Registry
Module Specifications
Archived Version 2020 - 2021
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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. | |||||||||||||||||||||||||||||||||||||
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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 | |||||||||||||||||||||||||||||||||||||
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 |
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Indicative Content and
Learning Activities Differential and Integral CalculusReview 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 StatisticsProbability 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 AlgebraSolution 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 equationsOrdinary 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 TheoryLaplace 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 convolutionMultivariate calculus and vector calculusVectors, 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, | |||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||
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