** **

Title: Mathematical methods in EconoPhysics |
Semester: Winter (1^{st}) |

Loukas Zachilas, Assistant Professor on Applied MathematicsTutor: |

** **

__Course Outline__

Differential equations of the 1^{st} order, Linear Differential equations, Systems of Differential equations, Phase plane, Stability, Series solutions of Differential equations, Laplace transformation, Vectors, Matrices and Determinants, Vector Differential Calculus, Line and Surface integrals, Fourier Series, Partial Differential equations, Complex numbers, Complex Analytic Functions, Power Series, Taylor Series, Laurent Series, Numerical methods in general, Numerical methods in Linear Algebra, Numerical methods for Differential equations, Linear programming, Graphs and Combinatorial Optimization, Probability Theory, Mathematical Statistics.

__Aim:__

The aim of the course is to introduce the students in the various mathematical methods usually applied in Economics and Econophysics. Another important aim is to introduce the students in the new numerical techniques that are used in the study of the economic models. Having taken into account a rather big number of economic models, we will try to answer the question: «What are the mathematical methods we need, so as to understand the nature of the problem?». For this reason, we emphasized the suitable mathematical chapters that are mainly used in the contemporary studies of Economic and Econophysical models. The continuous growth of computer technology has led the economists in studying more easily the various models. During the course, it will be given a strong computer algebra software (called Maxima, which is freeware) and the students will be trained on the computer.

__Learning Objectives:__

The module is appropriate to students who want to involve in economic models, which come from various economic branches. In all cases the study of such models needs the good knowledge of the advanced mathematical methods and tools. The module is designed for students who would like to understand how they could use such techniques in their models.

*On completion of this module, students are expected to be able to:*

- Understand the advanced mathematical methods
- Understand the complexity of an economic model
- Use the various tools of modern techniques
- Distinguish the similarities of models of physics to economic models
- Involve to econometric methods of quantitative analysis

__Suggested for further ____reading:__

1. Ronald Shone, “Economic Dynamics. Phase diagrams and their Economic application”, Cambridge University Press, 2002.

2. Daniel Kaplan and Leon Glass, “Understanding Nonlinear Dynamics”, Springer-Verlag, 1995.

3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 10th edition, John Wiley & Sons, 2011.

4. Finney Ross L., Weir Maurice D. & Giordano Frank R. (2015): “Thomas Απειροστικός λογισμός” (ενιαίος τόμος), Παν. Εκδόσεις Κρήτης

5. William Greene (2012): “Econometric Analysis”, 7th edition, Prentice Hall

6. Damodar Gujarati (2002): “Basic Econometrics”, 4th edition, Mc Graw Hill