Module: Numerical Problem Solving for Engineers

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title	Numerical Problem Solving for Engineers
Module Code	EM114
School	School of Electronic Engineering
Module Co-ordinator	Semester 1: Marissa Condon Semester 2: Marissa Condon Autumn: Marissa Condon
Module Teachers	Marissa Condon
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

None

Description

This module is intended to complement the formal, analytical mathematical theory presented in Engineering Mathematics I and II and focuses instead on practical problem-solving skills. This includes problem specification skills, problem solving skills, numerical skills as well as visualisation and verbal skills. The module will integrate 1st year students’ mathematical knowledge more comprehensively with the real world and other first year modules. A particular focus is on the practical use of computers: both as a visualisation and instructional aid for mathematics and also as a flexible tool for analysing and solving complex, unfamiliar problems.

Learning Outcomes

1. Divide a larger technical problem into a series of sub-problems, identifying the inter-relationship and dependencies between them.
2. Identify the appropriate mathematical techniques required to solve the constituent elements of a large engineering problem.
3. Identify and apply suitable approximations needed to reduce the complexity of a problem and render it suitable for analysis.
4. Formulate algorithms capable of implementing these techniques discretely on a computer and articulate these algorithms in the form of a flowchart.
5. Translate algorithms into appropriate basic computer code.
6. Design and implement tests to assess the accuracy and efficiency of the resultant computer – based solutions.
7. Understand information expressed visually and design and implement appropriate visualisation methods for any problems being examined.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	2 hours per week
Laboratory	10	The student completes 5 2-hour labs working on Matlab and C code to solve computing problems
Independent Study	89	Including completion of on line homeworks
Directed learning	2	2 1-hour class tests
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

Visualisation:
Plotting functions: Polynomials, exponentials, trigonometric, logarithmic, rational, piecewise. Plotting the functions, their derivatives and integrals and interpreting the relationship between the resultant curves. Taylor series approximations to functions – accuracy, dependence on expansion point, remainder term, linear approximation. Representing and manipulating complex numbers in computer code. Visualising the complex plane, Argand diagrams. Representing and manipulating vectors in computer code. Visualising vectors and vector operations, cross and dot products etc.

Curve fitting
Choosing and fitting curves to real-life data, i.e. a periodic curve to real-life tidal height data, exponential curve to real-life population growth data etc.

Vectors
Basic manipulation of vectors. Develop an algorithm to determine whether a point is inside or outside a polygon (application of cross product and dot product). Write code to determine the intersection between two line segments, or line segment and plane. Application of above to determine whether line of sight (LOS) exists between GPS satellite and receiver in presence of buildings, or whether LOS exists between sun and solar energy panel.

Complex numbers
Visualisation of complex plane, visualisation of mathematical operations involving complex numbers (e.g. Develop an algorithm to generate the Mandelbrot fractal).

Matrix Algebra
Examples of large linear systems from engineering. Solution via Gaussian elimination.

Calculus
Identification of maxima and minima. Maximum power transfer – Simulation of maximum power transfer theorem and comparison with analytical result (from EM113). Ballistics – Simulation of simple projectile motion and identification of maximum range, point of maximum height etc. Comparison with analytical result (from EM112). Generation of simple “angry birds” type game (in conjunction with root finding – see below).

Introduction to numerical methods
Forward backward and central difference, Euler integration, computation of sequences and series, root finding via Newton Raphson and bisection methods, Euler method for solution of ODEs.

Assessment Breakdown
Continuous Assessment	100%	Examination Weight	0%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	Computerised class test(s) will be held during the semester	20%	n/a
Practical/skills evaluation	There will be a number of labs to be completed.	60%	n/a
Short Answer Questions	Homeworks	20%	n/a

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 1

Indicative Reading List

Croft, Davison and Hargreaves: 0, Engineering Mathematics: A foundation for electronic, electrical, communications and systems engineers,

Other Resources

None

Programme or List of Programmes

BMED	B.Eng. in Biomedical Engineering
CAM	B.Eng. Mechanical & Manufacturing Eng
CE	Common Entry into Engineering
ECE	BEng Electronic & Computer Engineering
ECSA	Study Abroad (Engineering & Computing)
ECSAO	Study Abroad (Engineering & Computing)
HDEAT	H.Dip Engineering Analysis & Technology
ME	B.Eng. in Mechatronic Engineering
SSE	BEng in Mechanical & Sustainability Eng

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