Registry
Module Specifications
Current Academic Year 2012 - 2013
Please note that this information is subject to change.
| |||||||||||||||||||||||||||||||||||||||||||||
| Description | |||||||||||||||||||||||||||||||||||||||||||||
|
To develop a solid and instinctive understanding of the fundamental mathematical generalisations, associated methods and practical mathematical skills central to engineering problem-solving in the fields of electronic and mechanical engineering.To continue the students' development of their skills of analysing problems in a rational and methodical manner and their use of reasoning by analogy.A significant element of the T&L strategy is to motivate the relevance of the mathematical ideas by appropriate applications. The emphasis throughout is on student insight and understanding, not rigorous proof, and on communication of mathematical ideas in terms of diagrams, words, formulas and numbers, not formulas alone. However, some mathematical proofs are used as tools for developing logical and mathematical reasoning | |||||||||||||||||||||||||||||||||||||||||||||
| Learning Outcomes | |||||||||||||||||||||||||||||||||||||||||||||
|
1. Compute Fourier Series and Fourier, Laplace and Z-transforms of functions and sequences 2. Solve differential and difference equations using transform methods 3. Differentiate and integrate standard functions of several variables 4. Define and calculate selected quantities in vector calculus 5. Solve optimisation problems in several variables 6. Justify or prove key facts pertaining to optimisation, vectors and the calculus of several variables 7. Communicate in writing the solution of mathematical problems to his/her peers | |||||||||||||||||||||||||||||||||||||||||||||
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 | |||||||||||||||||||||||||||||||||||||||||||||
|
Semester 1 - Transform Theory. 1. Further development of methods for the solution of ordinary differential equations.2. Introduction to the theory and properties of the Fourier series.3. Fourier Transform.4. Laplace transform.5. Z-transform.6. Transform theory in the solution of ordinary differential and difference equations.. Semester 2 - Multivariate Calculus and the solution of ODEs and PDEs. 1. Mathematical optimization, Lagrange multipliers. Review of vectors; vector algebra, dot and cross products; lines and planes in space; Cartesian and other coordinate systems; Review of matrix algebra, eigenvectors, determinants; 2-D linear transformations and complex numbers; Review of (basic) abstract linear abgebra, vector spaces, subspaces, basis, dimension, etc;2. Introduction to multi-variate and vector-valued functions; complex functions; vector fields;3. Vector-valued functions and space-curves, arc-length, velocity & tangent vectors, acceleration, curvature;4. Differentiation in multi-dimensions, linear approximation of multi-variate functions, max/min problems chain rule, directional derivatives, gradient vector field, Taylor;5. Double and triple integrals, areas, moments and centre of mass; substitutions in multiple integrals;6. 2-D Vector Analysis: div and curl of vector fields, line integrals, work, circulation and flux, Green;7. Vector Analysis in 3-D, surface integrals, divergence and Stokes' theorems;8. Boundary-value PDE problems and their solution, including the method of separation of variables.. | |||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||
| Indicative Reading List | |||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||
| Other Resources | |||||||||||||||||||||||||||||||||||||||||||||
| None | |||||||||||||||||||||||||||||||||||||||||||||
| Array | |||||||||||||||||||||||||||||||||||||||||||||
| Programme or List of Programmes | |||||||||||||||||||||||||||||||||||||||||||||
| Timetable this semester: Timetable for | |||||||||||||||||||||||||||||||||||||||||||||
| Archives: |
| ||||||||||||||||||||||||||||||||||||||||||||
