# LINEAR ALGEBRA

 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: 281
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course114

 Academic Year 2021 – 2022 Class Period Winter Faculty Instructors Vasileios Rothos 3hrs Instructors from Other Categories Weekly Hours 3 Class ID 600192511
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
Digital Course Content
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 college-level 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 Gram-Schmidt process Linear models and least-squares 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 n-space,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
Lectures722.4
Tutorial200.7
Interactive Teaching in Information Center200.7
Written assigments50.2
Exams30.1
Total1204
Student Assessment
Description
Final exam 3hrs or final coursework and 2 midterm courseworks
Student Assessment methods
• Written Exam with Multiple Choice Questions (Formative, Summative)
• Written Exam with Short Answer Questions (Summative)
• Written Exam with Extended Answer Questions (Formative, Summative)
• Written Assignment (Formative, Summative)
• 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 Θεοχάρη-Αποστολίδη, Χαρά Χαραλάμπους, Χαρίλαος Βαβατσούλας Βιβλίο [4649]: ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ ΚΑΙ ΑΝΑΛΥΤΙΚΗ ΓΕΩΜΕΤΡΙΑ, ΦΙΛΙΠΠΟΣ Ι. ΞΕΝΟΣ Λεπτομέρειες
Last Update
12-01-2022