Module: Introduction to Differential Equations

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Introduction to Differential Equations
Module Code	MTH1036 (ITS: MS211)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

The purpose of this module is to equip students with the knowledge and skills relevant to elementary ordinary differential equations. This will involve dealing with the theory of such equations, as well as learning methods of solution for the most important classes of these equations. The importance of using rigorous mathematical arguments in this analysis will be emphasised. Students will attend workshop style lectures in which they reconstruct the main results and methods of the topic through guided enquiry. They will also attend review lectures and tutorials that recap on previously encountered material. They will undertake exercises and problems to be presented for assessment.

Learning Outcomes

1. Classify ordinary differential equations;
2. Synthesise different mathematical techniques to determine quantitative and qualitative information about those equations and their solutions;
3. Construct mathematical models using differential equations and study those models and their applications;
4. Apply rigorous mathematical analysis to the study of the theory of ordinary differential equations.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	No Description
Tutorial	12	No Description
Independent Study	89	No Description
Total Workload: 125

Section Breakdown
CRN	20786	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Paul Razafimandimby	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	This is on methods of solving elementary differential equations	20%	Week 28
Formal Examination	End-of-Semester Final Examination	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Introduction
Definitions and classification. Solutions of differential equations. Applications of ordinary differential equations.

First Order Equations
Initial value problems. Geometric interpretation and direction fields. The existence and uniqueness theorem. Linear, separable, homogeneous and exact equations.

Modelling with First Order Equations
Radioactive decay. Newton s law of cooling. Modelling populations: exponential and logistic growth; logistic growth with harvesting. Mixing problems.

Second Order Linear Equations
Homogeneous equations with constant coefficients. Non-homogeneous equations; method of undetermined coefficients, variation of parameters. Fundamental solutions and Wronskians; Abel s theorem.

Linear Systems
Homogeneous linear systems solved by finding eigenvalues and eigenvectors (or generalised eigenvectors), simple inhomogeneous systems

Indicative Reading List

Books:

W.E. Boyce and R.C. Di Prima: 1996, Elementary Differential Equations and Boundary Value Problems, John Wiley,
W. Kohler and L. Johnson: 2006, Elementary Differential Equations with Boundary Value Problems, Pearson/Addison-Wesley,

Articles:
None

Other Resources

None