Module: Introduction to Differential Equations

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Introduction to Differential Equations
Module Code	MS211 (ITS) / MTH1036 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	-
Module Teachers	Paul Razafimandimby
NFQ level	8	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

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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

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

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	This is on methods of solving elementary differential equations	20%	Week 28

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

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,

Other Resources

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