Description and aims :

Numerical analysis is a discipline of mathematics concerned with the development of efficient methods for getting numerical solutions to complex mathematical problems. There are three sections to the numerical analysis. The first section of the subject deals with the creation of a problem-solving approach. The analysis of methods, which includes error analysis and efficiency analysis, is covered in the second section. The efficiency analysis shows us how fast we can compute the result, while the error analysis informs us how correct the result will be if we utilize the approach. The construction of an efficient algorithm to implement the approach as a computer code is the subject’s third part. All three elements must be familiar to have a thorough understanding of the numerical analysis

Content
The content of this course consists of the following topics: The Solution of Nonlinear Equations f(x)=0, The Solution of Linear Systems AX=B, Interpolation and Polynomial Approximation, Curve Fitting, Numerical Integration.

Learning Objectives

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge
The student
• has knowledge of state-of-the-art numerical methods in the field.
• Knows root finding problem and their analysis.
• Knows the solving large linear system and its computer applications.
• Knows different interpolation methods and their error analysis.
• Knows different integration methods and their error analysis.
• Knows curve fitting methods.
• Simulates the numerical methods with MATLAB
• Applies the schemes to real life problems
• Writes a report and present it.
• Presents the self-learning Materials

Skills
The student
• is able to used the methods in numerical calculations. That is; to be able to implement them on a computer.
• is able to analyze a numerical method.
• Understands the possibilities and the limitations of the different methods.