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Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

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Module Title
Module Code (ITS)
Faculty School
Module Co-ordinatorSemester 1: Nina Snigireva
Semester 2: Nina Snigireva
Autumn: Nina Snigireva
Module TeachersRonan Egan
Nina Snigireva
NFQ level 8 Credit Rating
Pre-requisite Not Available
Co-requisite Not Available
Compatibles Not Available
Incompatibles Not Available
None
Array
Description

This module will introduce students to the notions of vectors, matrices and linear maps in (finite dimensional) Euclidean Spaces. Infinite dimensional vector spaces, in the context of Fourier Series, will be considered also. The module aims to give students a working knowledge of the methods and applications of linear algebra. Applications will be chosen with their significance to the students disciplines in mind. Students will attend lectures on the course material and will work, independently, to solve problems on topics related to the course material. The students will have an opportunity to review their solutions, with guidance, at weekly tutorials.

Learning Outcomes

1. solve systems of linear equations.
2. perform various operations with vectors and matrices, in particular, be able to calculate eigenspaces and apply such calculations to the diagonalization of matrices.
3. apply linear algebraic methods to geometic problems in 2 and 3 dimensions.
4. calculate trigonometric Fourier Series of elementary functions defined on finite intervals and sketch the periodic extensions of such functions
5. demonstrate an understanding of concepts by use of examples or counterexamples.



Workload Full-time hours per semester
Type Hours Description
Lecture36Students will attend lectures where new material will be presented and explained. Also attention will be drawn to various supporting material and tutorials as the course progresses.
Tutorial12Students will show their solutions to homework questions and will receive help with and feed-back on these solutions.
Independent Study139.5Corresponding to each lecture students will devote approximately two additional hours of independent study to the material discussed in that lecture or to work on support material when attention is drawn to such in lectures. Before each tutorial students will devote approximately four hours to solving homework problems which are to be discussed in that tutorial.
Total Workload: 187.5

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

Systems of Linear Equations
Introduction to Systems of Linear Equations, Gaussian Elimination, Consistent and Inconsistent Systems.

Vectors
Vectors in the plane, Vectors in space, Applications to Geometry, n-component vectors, linear independence and bases, Gram-Schmidt Process Linear transformations

Matrices
Matrices and Matrix Operations, Square Matrices, Determinants, Inverses, More Systems of Linear Equations

Eigenvectors
Eigenvalues, Eigenvectors and Diagonalization.

Fourier Series
Function spaces, Orthogonal projections onto finite dimensional spaces. Calculation of trigonometric Fourier Series, Bessel's Inequality, Parseval's Identity

Assessment Breakdown
Continuous Assessment% Examination Weight%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class Testn/a20%
Indicative Reading List

  • Howard Anton and Chris Rorres: 2000, Elementary Linear Algebra, (Applications Version)., 8, Wiley, 0471170526
  • Howard Anton: 2005, Elementary Linear Algebra., 9, Wiley, 0471669601
  • Noble, B. and Daniels, J.: 1988, Applied Linear Algebra, 3, Prentice Hall, 0130412600
Other Resources

None

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