Course Description
Linear Algebra explores the fundamental concepts and techniques focusing on vectors, matrices, systems of linear equations, and methods for solving them, vector spaces and subspaces. Also, the course also introduces eigenvalues and eigenvectors and their applications. Students learn about matrix operations, determinants, and vector spaces, which are essential tools in many areas of science and engineering. The course combines conceptual understanding with practical applications to develop strong analytical skills. By the end of the course, students build a strong base for further study in math, computing, and similar subjects.
Course Objectives
Mathematical topics aimed at applications in engineering. Matrices, operations on them. Row-echelon form. Simultaneous linear equations. Square matrices, determinants, matrix inversion. Vector spaces, subspaces, span, linear independence, change of basis, fundamental subspaces. Eigenvalues and eigenvectors, diagonalization, singular-value decomposition.
Key Concepts
- Ability of identifying the potential algebraic resources for information or knowledge regarding a given engineering issue.
- Algebraically, computationally, engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with consideration for appropriate analytical solutions in all necessary situations
- Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice.
- Ability of designing and conducting experiments, conducting data acquisition and analysis and making conclusions.
- Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.
- Consciousness for the results and effects of engineering solutions on society and universe, awareness for the developmental considerations with contemporary problems of humanity.
- Engineering graduates who are aware of the importance of safety and healthiness in project management, workshop environment as well as related legal issues.
- Engineering graduates with well-structured responsibilities in profession and ethics.
- The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.
- Engineering graduates with motivation to life-long learning and have known significance of continuous education beyond Level 6 studies for science and technology.
Learning Outcomes
- The students will demonstrate an understanding of the matrix semantics, operations on matrices.
- The students will demonstrate an understanding of the matrix semantics, operations on matrices.
- Evaluate determinants and find inverses in several methods.
- Using methods to determine the row-echelon form and rank of matrix.
- Gauss elimination process understanding matrixes concepts performance.
- Performing well to solve systems of linear equations,
- The student perform in matrix form equation and solve it using Gauss elimination method
- To understand eigenvalues and eigenvectors and solve problems applying these concepts.
- The students will develop an understanding of vector spaces. Operations on it.
- Working on subspaces, span, linear independence, basis, change of basis. SVD problem.
Recommended Textbooks
"Linear Algebra and Its Applications" by Gilbert Strang "Linear Algebra: Concepts and Methods" by Martin Anthony and Michelle Harvey