Course Overview
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Course Synopsis
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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
The goals of this subject are, how we can use Linear Algebra and its numerical applications in different fields.
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Course Learning Outcomes
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Upon completing this course students should be able :
- To master the techniques for solving systems of linear equations.
- To introduce matrix algebra as a generalization of single-variable algebra of high school.
- To build on the background in Euclidean space and formalize it with vector space theory.
- To relate linear methods to other areas of mathematics such as calculus and differential equations.
- To develop an appreciation for how linear methods are used in a variety of applications.
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Course Calendar
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Week 01
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2
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Introduction to Matrices.
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3
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System Of Linear Equations.
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Week 02
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4
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Row reduction and Echelon Form of a Matrix.
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Week 03
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7
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Solution Set of Linear Equations.
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8
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Linearly Dependent and Linearly Independent Sets.
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9
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Linear Transformations.
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Week 04
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10
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The Matrix of Linear Transformations.
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Quiz01
Week 05
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13
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Characterisation of Invertible Matrices.
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14
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Partitioning of a Matrix.
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Assignment 01
Week 06
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16
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Iterative Solution of Linear Systems.
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17
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Introduction to Determinants.
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18
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Properties of Determinants.
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Week 07
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19
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Cramer's rule, Volume and Linear Transformations.
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21
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Null Spaces,Column Spaces and Linear Transformations.
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Week 08
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22
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Bases for a vector Space.
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Mid Term Exam
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24
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Dimension of a Vector Space.
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Week 09
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25
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The Rank Theorem and Invertible Matrix Theorem.
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26
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Change of Bases of a Vector Space.
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27
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Applications of vector spaces to Difference Equations.
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Quiz 02
Week 10
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28
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Eigenvalues of a Matrix.
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29
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Characteristic Equation of a Matrix.
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30
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Diagonalization of a Matrix.
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Week 11
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31
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Eigen Vectors of linear Transformation.
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32
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Complex Eigenvalues and Vectors.
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33
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Discrete Dynamical Systems.
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Week 12
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34
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Applications to Differential Equations.
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35
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Iterative Estimates for Eigenvalues.
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Quiz 03
Week 13
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37
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Revision ( system of Linear Equations).
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38
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Inner Product and orthogonal vectors.
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Week 14
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40
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Orthogonal Projections.
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42
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Least Squares Problems.
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Quiz 04
Week 15
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44
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Applications of Inner Product Spaces.
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45
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Revision of the Course and Vector Spaces.
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Final Term Exam
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