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)

  • Functions and their representation
  • Preliminaries in differential and integral calculus and ordinary differential equations
  • Theoretical (analytical) models
  • Basics of numerical solutions of ordinary and partial differential equations
  • Introduction to simulation
  • Modelling the transport phenomena
  • Physical, chemical and biological transformation of matter

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.


  • W.H. Press et al. (1992). Numerical Recipes in C. The Art of Scientific Computing. Cambridge University Press.
  • Craig Finch (2011) Sage Beginner’s Guide. Packt Publishing.
  • Paul’s Online Notes (Paul Dawkins, Lamar University)

Calculus I –

Differential Equations –


Written exam (50%), oral exam (50%)

Lecturer's references

Assistant professor in field of Physics at School of Science at University of Nova Gorica.

Last 5 publications:

  • BADASYAN, Artem, MAVRIČ, Andraž, KRALJ CIGIĆ, Irena, BENCIK, Tim, VALANT, Matjaž, Polymer nanoparticle sizes from dynamic light scattering and size exclusion chromatography: the case study of polysilanes. Soft matter, 14, 4735-4740 (2018).
  • MAVRIČ, Andraž, BADASYAN, Artem, MALI, Gregor, VALANT, Matjaž. Growth mechanism and structure of electrochemically synthesized dendritic polymethylsilane molecules. European Polymer Journal, 90, 162-170 (2017).
  • MAVRIČ, Andraž, BADASYAN, Artem, FANETTI, Mattia, VALANT, Matjaž. Molecular size and solubility conditions of polysilane macromolecules with different topology. Scientific reports, 6, 1-8 (2016)
  • ŠKRBIĆ, Tatjana, BADASYAN, Artem, HOANG, Trinh Xuan, PODGORNIK, Rudolf, GIACOMETTI, Achille. “From polymers to proteins: the effect of side chains and broken symmetry on the formation of secondary structures within a Wang-Landau approach.” Soft matter, 12, 4783 (2016).
  • BADASYAN, Artem, MAMASAKHLISOV, Yevgeni S., PODGORNIK, Rudolf, PARSEGIAN, Vozken Adrian. “Solvent effects in the helix-coil transition model can explain the unusual biophysics of intrinsically disordered proteins.”, The Journal of Chemical Physics 143, 014102 (2015).

University course code: 1OK019

Year of study: 3

Semester: 1

Course principal:





  • Lectures: 30 hours
  • Exercises: 30 hours
  • Individual work: 60 hours

Course type: mandatory

Languages: slovene and english

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