Open Courses

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Mathematics for Business and Finance Grigorios Beligiannis - Undergraduate - (A+) Department of Business Administration of Food and Agricultural Enterprises, University of Patras Linear algebra: Linear systems, Gauss and Gauss-Jordan algorithms, Vectors, Matrices, Determinants. Functions with one dimensional variables: Limits, Continuity, Exponential functions, Logarithmic functions, Financial functions, Derivatives, Integrals. Applications of functions with one dimensional variables to finance and economic analysis (production functions, consumption functions, utility functions, etc.).
NUMERICAL ANALYSIS FRANK COUTELIERIS - Undergraduate - (A-) Department of Environmental and Natural Resources Management, University of Patras Introduction (discretization, error analysis), Numerical Differentiation (forward, backward and central differences), Numerical Integration (trapezoid rule, Simpson rule, Newton-Cotes formulae), Interpolation/Extrapolation (Taylor, Lagrange polynomials), Numerical solution of algebraic equations (trial & error, bisection, Newton-Raphson), Numerical solution of linear systems (Gauss, Jacobi, Gauss-Seidel), Numerical Integration of Ordinary Differential Equations (Euler, Runge-Kutta), Finite Differences.
Differential Geometry II Andreas Arvanitoyeorgos - Undergraduate - (A-) DEPARTMENT OF MATHEMATICS, University of Patras Review of central notions of theory of surfaces, global theorems, Godazzi and Gauss equations, covariant derivative, parallel transport, geodesics, the Gauss-Bonnet theorem
NUMERICAL ANALYSIS FRANK COUTELIERIS - Undergraduate - (A+) Chemical Engineering Department, University of Patras Introduction (discretization, error analysis), Numerical Differentiation (forward, backward and central differences), Numerical Integration (trapezoid rule, Simpson rule, Newton-Cotes formulae), Interpolation/Extrapolation (Taylor, Lagrange polynomials), Numerical solution of algebraic equations (trial & error, bisection, Newton-Raphson), Numerical solution of linear systems (Gauss, Jacobi, Gauss-Seidel), Numerical Integration of Ordinary Differential Equations (Euler, Runge-Kutta), Finite Differences.
Special Functions Chrysi Kokologiannaki - Undergraduate - (A-) DEPARTMENT OF MATHEMATICS, University of Patras Gamma, Beta and error functions. Bessel functions of the first and second kind. Linear independence and recurrence relations of them. Modified Bessel functions of the first and second kind. Linear independence and recurrence relations of them. Solving ordinary differential equations in terms of Bessel functions. Lommel's integrals. Roots of Bessel functions. Fourier-Bessel series. Orthogonal polynomials. Three-term recurrence relation. Darboux-Christoffel formula. Roots of orthogonal polynomials. Rodrigues' formula. Generating function. Applications to classical orthogonal polynomials.
Further Operational Research Techniques in Decision Making Ioannis Giannikos - Undergraduate - (A-) DEPARTMENT OF BUSINESS ADMINISTRATION, University of Patras This course is related to the "Operational Research" course offered in the 5th semester. Its aim is to present additional OR techniques, beyond Linear Programming, for making decisions in complex business environments. In addition, the course aims to demonstrate that these techniques are related to each other and constitute an integrated methodology for addressing realistic problem situations.
MATHEMATICS I FRANK COUTELIERIS - Undergraduate - (A-) Department of Environmental and Natural Resources Management, University of Patras Matrices. Determinants. Linear Systems. Gauss elimination. Vectors and Tensors. Vector Spaces. Base and dimension. Sub-spaces. Eigenvalues & Eigenvectors. Linear representations. Linear independence. Three-dimensional vectors.
Ordinary Differential Equations Chrysi Kokologiannaki - Undergraduate - (A-) DΕPARTMENT OF MATHEMATICS, University of Patras Introduction to Ordinary Differential Equations (ODE. Classification of ODEs. First order ODE: separable of variables, homogeneous with respect to x and y, exact ODE, integrating factor, first order linear, Bernoulli and Riccatti. ODE of first order and degree greater than one. Picard's theorem. Theory of linear ODEs second and higher order. Homogeneous ODE with constant coefficients. Non-homogeneous ODE. Euler's equations. Techniques in solving second order linear ODE with non-constant coefficients and certain forms of non-linear ODE.
ORDINARY DIFFERENTIAL EQUATIONS Frank Coutelieris - Undergraduate - (A-) Department of Environmental and Natural Resources Management, University of Patras On the fundamentals of the analytical solution of Ordinary Differential Equations.
Calculus George Brodimas - Undergraduate - (A-) Department of Physics, University of Patras The course is intended to the students at the first semester of their studies in Physics. The students usually have a good background on mathematics. as they have been taught them in the high school. This initial background differs from year to year and this made the first introductory chapter necessary. The Final goal for the student is to understand the basics of the Calculus and to use calculus intelligently for solving a wide variety of mathematical and physical problems.