# Mathematics Ι

## Educational goals

The aim of the course, as a general background course, is to provide students with the necessary mathematical knowledge, tools and techniques to handle a range of problems that arise in applications of computer science and electronic systems. Upon successful completion of the course, the student is expected to be able to:

• Handle complex numbers in orthogonal, polar and exponential form and utilizes key tools of complex analysis.
• Understand and be able to use the concepts of vector spaces, linear independence, basis and dimension.
• Recognizes key matrix form and perform operations on them. Compute the row reduced echelon form of a matrix, using elementary row operations using the Gauss - Jordan elimination algorithm.
• Solve systems of linear equations by utilizing the appropriate table methodology where appropriate. Compute the eigenvalues and eigenvectors of a matrix.
• Understand the basic concepts around the real functions (limits, continuity, derivatives) and is able to calculate derivatives using the associated rules. Be able to apply theorems related to differential calculus and compute the Taylor series expansion of a given function. Apply the process of function study to design its graph.
• Compute indefinite integrals by applying one of the three main methodologies (by parts, by factors, by substitution).
• Distinguish definite integrasl from the indefinite ones and be able to apply related integral calculus results to perform its calculation. Apply the relevant theory to calculate areas or volumes of geometric shapes that are appropriately described.
##### General Skills
• Work in multidisciplinary environement
• Development of new research ideas
• Improvement of open minded, creative and inductive thought

## Course Contents

Complex Numbers: Definition, operations, polar and exponential forms, form conversions, roots of complex numbers, solution of polynomial equations.

Linear Algebra: Vector Space, Linear dependence, Basis – Dimension of a vector space, Inner Product, Matrices, Matrix Operations and properties,  Matrix Inversion, Elementary Row Operations, Gauss – Jordan elimination, Determinants and properties, Linear Systems, Eigenvalues – Eigenvectors.

Differential Calculus: Real functions, Limits, Continuity,  Derivative, Derivative rules, Applications, Mean Value Theorem, Taylor Serial,  De Hospital’s rule, Study of functions.

Integral Calculus: Indefinite Integral Integration by Parts – by Factors – by Substitution, Definite Integral, Properties, The Fundamental Theorem of Integral Calculus, Mean Value Theorem of Integral Calculus, Geometric Applications of Definite Integrals.

## Teaching Methods - Evaluation

##### Teaching Method
• Face to face teaching.
##### Use of ICT means
• Notes and slides available in electronic form (in greek).
• Use of asynchronous learning platform (Moodle).
##### Teaching Organization
 Activity Semester workload Lectures 52 Self-study 108 Communication/Collaboration 20 Total 180
##### Students evaluation

The final exam consists of 7-8 thought development exercises, on the following subjects:

- Complex Numbers
- Vector Spaces and Matrices
- Linear Systems
- Function study
- Application of differential calculus resluts (Mean Value Theorem, Taylor, De Hospital, etc.)
- Calculation of definite and indefinite integrals
- Geometric application of definite integrals

The above examination scheme is communicated to the students through:

(a) The course web page
(b) The asynchronous learning platform Moodle
(c) Announcements at the begining of the semester and during the lectures.

Η γραπτή τελική εξέταση του μαθήματος που περιλαμβάνει 5-6 κύρια ερωτήματα ανάπτυξης, που εμπλέκουν τα παρακάτω ζητούμενα:

## Recommended Bibliography

##### Recommended Bibliography through "Eudoxus"
1. ΠΕΤΡΑΚΗΣ Λ. ΑΝΔΡΕΑΣ, ΠΕΤΡΑΚΗ Α. ΔΩΡΟΘΕΑ, ΠΕΤΡΑΚΗΣ Α. ΛΕΩΝΙΔΑΣ, "ΜΑΘΗΜΑΤΙΚΑ Ι", Εκδότης: ΠΕΤΡΑΚΗ ΔΩΡΟΘΕΑ , Έκδοση: 2, 2017, ISBN: 978-618-83244-0-4, [Κωδ. Ευδόξου 77107076]
2. Χ.Κ. Τερζίδης, "Λογισμός συναρτήσεων μιας μεταβλητής με στοιχειά διανυσματικής & γραμμικής άλγεβρας", Εκδόσεις Χριστοδουλίδου Ο.Ε,, 2η έκδοση, 2006, ISBN: 960-8183-56-1, [Κωδ. Ευδόξου 59367707]
##### Complementary greek bibliography
1. Α. Αθανασιάδης, "Διαφορικός και ολοκληρωτικός λογισμός συναρτήσεων μιας μεταβλητής και εισαγωγή στη γραμμική άλγεβρα", Εκδόσεις Α. Τζιόλα & Υιοί Α.Ε, 4η έκδοση, 2001, ISBN: 960-8129-08-7.
2. Δημητρακούδης, Θεοδώρου, Κικίλιας, Κουρής, Παλαμούρδας , "Διαφορικός Ολοκληρωτικός Λογισμός", Εκδόσεις Δηρός Α.Ε, 1η έκδοση, 2002,
##### Complementary international bibliography
1. Stewart J., "Single Variable Calculus", , Brooks/Cole Pub Co, 3rd ed, 1994, ISBN: 0534218288.
2. Thomas, G.B., Weir M.D., Hass, J., Thomas, "Calculus", Addison Wesley, 12th Edition, 2009, ISBN: 0321587995.
3. Strang G., "Linear Algebra and its applications¨", Thomson, Brooks/Cole, 2009.