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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Introduction to Differential Equations
Module Code MS211
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Nil Venet
Semester 2: Paul Razafimandimby
Autumn: Paul Razafimandimby
Module TeachersNil Venet
Paul Razafimandimby
NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
None
Array
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.



Workload Full-time hours per semester
Type Hours Description
Lecture24No Description
Tutorial12No Description
Independent Study89No 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 Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class TestThis is on methods of solving elementary differential equations20%Week 28
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
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

None
Programme or List of Programmes
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BSSAStudy Abroad (DCU Business School)
BSSAOStudy Abroad (DCU Business School)
CAFMCommon Entry, Actuarial, Financial Maths
HMSAStudy Abroad (Humanities & Soc Science)
HMSAOStudy Abroad (Humanities & Soc Science)
IESAStudy Abroad (Institute of Education)
IESAOStudy Abroad (Institute of Education)
SHSAStudy Abroad (Science & Health)
SHSAOStudy Abroad (Science & Health)
SMPSCSingle Module Prog Science and Health
Date of Last Revision22-AUG-11
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