Applied Mathematics

Course Description:

Continuous Dynamical Systems, Discrete Dynamical Systems, Differential Systems of 1st order, Discrete Systems of Difference Equations, Chaos theory.

Learning Objectives:

The aim of this module is the introduction of the students into the Dynamical Systems theory and into the new techniques that are used for the study of the economical models. Having studied a lot of economical models, we will try to answer the question: «What are the Mathematics that one should know, in order to be able to involve into those models?». The answer is given by emphasizing the main theories that are used in the contemporary study of Dynamical Systems. The keywords are: Phase Space, Stability, Bifurcations, Attractors and Chaos. The continuous computing growth has led the economists into more easily routes of modeling economical problems. During our courses we will use some of the most powerful software tools, such as Excel and Maxima.

Bibliography:

In Greek language

• Chiang, Alpha: «Μαθηματικές Μέθοδοι Οικονομικής Ανάλυσης», Τόμος Β’ (Κεφ. 13 – 18), εκδόσεις ΚΡΙΤΙΚΗ

• Λουκάκης, Μανώλης: «Μαθηματικά Οικονομικών Επιστημών», Τόμος Β’ (Κεφ. 18 – 24), εκδόσεις ΣΟΦΙΑ

In English language

• Shone, Ronald (2002): «Economic Dynamics. Phase diagrams and their Economic application», εκδόσεις Cambridge University Press, (Ch. 1 – 8, 10 και 11).

• Kaplan, Daniel and Glass, Leon (1995): «Understanding Nonlinear Dynamics», εκδόσεις Springer-Verlag, (Ch. 1, 4 και 5)

• Puu, Tönu (2003): «Attractors, Bifurcations and Chaos. Nonlinear Phenomena in Economics», εκδόσεις Springer-Verlag, (Ch. 1 – 10)

• Gandolfo, Giancarlo (2005): «Economic Dynamics: Study edition», εκδόσεις Springer-Verlag

• Day, Richard (1994): «Complex Economic Dynamics, Vol. 1: An Introduction to Dynamical Systems and Market Mechanisms», MIT Press

• Day, Richard (2000): «Complex Economic Dynamics, Vol. 2: An Introduction to Macroeconomic Dynamics», MIT Press

• Bertuglia, Cristoforo and Vaio, Franco (2005): «Nonlinearity, Chaos & Complexity», Oxford University Press (Ch. 1 – 23)