# Technical Mathematics

This course is part of the programme:

Bachelor's programme in Engineering and Management (First Level)

## Objectives and competences

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.

## Content (Syllabus outline)

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

## Intended learning outcomes

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.

## Readings

- R. Jamnik, Matematika, DMFA, Ljubljana 1994.

- M. Zeljko, Matematične metode, http://zeljko.dmfa.si/lectures/2011/BioT-Matematika.pdf

- R. Courant, J. Fritz, Introduction to Calculus and Analysis, vol.1, Springer, 1999

- W. Trench, Introduction to Real Mathematics, http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

- Slovensko angleški matematični slovar:http://www2.arnes.si/~mpavle1/slovar.html

## Assessment

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

## Lecturer's references

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

KANKARAS, Milica, CRISTEA, Irina Elena. Fuzzy reduced hypergroups. Mathematics, ISSN 2227-7390, 2020, vol. 8, iss. 2, str. 1-12. [COBISS.SI-ID 5566715]

SONEA, Andromeda Cristina, CRISTEA, Irina Elena. The class equation and the commutativity degree for complete hypergroups. Mathematics, ISSN 2227-7390, 2020, vol. 8, iss. 12, str. 1-15. [COBISS.SI-ID 43881731]

ZADEH, Azam Adineh, NOROUZI, Morteza, CRISTEA, Irina Elena. The commutative quotient structure of m-idempotent hyperrings. Analele Universitǎţii “Ovidius” Constanţa, Seria Matematicǎ, ISSN 1224-1784, 2020, vol. 28, no. 1, str. 219-236. [COBISS.SI-ID 5593595]

BORDBAR, Hashem, NOVAK, Michal, CRISTEA, Irina Elena. A note on the support of a hypermodule. Journal of algebra and its applications, ISSN 0219-4988, 2020, vol. 19, no. 1, str. 1-19. [COBISS.SI-ID 5335291]

CRISTEA, Irina Elena, HASSANI SADRABADI, Elhan, DAVVAZ, Bijan. A fuzzy application of the group Zn to complete hypergroups. Soft computing, ISSN 1432-7643. [Print ed.], 2020, vol. 24, iss. 5, str. 3543-3550, ilustr., doi: 10.1007/s00500-019-04121-0. [COBISS.SI-ID 5404667]

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]

University course code: 1GI001

Year of study: 1

Semester: 1

Course principal:

Lecturer:

Assistant:

ECTS: 7

Workload:

- Lectures: 60 hours
- Exercises: 30 hours
- Individual work: 85 hours

Course type: mandatory

Languages: slovene

Learning and teaching methods:

lectures, exercises and homework