Registry
Module Specifications
Archived Version 2014  2015
 
Description This module is intended to complement the formal, analytical mathematical theory presented in Engineering Mathematics I and II and focuses instead on practical problemsolving skills. This includes problem specification skills, problem solving skills, numerical skills as well as visualisation and verbal skills. The module will integrate 1st year students’ mathematical knowledge more comprehensively with the real world and other first year modules. A particular focus is on the practical use of computers: both as a visualisation and instructional aid for mathematics and also as a flexible tool for analysing and solving complex, unfamiliar problems.  
Learning Outcomes 1. Divide a larger technical problem into a series of subproblems, identifying the interrelationship and dependencies between them. 2. Identify the appropriate mathematical techniques required to solve the constituent elements of a large engineering problem. 3. Identify and apply suitable approximations needed to reduce the complexity of a problem and render it suitable for analysis. 4. Formulate algorithms capable of implementing these techniques discretely on a computer and articulate these algorithms in the form of a flowchart. 5. Translate algorithms into appropriate basic computer code. 6. Design and implement tests to assess the accuracy and efficiency of the resultant computer – based solutions. 7. Understand information expressed visually and design and implement appropriate visualisation methods for any problems being examined.  
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 Visualisation: Plotting functions: Polynomials, exponentials, trigonometric, logarithmic, rational, piecewise. Plotting the functions, their derivatives and integrals and interpreting the relationship between the resultant curves. Taylor series approximations to functions – accuracy, dependence on expansion point, remainder term, linear approximation. Representing and manipulating complex numbers in computer code. Visualising the complex plane, Argand diagrams. Representing and manipulating vectors in computer code. Visualising vectors and vector operations, cross and dot products etc. Curve fitting Choosing and fitting curves to reallife data, i.e. a periodic curve to reallife tidal height data, exponential curve to reallife population growth data etc. Vectors Basic manipulation of vectors. Develop an algorithm to determine whether a point is inside or outside a polygon (application of cross product and dot product). Write code to determine the intersection between two line segments, or line segment and plane. Application of above to determine whether line of sight (LOS) exists between GPS satellite and receiver in presence of buildings, or whether LOS exists between sun and solar energy panel. Complex numbers Visualisation of complex plane, visualisation of mathematical operations involving complex numbers (e.g. Develop an algorithm to generate the Mandelbrot fractal). Matrix Algebra Examples of large linear systems from engineering. Solution via Gaussian elimination. Calculus Identification of maxima and minima. Maximum power transfer – Simulation of maximum power transfer theorem and comparison with analytical result (from EM113). Ballistics – Simulation of simple projectile motion and identification of maximum range, point of maximum height etc. Comparison with analytical result (from EM112). Generation of simple “angry birds” type game (in conjunction with root finding – see below). Introduction to numerical methods Forward backward and central difference, Euler integration, computation of sequences and series, root finding via Newton Raphson and bisection methods, Euler method for solution of ODEs.  
 
Indicative Reading List
 
Other Resources None  
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