Module: Engineering Mathematics III

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Engineering Mathematics III
Module Code	EEG1009 (ITS: EM201)
Faculty	Engineering & Computing	School	Mechanical & Manufacturing Eng
NFQ level	8	Credit Rating	5

Description

This module provides students with the mathematical techniques and skills (analytic and computational) to solve engineering problems involving multivariate calculus and second order ordinary differential equations with constant coefficients.

Learning Outcomes

1. Solve second order ordinary differential equations with constant coefficients.
2. Differentiate and integrate standard functions of several variables.
3. Define and calculate selected quantities in vector calculus.
4. Formulate and solve engineering problems using the analytical techniques of differential equations, multi-variate and vector calculus. Verify analytical solutions using a computer algebra system (CAS).

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	Class based instruction on theory, analytical solution and problem formulation using a computer algebra system (CAS).
Tutorial	12	Group discussion, analytic problem solving and solution verification using CAS.
Independent Study	77	Problem solving relating to tutorial material and weekly review of class materials in preparation for the final examination. Home work exercises may be assigned using a STEM online homework system.
Total Workload: 125

Section Breakdown
CRN	10191	Part of Term	Semester 1
Coursework	20%	Examination Weight	80%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Donnacha Lowney	Module Teacher	Brian Corcoran, Harry Esmonde, Jeremiah Murphy

Section Breakdown
CRN	12079	Part of Term	Semester 1
Coursework	20%	Examination Weight	80%
Grade Scale	50PASS	Pass Both Elements	N
Resit Category	RC3	Best Mark	N
Module Co-ordinator	Donnacha Lowney	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	Individual class test to solve problems.	10%	Week 4
In Class Test	Individual class test to solve problems	10%	Week 8
Formal Examination	End of semester exam.	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

Fundamentals
Vectors and matrix algebra.

Differential equations
First and second order with constant coefficients.

Partial differentiation
First, higher order and mixed partial derivatives; multi-variate Taylor series; stationary values; max/min problems; Hessian matrix; composite functions, chain rule and total derivative; material time derivative; change of independent variable; dependent and independent functions; Jacobian determinant.

Modelling data and approximating functions
Least squares; linearised models, optimisation using Lagrange multipliers; error analysis.

Coordinate systems
Cartesian; polar; spherical; transformations and Jacobian matrix.

Introduction to common partial differential equations (PDEs)
Wave, heat, Laplace and Schrodinger equations; configurations tractable to analytical solution.

Operators
Gradient of scalar field, divergence and curl of vector fields; directional derivative; Laplacian; irrotational and conservative vector fields.

Calculus of vector-valued functions
Arc-length; unit tangent and normal vectors; curvature; velocity.

Double and triple integrals: formalism
Line, area and volume integrals; applications to areas, moments and centre of mass

Vector calculus
Line, surface and volume integrals; Stokes, Greens and Divergence Theorems; applications: work, circulation and flux

Indicative Reading List

Books:

Croft, Davidson and Hargreaves: 0, Engineering Mathematics,
Anthony Croft,Tony Croft,Robert Davison,James Flint,Martin Hargreaves: 2017, Engineering Mathematics, Pearson Education, 978-1-2921-4665-2
Erwin Kreyszig: 2010, Advanced Engineering Mathematics, John Wiley & Sons, 267, 978-0-4704-5836-5
Seán Dineen: 2014, Multivariate Calculus and Geometry, Springer, 978-1-4471-6418-0
K. B. Vijaya Kumar,Antony P. Monteiro: 2023, Mathematica for Physicists and Engineers, John Wiley & Sons, 421, 978-3-5274-1424-6
Pragati Gautam,Swapnil Verma,Komal Negi: 2024, Getting Started with Maxima, Techsar Pvt Ltd, 451, 978-81-971909-1-9

Articles:
None

Other Resources

None