Dr. Loukas Zachilas Assistant Professor, Department of Economics

 

Address of communication:
Profitis Ilias, Ano Volos
38500 Volos
Hellas

Tel.:
2421074916 (office)
2421041404 (home)

e-mail address:
zachilas@uth.gr

Assistant Professor in «Applied Mathematics»

-----Under construction----

1. Zachilas L.: 1988, “Numerical and Theoretical Study of 3D Stellar Systems”, Thesis, Department of Physics, Univ. of Athens.
   
2. Contopoulos, G. & Zachilas, L.: 1988, “Complex instability in 3D systems” in “Singular behavior and Nonlinear Dynamics”, Samos 1988, eds. Pneumatikos, St., Bountis, A. & Pneumatikos, Sp.
   
3. Patsis, P. A. & Zachilas, L.: 1988, “Complex Instability of Simple Periodic Orbits in a Realistic Galactic Potential”, in “The World of Galaxies”, Paris, eds. Corwin, H. & Bottinelli,L.
   
4. Patsis, P. A. & Zachilas, L.: 1990, “Complex Instability Of Simple Periodic-Orbits In A Realistic 2-Component Galactic Potential”, Astron. & Astroph., 227, 37
   
5. Zachilas, L. & Farantos, S. C.: 1991, “Periodic-Orbits and Quantum Localization in the van der Waals System Co-Ar”, Chem. Phys., 154, 55
   
6. Zachilas, L.: 1993, “Complex Instability”, Astron. & Astroph. Suppl. Series, 97, 549
   
7. Farantos, S. C. & Zachilas, L.: 1993, “Testing Molecular-Potential Functions with Bifurcation Diagrams of Periodic-Orbits”, Molec. Phys., 80, No 6, 1499
   
8. Patsis, P. A. & Zachilas, L.: 1994, “Using Color and Rotation for Visualizing 4-Dimensional Poincaré Cross-Sections - with Applications to the Orbital Behavior of A 3-Dimensional Hamiltonian System”, Int. J. of Bifurcation & Chaos, Vol. 4, No. 6, 1399 - 1424
   
9. Patsis, P. A. & Zachilas, L.: 1994, “A method for visualizing the 4-D space of section in 3-D Hamiltonian systems”, in “Integrability and Chaotic Behavior”, Torun 1993, Κluwer Publications NATO Asi Series B, Physics, Vol. 331, J. Seimenis et al. pg. 399
   
10. Zachilas L.: 1999, Notes on: «FORTRAN 90 and applications for Civil Engineers, Part I», pp. 38, University of Thessaly Press.
    
11. Zachilas L.: 1999, Notes on: «FORTRAN 90 and applications for Civil Engineers, Part II», pp. 74, University of Thessaly Press.
12. Zachilas L., Patsis, P.A. & Mavrommatis, C.: 2007, "The Society for Space and Astronomy at Volos, Greece", in Communicating Astronomy with the Public 2007: Proceedings from the IAU/National Observatory of Athens/ESA/ESO Conference, Athens, Greece, Christensen, L.L., Zoulias, M. & Robson, I. (eds.), published by Eugenides Foundation, pg. 540.
13. Katsanikas, M., Patsis, P.A. & Zachilas, L.: 2009, "The Structure of the Phase Space in Galactic Potentials of Three Degree of Freedom", Proceedings of "Chaos in Astronomy, Astrophysics and Space Science", G. Contopoulos & P.A. Patsis (eds.) Springer-Verlag, pg.235
14. Zachilas L.: 2010a, "A review study of the 3-particle Toda lattice and higher order truncations: The odd-order cases (Part I)", Int. J. of Bifurcation & Chaos, Vol. 20, No.10, 1-50
15. Zachilas L.: 2010b, "A review study of the 3-particle Toda lattice and higher order truncations: The even-order cases (Part II)", Int. J. of Bifurcation & Chaos, Vol. 20, No.11, 1-51
16. Zachilas L.: 2010, "Computational methods using Maxima", Notes on Maxima for the students of Economics, University of Thessaly Press, pp. 254.

MATHEMATICS FOR ECONOMISTS I

ECTS: 4

1^st Semester

1. Sets and numbers. Sets, operations with sets, sets of numbers, real numbers, Cartesian product, relationships, functions.
2. Vectors and Matrices: Operations with vectors, geometric interpretation, inner product of two vectors, linear combination of vectors, linear independence of n-vectors, matrix algebra, determinant of a square matrix, properties of determinants, the a Laplace method, inverse matrices, the method of inverse matrices to solve systems of linear equations, Cramer’s rule, homogeneous systems of linear equations.
3. Calculus-Functions of one variable: Continuity and limits, average rate of change, definition and economic interpretation of the derivative, techniques for finding derivatives, derivatives of exponential and logarithmic functions, the chain rule, differentials, economic applications.
4. Maxima and Minima: Concavity, maxima and minima of functions of two or more variables, first and second order conditions using differentials, restricted maxima and minima, Lagrange multipliers.

 

COMPUTER SCIENCE I

ECTS: 4

1^st Semester

1. Introduction to Computer Science.
2. Computer’s infrastructure and the description of its parts.
3. The function of the PC.
4. Operating Systems and an Introduction to Windows.
5. Introduction to word processing with the use of Word.
6. Introduction to spreadsheets with the use of Excel.

 

MATHEMATICS FOR ECONOMISTS II

ECTS: 4

2^nd Semester

1. Real-valued functions: Linear and quadratic functions, rational functions, exponential and logarithmic functions, and economic applications.
2. Quadratic forms: Eigenvalues and eigenvectors of a square matrix, orthogonal transformations, diagonalization of real-valued symmetric matrices, positive definite forms, unrestricted and restricted maxima and minima of functions of two or more variables, the Hessian matrix, the bordered Hessian matrix.
3. Calculus-Functions of many variables: Partial derivative, total differential, techniques for finding differentials, differentials of second or high order, total derivative – two or more independent variables, implicit differentiation and implicit functions, homogeneous functions, Euler’s theorem, partial elasticities.

 

COMPUTER SCIENCE II

ECTS: 4

2^nd Semester

1. An advanced description of the PC and the Operating System Windows.
2. Advanced techniques in word processing with Word.
3. Advanced techniques in spreadsheets with Excel.
4. Special topics of Excel and applications of Financial Analysis.
5. Introduction to presentations with the user of Powerpoint.
6. Networks (LAN-WAN) and an Introduction to Internet.
7. Search engines and how to search in the Internet.

 

ADVANCED MATHEMATICS FOR ECONOMISTS

ECTS: 4

7^th Semester

1. Difference equations: Finite differences, difference operators, solution of difference equations, homogeneous linear equations with constant coefficients, non homogeneous linear difference equations of first and second order, the Cobweb model.
2. Differential equations: Solution of differential equation, non-linear differential equations of order one, linear differential equations of order one, linear differential equations of order two with constant coefficient.
3. Differential Systems of Equations: Linear systems of 1^st order, the use of Matrix Theory in the solution, autonomous systems, sinks, spirals and saddles, stability and instability, phase plane, nonlinear differential equations
4. Difference systems of Equations: Eigenvalues, eigenvectors, graphical solution, stability of difference systems, phase plane, nonlinear difference systems of equations.