniques.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
On completion of this module, students should be able to:
Identify and solve first-order separable, homogeneous, exact and linear differential equations;
use differential equations techniques to solve simple applied problems;
determine whether a first order initial value problem has a unique solution;
solve higher-order constant-coefficient linear differential equations and systems of differential equations;
find series solutions of differential equations at ordinary points;
use Frobenius method to find series solutions at regular singular points;
solve simple Sturm Liouville problems;
use phase plae methods to determine stability of simple systems of ordinary differential equations.
Affective (Attitudes and Values)
None
Psychomotor (Physical Skills)
None
How the Module will be Taught and what will be the Learning Experiences of the Students:
The module is taught in a traditional format of lectures and tutorials/exercise classes.
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
W.E. Boyce & R.C. di Prima (2004)
Elementary differential equations and boundary value problems
, Wiley
Other Relevant Texts:
R.L. Borelli & C.S. Coleman (1998)
Differential equations: a modelling perspective
, Wiley
G.F. Simmons & S. G. Krantz (2007)
Differential Equations:
, McGraw Hill
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
Romina.Gaburro@ul.ie