Growth processes: mathematical basics and projects for students


Growth is a phenomenon occurring everywhere, in nature, in the economy and in society. Mathematical models are hidden behind the different growth processes. After explaining the mathematical basics in the context of growth and after introducing growth models and some of their applications, it is illustrated how teams of students can start a lot of project work containing mathematics, modelling and simulation. During this work, students can learn a lot about mathematics and its relation to practical problems, about the gap between models and reality, about problem solving in teams and about the translation of solutions into software products.


1. Chen, K., Giblin, P. and Irving, A., Mathematical Explorations with MATLAB. Cambridge: Cambridge University
Press (1999).
2. Edwards, C.H. and Penney, D.E., Differential Equations & Linear Algebra. New Jersey: Prentice Hall (2001 ).
3. Gilpin, M.E. and Ayala, F.J., Global models of growth and competition. Proc. Nat. Acad. Sci., 70, 3590-3593
4. Meadows, D., The Limits to Growth. New York: Universe Books (1972).
5. Murray, J.D., Mathematical Biology: I. An Introduction. (3rd Edn), New York: Springer (2002).
6. Polking, J. and Arnold, D., Ordinary Differential Equations Using MATLAB. New Jersey: Prentice Hall (1999).
7. Schott, D., Processes in nature - students train modelling and simulation using mathematics and Matlab. Proc. 2nd
World Conf. on Technol. and Engng. Educ., Ljubljana, Slovenia, 71 -77 (2011).
8. Schott, D., Limits to growth and mathematical basics. Proc. 8th Southern Hemisphere Conf. on Teaching and
Learning Undergraduate Mathematics and Statistics, Rotorua, New Zealand, 336-344 (2011).
9. Stuart, J., Calculus: Concepts and Contexts. Pacific Grove, CA: Brooks/Cole, Thomson Learning (2001 )