COMPUTATIONAL MATHEMATICS

Learning outcomes:

The aim of this course is to introduce students to computational mathematics. This includes numerical methods for the solution of linear and nonlinear systems, basic data fitting problems, and ordinary differential equations.

On successful completion of this module the learner will:

be able to appreciate for the role of computers in mathematics and economic science as a complement to analytical and experimental approaches.
have the knowledge of numerical approximation techniques, know how, why, and when these techniques can be expected to work
be able to program simple numerical algorithms in MATLAB and MATHEMATICA

be able use and evaluate alternative numerical methods, communicate the results of numerical computation, with adequate explanations, in written and graphical form.

Features

Code : X62
Semester : 6th
Effort : 7.5 ECTS
Hours : 4 per week
Type : Mathematics
Department : Mathematics
Instructor : Zacharoula KALOGIRATOU
Exams : Yes

FULL course outline

Course Contents:

Review of Taylor series. Νumerical error (floating-point representation, computer arithmetic, round-off errors)
Locating Roots of Equations, bisection method, Newton's method, secant method.
Introduction to the solution of systems of nonlinear equations - Newton's method for systems.
Solving Systems of Linear Equations: Direct methods, Gaussian elimination, LU factorization Iterative methods Jacobi, Gauss-Seidel, SOR.
Polynomial interpolation
Numerical Integration Newton-Cotes methods, adaptive quadrature.
Numerical differentiation.
Numerical Integration of ordinary differential equations with Runge-Kutta methods and multistep methods.
Programming in MATLAB, implementation of all above methods.