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Syllabus ( MATH 103 )


   Basic information
Course title: Linear Algebra
Course code: MATH 103
Lecturer: Assist. Prof. Roghayeh HAFEZIEH
ECTS credits: 7
GTU credits: 3 (3+0+0)
Year, Semester: 1, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: Turkish
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: This course will present the fundamental concepts of linear algebra from an engineering prospective.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Formulate linear systems as mathematical models, and obtain the general solution to any linear system.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
  2. Find the nullity, kernel, image, and rank of a linear transformation.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  3. Prove the elementary statements related to eigenvalues and eigenvectors.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Algebra of matrices:matrix addition and multiplications, powers of matrices
Week 2: Special types of matrices, block matrices, echelon matrices
Week 3: Inverse of a matrix, systems of linear equations
Week 4: Systems of linear equations, Gaussian elimination
Week 5: Determinants, Cramer's rule
Week 6: Vector spaces, linear independence, linear combinations, linear span, basis, dimension
Week 7: Rank of a matrix, subspaces, linear mappings
Week 8: Linear mappings, kernel, image, rank, and nullity
Week 9: Midterm exam
Week 10: Matrix representation of linear mappings, characteristic and minimal polynomials,
Week 11: Eigenvalues and eigenvectors, diagonalization, similarity
Week 12: Inner product spaces, Cauchy-Bunyakowstky inequality
Week 13: Orthogonality, Gram-Schmidt orhogonalization process
Week 14: Canonical forms
Week 15*: -
Week 16*: Final Exam
Textbooks and materials: Elementary Lineer Algebra 7th Ed. Bernard Kolman ve David R. Hill
Recommended readings: Schaum's Outlines, Seymur Lipschutz, Lineer Cebir
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 9 30
Other in-term studies: 0 0
Project: 0 0
Homework: 2,3,4,5,6,7,8,10,11,12,13,14 20
Quiz: 0 0
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 4 12
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 2 1
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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