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Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Linear Mathematics
Module Code	MS227
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Brien Nolan Semester 2: Brien Nolan Autumn: Brien Nolan
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module introduces students to the theory of linear algebra, with an emphasis on the application of theoretical results to solving practical mathematical problems. The student will be introduced to the central role which vector spaces, matrices and linear transforms play in linear mathematics, and will be able to work competently with these objects. The student will be able to formulate many linear problems which arise in the scientific setting in terms of problems concerning vector spaces, matrices and linear transforms, and will be able to obtain solutions for these problems. Students will participate in the following learning activities:Lectures: Students will attend a series of lectures designed to introduce learners to the mathematical principles and techniques which underpin this module, with examples provided as motivation.Problem-solving: Weekly tutorials will take place where students will engage in problem solving exercises. Reading: Students are expected to fully use the recommended textbooks to supplement lectures.

Learning Outcomes

1. Apply standard methods and techniques in linear mathematics to solve a wide range of problems.
2. State a selection of theorems and definitions from linear mathematics.
3. Construct the proofs of selected theorems and results.
4. Apply these theorems and results to solve problems.
5. Interpret and implement mathematical formulae in order to compute linear tranforms of functions, namely Fourier series and Laplace tranforms.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	24	Weekly lecture
Tutorial	11	Supervised tutorials
Independent learning time	90	Recommended time for self-study
Total Workload: 125

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

Linear algebra.
Review of vectors, matrices and Gaussian elimination. Subspaces, spanning sets, linear independence, bases. Innerproducts and orthonormal bases. Linear maps and their matrix representations. Eigenvalues, eigenvectors, matrix diagonalization. Symmetric matrices and quadratic forms. The projection theorem..

Fourier series.
Functions on [a,b] viewed as a vector space. The integral as an inner product. Orthogonal expansions using sines and cosines. Conditions for convergence of Fourier series. Fourier sine/cosine series. Complex form of the Fourier series. Mean square error in the context of the projection theorem. Parsevals identity. Fourier Transforms, with motivation using the complex form of the Fourier series..

Laplace Transforms.
Definition and motivation from the Fourier transform. Transform of derivatives and integrals. Initial and final value theorems. Shifting theorem. Convolution Theorem. Inversion using partial fractions. Application to systems of (constant coefficient) linear ode's..

Assessment Breakdown
Continuous Assessment	30%	Examination Weight	70%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Short answer questions	Class test	30%	n/a

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List