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MTH501 : Linear Algebra

Course Overview

Course Synopsis

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.

Course Learning Outcomes

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.

Course Calendar

Introduction1Elementary Linear Algebra and its Application1-5
Introduction to Matrices.2(3rd edition)6-17
System Of Linear Equations.3By David C. Lay18-29
Row reduction and Echelon Form of a Matrix.430-43
Vector Equations.544-55
Matrix Equations.656-65
Solution Set of Linear Equations.766-73
Linearly Dependent and Linearly Independent Sets.881-88
Quiz No. 1
Linear Transformations.989-225
The Matrix of Linear Transformations.1098-107
Matrix Algebra.11121-133
Inverse of a Matrix.12134-143
Characterization of Invertible Matrices.13144-149
Partitioning of a Matrix.14150-157
Matrix Factorization.15158-167
Iterative Solution of Linear Systems.16168-201
Assignment # 1
Introduction to Determinants.17202-207
Properties of Determinants.18208-216
Cramer"s rule, Volume and Linear Transformations.19217-222
Vector Spaces.20232-241
Null Spaces, Column Spaces and Linear Transformations.21242-252
Bases for a vector Space.22253-261
Midterm Examination
Coordinate systems.23262-271
Dimension of a Vector Space.24272-278
The Rank Theorem and Invertible Matrix Theorem.25278-286
Change of Bases of a Vector Space.26287-289
Applications of vector spaces to Difference Equations.27290-301
Eigenvalues of a Matrix.28317-325
Quiz No. 2
Characteristic Equation of a Matrix.29326-334
Diagonalization of a Matrix.30335-343
Eigen Vectors of linear Transformation.31343-350
Assignment # 2
Complex Eigenvalues and Vectors.32351-358
Discrete Dynamical Systems.33358-364
Applications to Differential Equations.34369-373
Iterative Estimates for Eigenvalues.35379-384
Revision (system of Linear Equations).37386-387
Inner Product and orthogonal vectors.38387-399
Orthogonal Sets.39400-402
Orthogonal Projections.40402-407
Null Spaces, Column Spaces and Linear Transformations.41413-417
Gram-Schmidt Process for finding orthogonal Bases of a Vector Space.42418-423
Inner Product Spaces.43443-450
Applications of Inner Product Spaces.44452-454
Revision of the Course and Vector Spaces.45455-458
Final Term Exams
Note: Any kind of change in the course calandar can be done during semester. So please keep update yourself from 'Overview' on VULMS.
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