Registry

Module Specifications

Current Academic Year 2010 - 2011
This information is provisional and subject to change.

Module Title	Engineering Mathematics & Computation
Module Code	EM103
School	Mechanical Engineering
Online Module Resources
Module Co-ordinator	Dr Yann Delaure	Office Number	S385
Level	1	Credit Rating	10
Pre-requisite	None
Co-requisite	None

Module Aims

MODULE CO-ORDINATOR: Dr Yan Delauré, Dr Noel Murphy.

MODULE AIMS:

To introduce engineering students to the central role that mathematics plays in the development and practice of engineering.
To motivate the comprehension and use of important analytical concepts, calculus methods and linear mathematics fundamental to engineering.
To help students to begin to develop the skill of analysing problems in a rational (rigorous, logical) and methodical manner.
To develop the students’ ability to transfer their mathematical understanding (and the associated methods) to diverse engineering application areas.
To introduce students to mathematical computation, realisation and visualisation using Matlab.
To help students towards self-diagnosis and self-help in filling gaps in their mathematical education.

Learning Outcomes

On completion of this module, the student will be able

to find solutions for single-variable ODEs that would predict the behaviour of simple dynamic systems; (PO1)
to use complex numbers, matrices and vectors appropriately in the representation of measured quantities; (PO1)
to describe in their own words, using appropriate mathematical notation and relevant engineering examples, the primary mathematical tools used in the treatment of engineering problems (e.g. notions of linearity, linear algebra and functional approximation); (PO1)
to demonstrate a repertoire of problem-solving skills and an ability to generalise and transfer ideas, appropriate to simple engineering applications of mathematical concepts; (PO2)
to make effective use of a mathematical software tool such as Matlab or Octave in understanding and solving simple engineering mathematics problems; (PO2)
to demonstrate an ability to analyse experimental data for linear trends and simple statistical properties; (PO3)
to use references to appropriately acknowledge the work of others in any work they submit for assessment; (PO4)
to demonstrate self-learning skills for the use of mathematical techniques in engineering contexts, with particular reference to (i) recognisin and remedying gaps in their mathematical knowledge and (ii) developing strategies for life-long learning; (PO5)
to use mathematical terminology and formula to communicate effectively to other technically literate people; (PO6)

Indicative Time Allowances
	Hours
Lectures	48
Tutorials	24
Laboratories	48
Seminars	0
Independent Learning Time	30

Total	150
Placements
Assignments

NOTE

Assume that a 10 credit module load represents approximately 150 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.

Indicative Syllabus

Linear and Vector Algebra

Elementary operations with vectors, Scalar product, Vector product, Matrix algebra, Gaussian elimination, Determinants, Linear algebraic equations, Rectangular-polar conversions, Complex numbers and algebra of complex numbers (inc complex numbers as 2-D vectors and 2-D linear transformations), Eigenvalues and Eigenvectors, Linear independence, transformations and change of basis, Vector spaces, Introduction to abstract algebra and groups, Numerical methods in linear algebra.

Functions

Concepts of domain and range, composition and inverse, Standard functions including Trigonometric and exponential functions, Concepts of limits, continuity.

Calculus

Differentiation and application including differential calculus, extrema and sketching, Taylor series & approximation, Anti-differentiation and area, Definite and indefinite Integrals, Fundamental theorem of calculus, Applications involving the integral as a Sum, Systematic techniques for integration, Introduction to first and second order ordinary differential equations, Analytic solution methods for ODEs, Numerical methods in the solution of ODEs.

Assessment
Continuous Assessment	30%	Examination Weight	70%

Indicative Reading List

Required Text:

Essential:

Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers (Paperback), by Croft, Davison and Hargreaves, Prentice Hall; 3 edition (12 Dec 2000), ISBN-10: 0130268585, ISBN-13: 978-0130268587

Reference texts:

Calculus and ODEs, Pearson, D., Arnold , 1996.
Calculus with analytic geometry, Anton, H., 4^th ed., Wiley, 1992.
Essential Mathematics for Engineering, Bolton , W., Butterworth-Heinemann, 1997.

Contribution to Programme:

The module’s contribution to the IEI Programme Areas and Programme Outcomes is characterised according to a five point scale where 4 indicates a very strong contribution and 0 indicates no significant or intended contribution.

Science & Mathematics	Discipline - specific Technology	Information and Communications Technology	Design and Development	Engineering Practice	Social and Business Context
4	1	3	1	0	2

Knowledge and Its Application:

The ability to derive and apply solutions from a knowledge of sciences, engineering sciences, technology and mathematics

Problem Solving:

The ability to identify, formulate, analyse and solve engineering problems;

Design:

The ability to design a system, component or process to meet specified needs, to design and conduct experiments and to analyse and interpret data;

Ethics & Responsibility:

An understanding of the need for high ethical standards in the practice of engineering, including the responsibilities of the engineering profession towards people and the environment

Effective Work and Learning:

The ability to work effectively as an individual, in teams and in multidisciplinary settings together with the capacity to undertake lifelong learning;

Effective Communication:

The ability to communicate effectively with the engineering community and with society at large

Teaching & Learning Strategies/Pedagogical Approach:

Learning Outcomes relating to PO1 and PO2 are mostly evaluated using an end-of-year exam paper that includes multiple choice as well as longer format questions. The use of a mathematical software tool is evaluated through assignments.

Rapid feedback of frequent MCQ class tests is used to help develop good learning habits during the module. This is also facilitated by allowing the students to prepare and use a one-page “summary sheet” in the end-of-year exam.

A significant element of T&L strategy is to motivate the relevance of the mathematical ideas by appropriate applications. The emphasis throughout is on student insight and understanding, not rigorous proof, and on communication of mathematical ideas in terms of diagrams, words, formulas and numbers, not formulas alone.

Programme or List of Programmes

BME

BEng Manufacturing Engineering &Business

BMED

B.Eng. in Biomedical Engineering

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

CAM

B.Eng. Mechanical & Manufacturing Eng

B.Eng. in Common Entry into Engineering