Dr. Loukas Zachilas, Assistant Professor in «Applied Mathematics»
Dr. Loukas Zachilas was born in Athens, Hellas, in 1960. He studied Mathematics at the University of Athens and he graduated in 1983. In 1988, he obtained his Ph.D. titled “Numerical and Theoretical study of three dimensional stellar systems” from the Department of Physics, University of Athens.
He has published a lot of papers in scientific journals such as: Astronomy & Astrophysics, Astronomy & Astrophysics Supplement Series, Chemical Physics, Molecular Physics, και International Journal of Bifurcation & Chaos. His research interests focus in dynamical systems in two-dimensional and three-dimensional spaces. Models like these arise in Galactic Dynamics, in Applied Economics, in time series analysis and in arms races problems. Since 1982, he has participated in a lot of Symposia and Summer Schools.
Since 1990, he has taught several undergraduate and graduate courses concerning Applied Mathematics, Computer Science and Differential Equations at the University of Crete, at the TEI of Heraklion, Crete, at the University of Thessaly, at the TEI of Larissa etc. Since 2012, Dr L. Zachilas is Assistant Professor of Applied Mathematics in the Department of Economics at the University of Thessaly and in the year 2012 became .
Address of communication:
Profitis Ilias, Ano Volos
Assistant Professor in «Applied Mathematics»
- Sets and numbers. Sets, operations with sets, sets of numbers, real numbers, Cartesian product, relationships, functions.
- 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.
- 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.
- 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
- Introduction to Computer Science.
- Computer’s infrastructure and the description of its parts.
- The function of the PC.
- Operating Systems and an Introduction to Windows.
- Introduction to word processing with the use of Word.
- Introduction to spreadsheets with the use of Excel.
MATHEMATICS FOR ECONOMISTS II
- Real-valued functions: Linear and quadratic functions, rational functions, exponential and logarithmic functions, and economic applications.
- 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.
- 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
- An advanced description of the PC and the Operating System Windows.
- Advanced techniques in word processing with Word.
- Advanced techniques in spreadsheets with Excel.
- Special topics of Excel and applications of Financial Analysis.
- Introduction to presentations with the user of Powerpoint.
- Networks (LAN-WAN) and an Introduction to Internet.
- Search engines and how to search in the Internet.
ADVANCED MATHEMATICS FOR ECONOMISTS
- 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.
- 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.
- Differential Systems of Equations: Linear systems of 1st order, the use of Matrix Theory in the solution, autonomous systems, sinks, spirals and saddles, stability and instability, phase plane, nonlinear differential equations
- Difference systems of Equations: Eigenvalues, eigenvectors, graphical solution, stability of difference systems, phase plane, nonlinear difference systems of equations.