### Undergraduate Programme

# Mathematics

# Course goal

• Providing in-depth comprehension of the notion of space and of the respective axiomatic notions of Spatial Analysis, which are useful for the study of space, place and distance.

• Providing basic knowledge on the principles, notions and techniques of analytic and spatial geometry and of their application in the solution of the problems of spatial analysis.

• Providing basic knowledge on the significances and methods of Single Variable and and Multivariate Calculus and on their applications in problems of Spatial and Regional Economics.

• Providing the required cognitive background in order the student to correspond in the requirements of the other courses of the Department

# Course subject

The courses provide the necessary knowledge in the field of Advanced Mathematics providing to the students the required cognitive supplies for dealing with problems of spatial and economic analysis. Within this framework the courses includes the following sections:

1. Matrix Calculus: Basic knowledge is provided, such as forms of matrices (simple, complex, reverse, matrix of functions), their operations and attributes, the determinant of a matrix and some advanced cases matrix equations and matrices including real functions.

2. Elements of Topology: Basic knowledge is provided for the comprehension, through the mathematic perspective, of the notions of space, set, topology, metric unction and distance, aiming at the enlargement and the in-depth comprehension of the corresponding notions taught in Spatial Analysis.

3. Elements of Analytic Geometry: Emphasis is given on the instruction of the 2D and 3D Euclidean space coordinates systems (Cartesian, polar, cylindrical and spherical), on coordinates’ transformation between systems and on the distance calculations within such systems, aiming at the comprehension and the enlargement of the notion of position and the corresponding problems of Spatial Analysis.

4. Vector Calculus: Basic knowledge is provided on vectors (dimension, norm, angle, interior and exterior product), given emphasis on their positioning attributes that exercise the students’ perception in the notion of space.

5. Differential Calculus: Basic knowledge is provided on Calculus regarding functions of one and more variables, given emphasis on the derivative (calculating derivative using the definition, using differentiation rules, differentiation attributes, partial derivatives and total differential).

6. Integral Calculus: Basic knowledge is provided on Integral Calculus regarding functions of one, two and three variables (definite and indefinite integrals, rules of integration, calculation of area between functions, double and triple integrals, volume calculation).

# Bibliography

- Καρανικόλας Ν.Δ. (2010), Εισαγωγή στο διαφορικό λογισμό συναρτήσεων πολλών μεταβλητών, ΕΚΔ. ΖΗΤΗ (Εύδοξος: 11270)
- Παντελίδης Γ. (2001), Ανάλυση, Τόμος ΙΙ, ΕΚΔ. ΖΗΤΗ (Εύδοξος: 10967)
- Γεωργίου Δ., Ηλιάδης Στ. (2008) Αναλυτική Γεωμετρία, (Αυτοέκδοση) Γεωργίου Δ,, Ηλιάδης Στ, (Εύδοξος: 2941)