1001 Numerical Analysis

Introduction to Numerical Analysis with emphasis on methods useful for Civil Engineers. Number representation on computers. Numerical solution of Linear Systems: Direct Methods (Gauss, LU factorization methods). Stability of linear systems. Iterative methods (Jacobi method, Gauss-Seidel, SOR). Solution of Non-Linear Equations: Bisection method, Regula-Falsi method, Fixed Point iterative methods, Newton-Raphson method, Secant method. Newton method for nonlinear systems. Interpolation: Polynomial Interpolation in Lagrange and Newton form and Interpolation Error. Hermite and cubic splines interpolation. Numerical Integration: Newton-Cotes formulas, Simple and Composite Trapezoidal and Simpson integration rules, Gauss Integration. Approximation theory: Discreate least squares method, polynomial and exponential approximation. Differential Equations: Initial value Problems for ordinary differential equations. Single step methods (Euler, Taylor, Runge-Kutta). Multi-step methods (Adams, Predictor-Corrector methods). Numerical solution of systems of Differential Equations
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 d) for the approximate calculation of integrals. • Have knowledge of the tools and techniques of iterative methods and will be able to effectively use their appropriate stopping criteria. • ​​Have realized the importance of using stable algorithms to ensure the reliability of the results obtained by the taught numerical methods. • 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. • Understand the effect of finite arithmetic errors of the computer and of method errors and be able to calculate bounds of the errors of approximate solutions. • Be able to collaborate with fellow students to solve complex practical problems using methods of Numerical Analysis.