Courses

Linear Algebra and Complex Number Theory

General

Course Contents

1 – Linear Systems and Tables
1.1 Systems of linear equations
1.2 Tables
1.3 Table operations and properties
2 – Solving linear systems
2.1 Elementary tables and equivalent tables
2.2 Gaussian sequential deletion method
2.3 Determinant method (Cramer rule)
2.4 Finding an inverted array
3 – Determinant
3.1 Definition
3.2 Determinant properties
3.3 Inverse array
3.4 Other applications of determinants
4 – Diagonalization of tables
4.1 Tables and linear representations
4.2 Eigenvalues and eigenvectors
4.3 Diagonalization of tables
4.4 Finding v-th power of an array
5 – Complex Numbers
5.1 Basic concepts
5.2 Complex Number Algebra
5.3 Forms of a complex number
5.4 Complex level
5.5 Types de Moivre and Euler
5.6 Fundamental theorem of algebra
5.7 Polynomials with complex coefficients
5.8 Roots of complex numbers
5.9 Complex forces
5.10 Logarithm of complex number
6 – Applications in MATLAB environment

Educational Goals

This is a basic introductory course in higher mathematics that offers an important background of knowledge and basic concepts that are considered absolutely necessary for the understanding of the methodology and the scientific foundation of a variety of specialized courses in the science of engineering.

General Skills

Research, analysis and synthesis of data and information
Autonomous work
Promoting free, creative and inductive thinking
Adherence to good practice guidelines

Teaching Methods

Lectures
Exercises
Project assignments
Online guidance
E-mail communication
Online synchronous and asynchronous teaching platform (moodle).
Interactive teaching

Students Evaluation

Assessment Language: English / Greek
The final grade of the course is formed 100% by the grade of the theoretical part. The grade of the theoretical part is formed by a written final examination. The written final examination of the theoretical part may include: a) Multiple choice questions, b) Solving problems of application of the acquired knowledge, c) Short answer questions, d) Comparative evaluation of theory elements.

Recommended Bibliography

Higher Mathematics, Kreyszig Erwin, Ed., A.Tziola & Sons SA
Advanced Mathematics, Voskoglou Michalis, Ed., Gotsis K. & Co. EE.
Linear Algebra, Georgiou & Kougias & Megaritis, Ed., A.Tziola & Sons SA
Advanced Mathematics for Engineers, Tsiantos V., Ed., A.Tziola & Sons SA
Advanced mathematics lessons, Bratsos Athanasios
An introduction to linear algebra-for the positive sciences, Charalambous Chara, Fotiadis Anestis
Mathematics I, Elements of linear algebra-differential and integral calculus, Papaioannou Stavros, Vogiatzi Despina