Course Description
Description: The course offers a general view to some important ideas and techniques in the field. Starting with a discussion of systems of linear equations (the natural source of the subject) the important technique of matrices, matrix operations and determinants is considered. An illustration of the general concepts in the plane and space geometry helps the students to cultivate their intuition and interpretative skills in the area. An elementary introduction to General vector spaces, Linear Transformations and Eigenvalue problems initiates the students into this powerful technique.
Prerequisite(s): Calculus 1, Calculus 2 (Mandatory)
Course Format
This course follows the sequence of mathematical courses for engineers offered in IUT. In general, the content contains four conceptual different topics:
- System of linear equations Ax = b and their solutions.
- Operations with matrices. Determinants.
- Eigenvalues problem Ax =λx
- Linear transformations and their matrices.
Homework and Quiz: Optional Homework will be assigned but not collected. We take weekly short-quizzes during the lectures with similar questions from homework assignments. Students performed the homework should be able to succeed the quiz. The worst two quiz results will be dropped to allow students to be absent. There are also two Mandatory Homework assignments per semester.
Tentative Course Outline
Week 1: Introduction to Linear Algebra. Basics of vectors.
Problems
Quiz
Week 2: Operations with Vectors. Vector Equations of planes and lines.
Problems
Week 3: System of linear equations. Gauss-Jordan elimination.
Problems
Week 4: Operations with Matrices. Invertible matrices.
Problems
Week 5: Matrices in Special Forms. LU - decomposition.
Problems
Week 6: Vector spaces. Columns Space and Null Space.
Problems
Week 7: Independence. Rank and Dimension.
Problems
Week 8: Mid-term exam.
Week 9: Orthogonal Matrices. Projections. QR-decomposition.
Problems
Week 10: Determinants. Algorithms of determinants.
Problems
Week 11: Applications of determinants.
Problems.
Week 12: Eigenvalues and Eigenvectors. Diagonalization and its applications.
Problems
Week 13: Eigenvalues of symmetric matrices. Positive-definite matrices.
Problems
Week 15: Linear Transformations and their applications.
Problems
Week 16: Final Exam.