Technical Mathematics

Meet and complement the basic concepts and principles
of higher mathematics and their applications in science
and technology. Developing thinking skills specific to
problem solving: understanding the problem, finding
appropriate data rescue plan, rescue, checking
compliance solutions and analysis solution. Expression of
the mathematical reasoning and use it in the science and
technical research.

1. Functions
   • Fundamental concepts
   • Compositions and invertible functions
   • Elementary functions
   • Limits and continuity

2. Derivatives
   • Introduction and definition
   • Rules and derivatives of elementary functions
   • Higher derivatives

3. Application of derivatives
   • Increasing, decreasing functions, relative extrema
   • Convexity and inflection points
   • Graphic of a function
   • L'Hopital's rule

4. Integrals
   • Indefinite integral
   • Definite integral
   • The connection between indefinite and definite integrals
   • Methods of integration (by parts and by substitution)
   •

5. Applications of integrals
   • Arc length. Area. Volumes
   • Applications in physics

6. Differential equations
   • Linear differential equation of first order
   • Linear differential equation of second order with constant coefficients
   • Examples

7. Functions in more variables
   • Fundamental concepts, graphs, level curves
   • Partial derivatives, gradient, divergence
   • Relative extrema
   • Method of least squares

Knowledge and understanding:
By the end of this course students will be able to:
-calculate limits, derivatives, integrals
-draw the graphic of a function
-solve linear differential equations of first and second order
-calculate partial derivatives and relative extrema of
functions with more variables.

• G. Tomšič, B.Orel, N. Mramor Kosta, Matematika I, Založba FE in FRI, Ljubljana, 2000 (3.izdaja).
• B. Orel, Linearna algebra, 2020. E-version
• M. Zeljko, Matematične metode. E-version
• P. Oblak, Matematika. E-version
• R. Courant, J. Fritz, Introduction to Calculus and Analysis, vol.1, Springer, 1999. Catalogue
• David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron, Linear Algebra, 2013. E-version
• W. Trench, Introduction to Real Mathematics, 2013. E-version
• Slovensko angleški matematični slovar. E-version

Seminar work and homeworks. Written exam. 30%/ 70%

Prof. Dr. Irina Elena Cristea
Habilitation: Assoc. Prof. in the field of Mathematics
Principal education and research areas: Mathematics, algebraic hyperstructures and connections with fuzzy sets and their generalizations.
Professional career: Prof. Irina Elena Cristea received the PhD in Mathematics, with specialization in Algebra, in 2007, from the University of Constanta, Romania. She started the research career in 2003 at the University of Iasi, Romania, where she worked as Teaching Assistant for 4 years. After a postdoctoral position at Udine University, Italy, in January 2012, she was employed at the University of Nova Gorica, as Assistant Professor in Mathematics, conducting research in Algebraic Hyperstructure Theory. Since 2017, she is Associate Professor in Mathematics, being affiliated with the Centre for Information Technologies and Applied Mathematics. She is currently teaching Mathematics at the School of Engineering and Management, School of Environmental Sciences, School of Sciences at the University of Nova Gorica.

Selected bibliography

1. SONEA, Andromeda Cristina, CRISTEA, Irina Elena. Eulerʹs totient function applied to complete hypergroups. AIMS mathematics. 2023, vol. 8, iss. 4, str. 7731-7746. ISSN 2473-6988. [COBISS.SI-ID 138561795]

2. LINZI, Alessandro, CRISTEA, Irina Elena. Dependence relations and grade fuzzy set. Symmetry. 2023, vol. 15, iss. 2, 311, str. 1-18, ilustr. ISSN 2073-8994. [COBISS.SI-ID 138966275]

3. BORDBAR, Hashem, JANČIĆ-RAŠOVIĆ, Sanja, CRISTEA, Irina Elena. Regular local hyperrings and hyperdomains. AIMS mathematics. 2022, vol. 7, iss. 12, str. 20767-20780. ISSN 2473-6988. [COBISS.SI-ID 123160323]

4. CRISTEA, Irina Elena, NOVAK, Michal, ONASANYA, Babatunde Oluwaseun. Links between HX-groups and hypergroups. Algebra colloquium. [Print ed.]. 2021, vol. 28, iss. 3, str. 441-452. ISSN 1005-3867. [COBISS.SI-ID 65771011]

5. CRISTEA, Irina Elena, KANKARAS, Milica. The reducibility concept in general hyperrings. Mathematics. 2021, vol. 9, iss. 17, str. 1-14, ilustr. ISSN 2227-7390. [COBISS.SI-ID 73968899]

6. DAVVAZ, Bijan, CRISTEA, Irina Elena. Fuzzy algebraic hyperstructures : an introduction, (Studies in fuzziness and soft computing, vol. 321). Cham: Springer, cop. 2015. X, 242 str., ilustr. ISBN 978-3-319-14761-1 [COBISS.SI-ID 3704571]