NUMERICAL ANALYSIS

General Info

• Course Title: Numerical Analysis
• Course Code: NAOME1114
• Semester: 3rd
• Course Type: G.B.¹
• Weekly Teaching Hours: 4 (Lectures)
• Credits (ECTS): 5
• Offered to ERASMUS+ students: Yes
• Course Website: https://eclass.uniwa.gr/courses/NA184/
• Professors: Th. Gerostathis , C. Politis

Course Content / Syllabus

1. Computer Arithmetic and round-off errors Computer representation of numbers, floating-point representation, rounding and chopping, computer errors in representing numbers and in arithmetic operations, algorithms and stability. 2. Solution of nonlinear equations The bisection method, iterative solution of equations, Newton’s method, the secant method. 3. Solution of systems of linear equations Linear Algebra: Vector Spaces, Matrices, and Linear Systems. Eigenvalues and eigenvectors, Canonical Forms for Matrices. Special matrices. Vector and matrix norms. Direct methods for solving linear systems: Gauss elimination, LU factorization, Cholesky decomposition. Iterative techniques for solving linear systems: Jacobi, Gauss-Seidel and SOR. 4. Polynomial interpolation Lagrange interpolation. Newton’s form. Piecewise polynomial interpolation: linear and cubic splines. 5. Least squares approximation Introduction, polynomial approximations, System of normal equations. 6. Numerical integration Introduction, Newton-Cotes formulae, Composite numerical integration. 7. Initial value problems for ordinary differential equations Elementary theory of initial value problems, Euler’s method, Implicit one-step methods, Runge-Kutta methods, Error control and the Runge-Kutta-Fehlberg method.

Course Outline