Latest Module Specifications
Current Academic Year 2025 - 2026
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Description To introduce students to the theoretical framework and skills of numerical methods in engineering contexts such as circuit simulation, signal processing and telecommunications. To make students aware of the appropriate use of numerical methods, the power, and limitations of such techniques. To provide experience in the use of computational environments for analysis and simulation of systems in a range of engineering applications. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Learning Outcomes 1. From a generic starting point, with due regard to the limitations and inherent assumptions, derive mathematical formulae and develop numerical algorithms for solving complex engineering problems. 2. Select an appropriate numerical method/simulation technique to solve an ill-defined engineering problem/explore a nascent design solution, recognising the strengths and limitations of various methods. 3. Demonstrate an ability to work collaboratively in a team environment to solve engineering problems using numerical methods and communicate technical results arising within the engineering community and society at large. 4. Critically appraise the evolution and impact of numerical techniques on scientific, economic, and societal domains with respect to sustainability and equality. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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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
Overview Numerical methods and computation algorithms. Issues and limitations of engineering computation. Solutions to sets of linear equations Jacobi, Gauss-Siedel and successive over relaxation (SOR) iterative techniques; sequential and parallel implementations; applications. Approximation theory Taylor’s Theorem; Lagrange polynomials; remainders; order notation. Numerical differentiation Forward, backward and central difference schemes; Richardson’s extrapolation and higher order schemes; error bounds. Root finding techniques Bisection; Newton-Raphson and secant. Quadrature techniques Rectangular, trapezoidal, Simpson’s rule; Integral Mean Value Theorem; error bounds. Ordinary differential equations Initial value and well-posed problems; direction fields and Euler’s method; first order predictor-corrector (Heun, midpoint and Runge-Kutta) methods; Taylor methods; technique properties: convergence, consistency, order and stability; first order multi-step methods (explicit: Adams Bashford, implict: Adams Moulton); second order methods (Runge-Kutta-Nystrom); error bounds; application: circuit simulators. Partial differential equations Classification (elliptic, parabolic, hyperbolic), initial value and boundary value problems; discretisation approaches; consistency tests; von Neumann stability analysis; convergence and Lax-Richtmyer Theorem; explicit and implicit (Crank-Nicolson) numerical solution schemes; application: finite element and finite difference field solvers. Random number generation Linear Congruential Generators (LCGs); randomness quality; application: encryption/decryption algorithms. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List Books:
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Other Resources None | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||