School of Environmental Sciences


This course is part of the programme:
Bachelor's programme in Environment (1. Level)

Objectives and competences

Model is any formal expression about a natural phenomenon. If put into mathematical language, then we speak of a mathematical model.

Why do we need mathematical model at all?

First, “when you can measure what you are speaking about, and express it in numbers, you know something about it” (lord Kelvin). Second, mathematical models and computers today allow for detailed understanding of the most complicated environmental phenomena (e.g. typhoons), prediction of the evolution of the environmental processes (e.g. global warming), quantitative assessment of intrusions in the environment as well as control of the environmental processes (e.g. wastewater treatment plants). The course will get students acquainted with elementary modelling approaches based on first principles, initial skills in computer simulation of dynamic systems as well as ability to identify (simple) models from data.


Since the topic is multi-disciplinary, it assumes the students are familiar with fundamentals obtained in the courses of Mathematics and Physics as well as Statistics and Computer Science. Knowledge that the student gets in this course is generic and usable in almost every area of environmental sciences.

Content (Syllabus outline)

  • Preliminaries in differential and integral calculus and ordinary differential equations
  • Introduction to simulation
  • Basics of numerical solutions of ordinary and partial differential equations
  • Modelling the transport phenomena in water and air
  • Physical, chemical and biological transformation of matter
  • Modelling population dynamics
  • Callibration and model identification from data

Intended learning outcomes

Students will acquire:

  • the ability to set up the mathematical model from process description and inventory of physical phenomena,
  • the capacity to implement a model in simulation tool,
  • students will become familiar with model assessment in the context of application,
  • capacity to callibrate simple static models from data.


  • Schnoor, J. L. (1996). Environmental Modeling; Fate Transport of Pollutants in Water, Air and Soil. John Wiley & Sons, New York.
  • Socolofsky, S. A. and G. H. Jirka (2002). Environmental Fluid Mechanics, Part I: Mass Transfer and Diffusion. Lecture notes, Institut für Hydromechanik, Universität Karlsruhe.
  • Ljung, L. in T. Glad (1994). Modelling of Dynamic Systems. Prentice Hall, N. J.


Completed homework (40 %), written exam (50 %), oral exam (10 %)

Lecturer's references

Full Professor of electrical engineering at the School of Engineering and Management

DEBENJAK, Andrej, BOŠKOSKI, Pavle, MUSIZZA, Bojan, PETROVČIČ, Janko, JURIČIĆ, Đani. Fast measurement of proton exchange membrane fuel cell impedance based on pseudo-random binary sequence perturbation signals and continuous wavelet transform. Journal of power sources, ISSN 0378-7753, maj 2014, vol. 254, str. 112-118, doi: 10.1016/j.jpowsour.2013.12.094. [COBISS.SI-ID 27386663]

STRMČNIK, Stanko (editor), JURIČIĆ, Đani (editor). Case studies in control : putting theory to work, (Advances in industrial control). London [etc.]: Springer, 2013. XI, 411 str., ilustr. ISBN 978-1-4471-5175-3. ISBN 978-1-4471-5176-0. [COBISS.SI-ID 26888999]

VIŽINTIN, Jože, MARQUES QUERIDO SALGUEIRO, Jose Miguel, KRŽAN, Boris, PERŠIN, Gabrijel, JURIČIĆ, Đani, BOŠKOSKI, Pavle, DOLANC, Gregor. Naprava in postopek za stalno spremljanje maziva in vsebnosti delcev v njem : patentna prijava P-201300409. Ljubljana: Urad RS za intelektualno lastnino, 3. dec. 2013. [COBISS.SI-ID 27344167]

BOŠKOSKI, Pavle, JURIČIĆ, Đani. Fault detection of mechanical drives under variable operating conditions based on wavelet packet Rényi entropy signatures. Mechanical systems and signal processing, ISSN 0888-3270. [Tiskana izd.], avg. 2012, vol. 31, str. 369-381, doi: 10.1016/j.ymssp.2012.04.016. [COBISS.SI-ID 25765159]

GAŠPERIN, Matej, JURIČIĆ, Đani, BOŠKOSKI, Pavle, VIŽINTIN, Jože. Model-based prognostics of gear health using stochastic dynamical models. Mechanical systems and signal processing, ISSN 0888-3270. [Tiskana izd.], 2011, vol. 25, no. 2, str. 537-548, doi: 10.1016/j.ymssp.2010.07.003. [COBISS.SI-ID 23786791]

University course code: 1OK019

Year of study: 3

Semester: 1

Course principal:





  • Lectures: 45 hours
  • Exercises: 15 hours
  • Individual work: 60 hours

Course type: mandatory

Languages: slovene and english

Learning and teaching methods:
• lectures • exercises/tutorial • homework