Introduction to Numerical Analysis. Elements of the theory of errors in calculations. Solution of non linear equations: Bracketing methods (bisection, false position) Open methods: (basic iteration, Newton-Raphson). Systems of linear equations: Matrix inversion, Gauss και Gauss-Jordan elimination methods. Iteration methods (Jacobi and Gauss-Seidel).The Eigenvalue and eigenvector problem. Curve fitting: the least squares method to fit linear and nonlinear laws. Finite differences: forward, backward and central difference operators and notation. Detection and location of errors. Interpolation: Newton-Gregory forward and backward interpolation polynomials. Lagrange polynomials, splines. Numerical differentiation. Numerical integration: Trapezoidal and Simpson’s rules, simple and composite. Romberg procedure. Gaussian integration. Solution of ODEs: Taylor series methods, simple and modified Euler methods, Runge-Kutta methods. Sets of ODEs. The subject is supplemented by laboratory work, with assignments implementing algorithms using FORTRAN and/or MATLAB, with emphasis on engineering applications..
