SCHOOL

ENGINEERING

ACADEMIC UNIT

ELECTRICAL & COMPUTER ENGINEERING

LEVEL OF STUDIES

Undergraduate

COURSE CODE

ECE_Υ104

SEMESTER

1^st  

COURSE TITLE

LINEAR ALGEBRA

INDEPENDENT TEACHING ACTIVITIES
if credits are awarded for separate components of the course, e.g. lectures, laboratory exercises, etc. If the credits are awarded for the whole of the course, give the weekly teaching hours and the total credits

WEEKLY TEACHING HOURS

CREDITS

Theory Lectures and Recitations

3hrs/wk

3

Add rows if necessary. The organisation of teaching and the teaching methods used are described in detail at (d).

COURSE TYPE

general background,
special background, specialised general knowledge, skills development

Skills development course for solving linear algebra problems,  which appear in almost all different subjects of electrical engineering and computer engineering

PREREQUISITE COURSES:

Typically there are no prerequisite courses, however the students are assumed to have the analytical skills required by the University Entrance System and the Pan-Hellenic Exams to enter in the Department.

LANGUAGE OF INSTRUCTION and EXAMINATIONS:

Greek

IS THE COURSE OFFERED TO ERASMUS STUDENTS

COURSE WEBSITE (URL)

https://eclass.upatras.gr/courses/EE764/

Learning outcomes

The course learning outcomes, specific knowledge, skills and competences of an appropriate level, which the students will acquire with the successful completion of the course are described.

Consult Appendix A

·    Description of the level of learning outcomes for each qualifications cycle, according to the Qualifications Framework of the European Higher Education Area

·    Descriptors for Levels 6, 7 & 8 of the European Qualifications Framework for Lifelong Learning and Appendix B

·    Guidelines for writing Learning Outcomes

After a successful completion of the course the student will be expected to know the basic notions of Matrix Algebra and the need of its usage for solving problems in different scientific fields. To understand the usage of the determinant and the inverse of a matrix and know how to calculate them efficiently, whenever needed.  To carry the theoretical background for solving homogeneous and non-homogeneous linear systems. To understand the notions of vector spaces and subspaces, linear independence of vectors, basis and dimension of a basis, and that of linear transformations.  To understand the notion of eigenvalues and eigenvectors, similarity and diagonalization of matrices and know how to use diagonalization for calculating powers of matrices, polynomials and series of matrices and quadratic forms.

 General Competences

Taking into consideration the general competences that the degree-holder must acquire (as these appear in the Diploma Supplement and appear below), at which of the following does the course aim?

Search for, analysis and synthesis of data and information, with the use of the necessary technology

Adapting to new situations

Decision-making

Working independently

Team work

Working in an international environment

Working in an interdisciplinary environment

Production of new research ideas

Project planning and management

Respect for difference and multiculturalism

Respect for the natural environment

Showing social, professional and ethical responsibility and sensitivity to gender issues

Criticism and self-criticism

Production of free, creative and inductive thinking

……

Others…

…….

The course aims at developing skills mainly for independent work and occasionally for team and collaborative work, for effective decision making, as well as for promoting free, creative and inductive thinking.

Matrices and Matrix Algebra. Linear systems. Definitions and basic operations. Transpose and its properties. Gauss elimination, partial pivoting and LU Decomposition. Determinant and its properties. Inverse of a matrix. Gauss-Jordan elimination. Rank of a matrix. Canonical form. Homogeneous and Non-homogeneous systems. Introduction in Vector Spaces. Linear dependence/independence of vectors. Eigenvalues, eigenvectors: definition and properties. Similarity and diagonalization. Quadratic forms. Matrices polynomials and Cayley-Hamilton theorem. Functions of matrices. The exponential matrix.

DELIVERY
Face-to-face, Distance learning, etc.

Face to Face in classroom

USE OF INFORMATION AND COMMUNICATIONS TECHNOLOGY
Use of ICT in teaching, laboratory education, communication with students

Lectures are performed with the help of viewgraphs projected in class simultaneously with the use of whiteboard for better understanding of the analytical techniques needed in theory and exercises. In addition, the electronic platform “eclass” of the University is used for better support of students’ educational needs and also for communicating with them. The   

TEACHING METHODS

The manner and methods of teaching are described in detail.

Lectures, seminars, laboratory practice, fieldwork, study and analysis of bibliography, tutorials, placements, clinical practice, art workshop, interactive teaching, educational visits, project, essay writing, artistic creativity, etc.

The student's study hours for each learning activity are given as well as the hours of non-directed study according to the principles of the ECTS

STUDENT PERFORMANCE EVALUATION

Description of the evaluation procedure

Language of evaluation, methods of evaluation, summative or conclusive, multiple choice questionnaires, short-answer questions, open-ended questions, problem solving, written work, essay/report, oral examination, public presentation, laboratory work, clinical examination of patient, art interpretation, other

Specifically-defined evaluation criteria are given, and if and where they are accessible to students.

Written final exam in Greek Language which consists of:

¬  4 -5 exercises (over the full length of the material) that require full development of a solution and justification

¬  3-4 questions that usually ask for a short justification or short proof and require critical thinking or in-depth understanding of the material

·        Linear Algebra and applications, Gilbert  Strang,

·        Applied Mathematics, V.V. Markellos, Editors: Gotsis (in greek)

·        Introduction to Linear Algebra and Analytic Geometry, Th. Ioannidou  A. Tziola & Sons (in greek)

·        Linear Algebra, Georgiou D., Kougias I. Megaritis A. Tziola & Sons (in greek)