Learning Outcomes
After having successfully completed the course, the students will be able to:
• calculate the error in representing numbers in computer memory and in computer arithmetic
• use numerical methods to calculate the values of polynomials and the solution of equations
• perform numerical differentiation and integration
• approximate functions and estimate the approximation error
Course Content (Syllabus)
Errors - Number systems and number representation - Floating point arithmetic – Evaluation of polynomials - Interpolation and approximation with difference methods - Interpolation by Lagrange, Newton and Hermite polynomials - Error analysis – Numerical differentiation - Numerical integration by rectangle, midpoint, trapezoid, corrected trapezoid, Simpson, Richardson and Romberg methods - Numerical solution of non-linear equations by methods of bisection, Regula-falsi, Newton-Raphson and secant. The fixed point iteration method. Convergence criteria.
Keywords
Errors, Machine representation, Polynomials, Interpolation, Numerical Differentiation, Numerical integration, Numerical solution of equations
Course Bibliography (Eudoxus)
Αριθμητική Ανάλυση, Μ. Χ. Γουσίδου-Κουτίτα, επανέκδοση 2017, Εκδόσεις Κυριακίδη.
Εισαγωγή στην Αριθμητική Ανάλυση, Γ.Δ. Ακρίβης & Β.Α. Δουγαλής, 2017, Πανεπιστημιακές Εκδόσεις Κρήτης.
Αριθμητική Ανάλυση: Εισαγωγή, Μ.Ν. Βραχάτης, 2012, Εκδόσεις Κλειδάριθμος.