Registry
Module Specifications
Archived Version 2018 - 2019
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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 6. demonstrate an ability to work collaboratively in a team environment to solve engineering problems using mathematical and algorithmic 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 Linear MathsReview 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 calculusTaylor’s theorem, linear approximation and numerical methods in differentiation and integration, including Richardson Extrapolation and Simpson’s rule.Multivariate and complex-valued functions and calculusReview 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 equationsNumerical solution of ordinary differential equations; boundary-value PDE problems and their solution, including Runge Kutta methods.Series representations and Transform TheoryTheory 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.StatisticsStatistical analysis, histograms and descriptive statistics; statistical significance, confidence intervals, hypothesis testing, linear regression and analysis of variance.Random Signals and SystemsStochastic signals, random variables and probability; birth-death process and introduction to queuing theory.Algorithmic Maths for Engineering ApplicationsProblems 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. | |||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||
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