Study programme

Quantitative methods for agriculture and environment science (169512)

ECTS 3.00
Teaching hours 30
Lectures 20
Auditory exercises 10
Assist. Prof. Biserka Kolarec, PhD
Associate teacher for exercises
Assist. Prof. Biserka Kolarec, PhD
Sufficient (2) 60-70 %
Good (3) 71-80 %
Very good (4) 81 -90%
Excellent (5) 91-100%

Course coordinator

Assist. Prof. Biserka Kolarec, PhD
Assist. Prof. Biserka Kolarec, PhD

Course description

Calculus: Exploring of mathematical approaches and solutions that cut across agriculture and environmental disciplines and introducing of analytical techniques that are thought infrequently in other courses. The goal is to provide students with the tools and confidence they need to apply quantitative methods in their own research (differential and integral calculus, multivariable calculus, with examples and applications from the environmental sciences).

Type of course

General competences

This course introduces the use of quantitative methods in environmental analysis. Students will learn how to apply basic principles of natural science to a variety of globally important problems.

Types of instruction

  • Auditory Exercises
  • Lectures
  • Practicum

Learning outcomes

Learning outcome Evaluation methods
have working knowledge of basic concepts, methods and techniques from calculus; exam, practical work, project
be able to apply mathematical knowledge, insights and methods to solve basic problems in life sciences (agriculture and environment) using a systematic approach; exam, practical work, project
be able to critically reflect upon the results; exam, practical work, project
be able to interpret the results in terms of the problem that was modelled mathematically; exam, practical work, project
be able to use mathematical software in elaborating mathematical models. exam, practical work, project

Working methods

Teachers' obligations

1. Course planning
2. Selection and creation of teaching materials
3. Evaluation of course, teaching materials and curriculum
4. Construct tests
5. Grade students on the basis of their achievement

Students' obligations

1. Attend lectures regularly
2. Do homeworks and participate actively during lectures
3. Write tests and win at least 25% of points on each test to get the signature
4. Do individual projects

Methods of grading

Evaluation elements Maximum points or Share in evaluation Grade rating scale Grade Direct teaching hours Total number of average student workload ECTS
1st exam 40 % 14 20 1
2nd exam 30 % 8 20 1
3rd exam 30 % 8 20 1
activity up to 10 %
Total 100 % 30 60 3
Evaluation elements Description Deadline Recoupment
3rd Exam functions of several variables 16th week

Weekly class schedule

  1. Introduction L - Survey of elementary functions. Real functions of one real variable
  2. Differential of a function L - Limit, derivative, interpretations of derivative, differential of a function, tabular differentiation
  3. Differentiation techniques E - Differentiation techniques, higher order derivatives
  4. Minimum and maximum problems I L+E - Applications to minimum and maximum problems
  5. Minimum and maximum problems II E - Exercises on minimum and maximum problems
  6. Integration I L - Definite and indefinite integrals, Newton-Leibnitz formula
  7. Integration II E - Methods of finding indefinite integrals
  8. Differential equations I L - Basic concepts and methods of solving
  9. Differential equations II L+E - Methods of solving
  10. Differential equations III E - Solving differential equations
  11. Matrix algebra I L - Survey of matrix algebra, determinants, eigenvalues and eigenvectors
  12. Matrix algebra II E - Exercises on matrix algebra
  13. Functions of several variables I L - Partial derivatives and differentials of functions of several variables
  14. Functions of several variables II L+E - Maximum and minimum of functions of several variables
  15. Functions of several variables III E - Exercises on maximum and minimum of functions of several variables

Obligatory literature

  1. K. Sydsaeter, P. J. Hammond: Mathematics for Economic Analysis, Prentice Hall, 2002
  2. K. Sydsaeter, P. J. Hammond, A. Seierstad, A. Strom: Further Mathematics for Economic Analysis, Prentice Hall, 2008

Recommended literature

  1. M. W. Klein: Mathematical methods for economics, Pearson Education, 2002.

Similar course at related universities

  • Mathematik, BOKU, Wien
  • Mathematik und Statistik, Agricultural Sciences, University of Hohenheim