Title  ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ / LINEAR ALGEBRA 
Code  131 
Faculty  Engineering 
School  Mechanical Engineering 
Cycle / Level  1st / Undergraduate 
Teaching Period  Winter 
Coordinator  Vasileios Rothos 
Common  Yes 
Status  Active 
Course ID  600014332 
Programme of Study: UPS of School of Mechanical Engineering
Registered students: 308
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Compulsory Course  1  1  4 
Academic Year  2019 – 2020 
Class Period  Winter 
Faculty Instructors 

Instructors from Other Categories  
Weekly Hours  3 
Class ID  600149879

Course Category
General Foundation
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600149879
 eLearning (Moodle):
Language of Instruction
 Greek (Instruction, Examination)
Learning Outcomes
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in collegelevel mathematics (and increasingly in high school).
After successfully completing the course, you will have a good understanding of the following topics and their applications:
Systems of linear equations
Row reduction and echelon forms
Matrix operations, including inverses
Block matrices
Linear dependence and independence
Subspaces and bases and dimensions
Orthogonal bases and orthogonal projections
GramSchmidt process
Linear models and leastsquares problems
Determinants and their properties
Cramer's Rule
Eigenvalues and eigenvectors
Diagonalization of a matrix
Symmetric matrices
Positive definite matrices
Similar matrices
Linear transformations
Singular Value Decomposition
General Competences
 Apply knowledge in practice
 Work autonomously
 Work in teams
Course Content (Syllabus)
Cartesian products, mathematical induction. Matrices, linear transformations on real nspace,solving linear algebraic systems, linear independence and dimension, bases and coordinates, determinants, orthogonal projections, least squares, eigenvalues and eigenvectors and their applications to quadratic forms. Complex eigenvalues and eigenvectors are also covered in the 2 by 2 and 3 by 3 cases.
Keywords
matrices linear systems bases vector spaces eignevalues eigenvectors quadratic forms applications
Educational Material Types
 Notes
 Slide presentations
 Book
Use of Information and Communication Technologies
Use of ICT
 Use of ICT in Course Teaching
 Use of ICT in Communication with Students
Description
projector PC
Course Organization
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  72  2.4  
Tutorial  20  0.7  
Interactive Teaching in Information Center  20  0.7  
Written assigments  5  0.2  
Exams  3  0.1  
Total  120  4 
Student Assessment
Description
Final exam 3hrs
Student Assessment methods
 Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [2898]: ΕΙΣΑΓΩΓΗ ΣΤΗ ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ, GILBERT STRANG
Βιβλίο [204]: ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ ΚΑΙ ΕΦΑΡΜΟΓΕΣ, STRANG GILBERT
Βιβλίο [33314]: Εισαγωγή στη ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ, Θεδοδώρα ΘεοχάρηΑποστολίδη, Χαρά Χαραλάμπους, Χαρίλαος Βαβατσούλας
Βιβλίο [4649]: ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ ΚΑΙ ΑΝΑΛΥΤΙΚΗ ΓΕΩΜΕΤΡΙΑ, ΦΙΛΙΠΠΟΣ Ι. ΞΕΝΟΣ Λεπτομέρειες
Last Update
09062020