8295 Manufacturing Processes, Corrosion, and Metal Material Protection
3rd Semester NAME
ECTS : 5
Language : el
Learning Outcomes :
8239 Ordinary Differential Equations and Complex Functions
3rd Semester NAME
ECTS : 5
Language : el
Learning Outcomes :
Introductory notes. Definitions , the solution concept and geometric characteristics. Initial- boundary value problems. Well posed problems. Differential equations of separate variables. Linear, homogeneous, exact differential equations. First order Dif. Eq. : The cases of Riccati,Lagrange and Clairaut dif. equations. Qualitative theory: Existence and uniqueness of solution. Picard and Peano theorems. Linear differential equations: General theory, linear independence of solutions, Wronski determinant. Homogeneous equations with constant coefficients. The nonhomogeneous case: the method of undetermined coefficients and Lagrange method. Power series solution of equations with variable coefficients. Frobenious method. The cases of a regular expansion point and of a regular singular point. The Legendre and Bessel differential equations. Differential systems: The method of eigenvalues and eigenvectors. Laplace transformation: Application to the solution of initial value problems involving ordinary dif. Equations. The Heaviside and Dirac function. Elements of Complex analysis. The concepts of continuity and differentiability. Holomorphic and analytic complex functions. Cauchy - Riemann conditions. Residue theorem. Determination of real integrals via complex analysis. Fourier integrals and applications.
8193 Numerical Analysis
3rd Semester NAME
ECTS : 6
Language : el
Learning Outcomes : Upon successful completion of the course, students will
• Have understood the basic methods of Numerical Analysis a) for solving linear systems, nonlinear equations and differential equations b) for interpolation and approximation of data and c) for the approximate calculation of integrals.
• Be able to distinguish the differences between numerical methods and choose the most appropriate one for solving different problems
• Be able to analyse a) the asymptotic properties and behaviour of approximate models b) the numerical stability of numerical solutions and c) the algorithmic and computational properties corresponding to numerical solution methods.
• Have understood the effect of finite arithmetic errors of the computer and of method errors and be able to calculate the error bounds of approximate solutions.
• Have knowledge of basic elements of appropriate software for the implementation of various approximation methods.
• Be able to collaborate with fellow students to solve complex practical problems using the methods of Numerical Analysis.
Computer numerical errors, Floating point arithmetic.
Linear Systems: Direct methods (Gauss elimination, LU factorization methods). Iterative methods (Jacobi, Gauss-Seidel, SOR methods). Eigenvalue calculation (power method).
Solving Nonlinear Equations: Bisection methods, general iterative method, Newton-Raphson, secant. Newton's method for nonlinear systems.
Interpolation and Approximation: Polynomial interpolation, Lagrange and Newton forms of the interpolation polynomial. Hermite interpolation. Interpolation with spline functions.
Least squares method.
Numerical Integration: Newton-Cotes integration formulas, simple and complex trapezoidal and Simpson formulas. Gauss integration.
Differential Equations: Initial value problems for ordinary differential equations. Single-step methods (Euler, Taylor, Runge-Kutta), Multi-step methods (Adams, Predict-Correct methods). Two-point boundary value problems, Finite difference methods.
The aim of the course is the derivation and analysis of numerical methods for solving problems in science and technology for which either no analytical solution exists or it is very difficult to calculate.
8041 Electrical Technology
3rd Semester NAME
ECTS : 4
Language : el, en
Learning Outcomes : Analysis of electrical circuits in steady and transient state conditions
Electricity, Signals and Systems, Electrical Circuits, Electrical Circuit Analysis, Steady State Sine Analysis (EMF), Power and Energy, Three-Phase Networks, Solving Electrical Networks with Laplace Transform, Methods of Electrical Network Analysis with Computer Programs, Solving Magnetic Circuits, Effects of electricity on the human body. Signals and systems, electric circuits and networks, electric circuit analysis, Sinusoidal Steady State Analysis, Electric power and energy, Three-phase networks, Electric Network analysis via Laplace transform, Electric Network analysis via computer programs, interference of electric current with the human body and tissues, magnetic circuits.