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Module Specifications

Archived Version 2020 - 2021

Module Title
Module Code

Online Module Resources

NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

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

Workload Full-time hours per semester
Type Hours Description
Lecture36Classroom or computer lab-based activities involving both lecturer and student-based input
Assignment Completion30Assignment work
Assignment Completion36Homework problems
Independent Study86Pre-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

Differential and Integral Calculus
Review of calculus of functions of a single variable. Definition of a derivative, basic rules, linearity, product rule, chain rule. Taylor and McLaurin series. Maxima and Minima. Integration, integration by parts, integration by substitution. Taylor’s theorem, linear approximation and numerical methods in differentiation and integration, including Richardson Extrapolation and Simpson’s rule.

Probability and Statistics
Probability theory, sample space, permutations and combinations, selection with and without replacement. Events, addition law, complementary events, conditional probability, Baye's law. Discrete and continuous random variables, probability distribution and density functions, expected values. Bernoulli, Binomial, Poisson, exponential and Gaussian random variables, Central Limit Theorem. Joint distributions. Histograms and descriptive statistics, sample statistics, confidence intervals, student t distribution, statistical process control.

Linear Algebra
Solution of linear systems. Matrices, matrix operations, forward and backward substitution, Gaussian Elimination. Inverse of a matrix, LU decomposition, Gauss Jordan method. Determinants, formula for inverse of a matrix, over determined and under determined systems, row-echelon form, rank of a matrix, Vectors, linear independence, basis of a vector space, row space, column space, null space, vector space, inner product, norm, orthogonality. Eigenvectors and eigenvalues, matrix diagonalisation, singular value decomposition, quadratic forms.

Ordinary differential equations
Ordinary Differential Equations, review of exponential function, interpretation of ODEs, separation of variables, superposition, linear independence, basis of solutions, homogeneous ODES, characteristic equation, Solution basis, particular solutions and general solutions, method of undetermined coefficients. Numerical solution of ordinary differential equations, Euler, predictor corrector and Runge Kutta methods.

Laplace and Fourier Transform Theory
Laplace transform definition, application to ODEs, causal functions, standard Laplace transform pairs, Laplace transform properties: linearity, derivative of a Laplace transform, s-shifting, transform of a derivative, inverse Laplace transform using tables, partial fractions. Periodic functions, Fourier series, even and odd functions, linearity, complex exponential form of Fourier series, Fourier transform, conditions on existence, relationship with Laplace transform, linearity, shifts and differentiation, Dirac-delta impulse, sifting property, convolution, Fourier transform of convolution

Multivariate calculus and vector calculus
Vectors, dot product, cross product, parameterised curves, tangent vectors, length of a curve, arc length, scalar fields, line integral, partial derivatives, gradient of a scalar field, vector field, divergence and curl of a vector field, work integrals,

Assessment Breakdown
Continuous Assessment% Examination Weight%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Reassessment Requirement
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
Indicative Reading List

  • Stroud and Booth: 0, Engineering Mathematics, 7th, Industrial Press, 9780831134709
  • Erwin Kreyszig: 2011, Advanced Engineering Mathematics, 10, John Wiley & Sons Ltd, 0470646136
  • Glyn James: 2015, Modern Engineering Mathematics, Pearson, 978-129208073
  • 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

Programme or List of Programmes