Module Specifications.
Current Academic Year 2024 - 2025
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Date posted: September 2024
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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. | |||||||||||||||||||||||||||||||||||||||||||
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
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 | |||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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