Module: Mathematical Techniques & Problem Solving

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Mathematical Techniques & Problem Solving
Module Code	EE488 (ITS) / EEN1054 (Banner)
Faculty	Engineering & Computing	School	Electronic Engineering
Module Co-ordinator	Conor Brennan
Module Teachers	Brendan Hayes, Xiaojun Wang
NFQ level	8	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination

Description

The aim of this module is to provide the opportunity to students taking Masters-level modules in the School of Electronic Engineering to ensure that they have acquired or regained the mathematical knowledge and competencies necessary to successfully undertake these Masters modules. While the coverage is targeted on prerequisites for a range of Masters modules, the emphasis is on practical applications of the relevant concepts and techniques. Hence, a student who has covered some or all of these topics previously and just needs to recap them is still likely to have a valuable learning experience on this module. The module may also be taken as a standalone module in its own right as providing a valuable foundation for the application of mathematics in industry and technology.

Learning Outcomes

1. demonstrate that they recognise the role of numerical, analytical, algebraic and algorithmic approaches to solving engineering problems
2. choose the appropriate mathematical method to solve a problem, recognising the strengths and limitations of various methods
3. derive mathematical formulas or models for solving particular problems from a generic starting point
4. design, implement, test and characterize an appropriate mathematical approach to a given engineering problem described in general terms
5. demonstrate that they can communicate technical results from engineering problems solved using mathematical approaches, including using graphical and statistical tools
6. demonstrate an ability to work collaboratively in a team environment to solve engineering problems using mathematical and algorithmic tools

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Classroom or computer lab-based activities involving both lecturer and student-based input
Group work	30	Group-based assignment work
Assignment Completion	24	Homework problems
Independent Study	98	Pre-lecture preparation through prescribed reading, independent study post lectures, informal tutor-supported study sessions if required
Total Workload: 188

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

Linear Maths
Review of linear algebra, vector spaces, matrix algebra, eigenvector decomposition, singular value decomposition, numerical applications and problem solving, including solutions to sets of linear equations; polynomial curve fitting; iterative techniques and applications.

Numerical approximations for differential and integral calculus
Taylor’s theorem, linear approximation and numerical methods in differentiation and integration, including Richardson Extrapolation and Simpson’s rule.

Multivariate and complex-valued functions and calculus
Review of complex-valued functions, vector-valued functions and vector fields; differentiation in multi-dimensions, linear approximation of multi-variate functions, max/min problems, chain rule, directional derivatives, gradient vector field; multiple integrals; vector analysis (div and curl of vector fields), line integrals, work, circulation and flux, Green’s Theorem and Stokes’ Theorem; complex analysis and contour integration.

Numerical solution of ordinary and partial differential equations
Numerical solution of ordinary differential equations; boundary-value PDE problems and their solution, including Runge Kutta methods.

Series representations and Transform Theory
Theory and properties of the Fourier series, Fourier Transform, Laplace transform, Z-transform; other orthogonal transforms; transform theory in the solution of ordinary differential and difference equations.

Statistics
Statistical analysis, histograms and descriptive statistics; statistical significance, confidence intervals, hypothesis testing, linear regression and analysis of variance.

Random Signals and Systems
Stochastic signals, random variables and probability; birth-death process and introduction to queuing theory.

Algorithmic Maths for Engineering Applications
Problems in networks and graphs, coding, searching and optimisation problems, statistical methods, Monte Carlo method, computing discrete transforms and signal processing applications. Parallelizable algorithms. Numerical limitations of finite precision machines.

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Group project	Computer-based assignment to solve a given engineering problem by selecting, implementing, testing and characterizing appropriate mathematical approaches.	25%	n/a
Assignment	A series of 'homework' problems completed by students working individually to practice and reinforce concepts met during in-class activities	10%	As required
In Class Test	A short MCQ at the beginning of each lecture session to encourage students to engage with assigned reading and research relevant to the session topic.	15%	Every Week

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 1

Indicative Reading List

Erwin Kreyszig: 2011, Advanced Engineering Mathematics, 10, John Wiley & Sons Ltd, 0470646136
K A Stroud: 2011, Advanced Engineering Mathematics, 5, Palgrave Macmillan, 0230275486
W. Bolton: 0, Mathematics for engineering, Oxford ; Newnes, 2000., 0750649313
Peter V. O'Neil: 0, Advanced Engineering Mathematics, Cengage India; 7 edition (2012), 8131517527
Robert Sedgewick, Kevin Wayne: 0, Algorithms, Addison-Wesley Professional, 032157351X
Holly Moore: 0, Matlab for Engineers, Pearson; 5 edition (January 14, 2017), 0134589645
D. Pearson: 1996, Calculus and ODEs, Edward Arnold, London, 0340625309
John H. McColl: 1995, Probability, Edward Arnold, London, 0340614269
A. Chetwynd and P. Diggle: 1995, Discrete mathematics, Arnold, London, 0340610476
R. B. J. T. Allenby: 1995, Linear algebra, Edward Arnold, London, 0340610441
Peyton Z Peebles: 2015, Probability, Random Variables, and Random Signal Principles, McGraw-Hill, 1259007642
Gene H. Golub, Charles F. Van Loan: 0, Matrix Computations, 4th, The Johns Hopkins University Press, 9781421407944
E. Oran Brigham: 1988, The fast Fourier transform and its applications, Prentice Hall, Englewood Cliffs, N.J., 0133075052
Tristan Needham: 1998, Visual complex analysis, Clarendon Press, Oxford, 0198534469

Other Resources

None