## NUMERICAL ANALYSIS 3008

Code no:

**(3008)**Semester:**3th**, Teaching hours: 4## CORE SYLLABUS

Computer arithmetic,

*Linear systems, polynomial Interpolation,**Non linear equations and systems, Least Squares Method,**Numerical Differentiation and Integration, Numerical solution of Ordinary Differential Equations, Finite Differences and Finite Elements for boundary value problems.*## SUBJECT CONTENT IN OUTLINE

The course aims at acquiring the knowledge for:

The solution of systems of linear equations, non-linear algebraic equations, ordinary Differential equations, interpolation and approximation of data and numerical approximation of integrals.

The aim of the course is to understand the importance of numerical methods for solving scientific and technological problems for which either there is no analytical solution, or it is very difficult to calculate it.

On completion of this course, students should be armed with numerical and computational techniques for solving a wide variety of fundamental mathematical problems that arise in diverse scientific areas.

In particular, upon successful completion of the course, the student will

The solution of systems of linear equations, non-linear algebraic equations, ordinary Differential equations, interpolation and approximation of data and numerical approximation of integrals.

The aim of the course is to understand the importance of numerical methods for solving scientific and technological problems for which either there is no analytical solution, or it is very difficult to calculate it.

On completion of this course, students should be armed with numerical and computational techniques for solving a wide variety of fundamental mathematical problems that arise in diverse scientific areas.

In particular, upon successful completion of the course, the student will

- understand the basic methods of Numerical Analysis a) to solve linear systems, non-linear equations and differential equations; b) to interpolate and approximate data and c) to approximate integrals.
- be familiar with the tools and techniques of iterative methods and can effectively use the appropriate stopping criteria.
- be able to distinguish the differences between the methods and choose the most appropriate to solve each problem.
- be able to analyse a) the asymptotic properties and the behaviour of the approximate models b) the numerical stability of the numerical solutions and c) the algorithmic and computational properties corresponding to the numerical methods.
- understands the effect of round-off errors in the computations and truncation errors of the methods and be able to calculate error bounds of approximate solutions.