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Description of MATE 123 LINEAR ALGEBRA| Course Name: | LINEAR ALGEBRA | | Course Code: | MATE 123 | | Type of Course: | Undefined | | Level of Course: | Undergraduate (First Cycle) | | Year of Study: | 1 | | Semester/Trimester: | Fall | | ECTS Credits: | 5 | | FU Credits: | 3 | | Name(s) of Lecturer(s): | Suat KARADENİZ A-335 ( skaradeniz@fatih.edu.tr )
Tevfik BİLGİN A-410 ( tbilgin@fatih.edu.tr )
İsmail Gökhan KELEBEK A-335 ( gkelebek@fatih.edu.tr ) | | Course Coordinator: | Tevfik BİLGİN | | Objectives of the Course: | Linear Algebra is a Math of the systems of linear equations and their solutions. There are a variety of applications of Linear Algebra. Sufficient knowledge in this field can assist students in learning other (more applicable) courses as Linear Programming Problems, Operations Research, Problems of Optimization ,etc. The main objectives of the course are • To extend the students knowledge on the Systems of Linear Equations • To realize the main areas of applicability of LA | | Course Description: | Introduction to matrices. Fields and vector spaces, linear transformations, change of basis. Linear equations, existence and classification of solutions, Gaussian elimination and LU decomposition. Characteristic equation of a matrix: eigenvalues, eigenvectors and the Jordan form. Numerical techniques for computing eigenvalues and eigenvectors. Inner product spaces, quadratic form. | | Learning Outcomes: | 1. Students will read, interpret, and use the vocabulary, symbolism and basic definitions used in linear algebra, including vectors, matrices, vector spaces, subspaces, linear independence, span, basis, dimension, linear transformation, inner product, eigenvalue and eigenvector
2. Students will identify and apply the theorems about and the characteristics of linear spaces and linear transformations. Determine bases, compute dimensions, evaluate linear transformations, solve systems of linear equations and find determinants
3. Students will apply properties and theorems about linear spaces to specific mathematical structures that satisfy the linear space axioms. | | Mode of Delivery: | Face-to-Face | | Prerequisites: | None | | Co-requisites: | None | Course Contents:
( Weekly Lecture Plan ) | | Week | Topics | | 1 | Systems of Linear Equations | | 2 | Types of matrices. Inverse Matrix. | | 3 | Solving Linear Systems. Gauss elimination method. Echelon form of a Matrix | | 4 | Determinants. Cramer’s Rule Determinant of 2x2 matrix, 3x3 matrix,..induction | | 5 | Solving Linear Systems. Analysis | | 6 | Vector Spaces Definition | | 7 | Linear independence | | 8 | Linear Transformations Definition | | 9 | Review Midterm | | 10 | Representation of LT by Matrix | | 11 | Eigenvalue, Eigenvector , Characteristic value, Charcteristic vector | | 12 | Inner Product Spaces Inner Product | | 13 | Inner Product Spaces Orthonormal basis, Orthogonalization process | | 14 | Quadratic Form Bilinear Forms, Sesqui-linear forms |
| | Recommended Reading: | Richard Hill: Elementary Linear Algebra Kenneth Hofman, Ray Kunze: Linear Algebra David C. Lay: Linear Algebra and its Applications | | Planned Learning Activities and Teaching Methods: | Lectures | | Assessment Methods: |
| Method | Quantity |
(%) | | Midterm Exam(s) | 1 | 40 | | Final Exam | 1 | 60 | | | Language of Instruction: | Turkish | | Work Placement(s): | N/A |
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