Numerical Analysis for Science, Engineering and Technology

Numerical Analysis for Science, Engineering and Technology

This textbook is intended as a guide for undergraduate and graduate students in engineering, science and technology courses. Chapters of the book cover the numerical concepts of errors, ...
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Theory of Approximations

Pp. 11-78 (68)

Said Gamil Ahmed Sayed Ahmed, Hossein Jafari, Mukhtar Yagoub Youssif and Roberto Datja

Abstract

Function approximations, interpolation, numerical differentiation and numerical integrations are very important topics in the numerical analysis. These topics are widely used and found in science and engineering applications. In the present chapter, we will present the main methods and techniques that had been developed for such topics. Differentiation and integration related together by so many relations as we will see later on. Finally, one can say that these topics are very important in our daily life, and therefore everyone should be aware of them.

Keywords:

Derivative approximations, Difference tables, Interpolation, Lagrange method, Numerical differentiation, Numerical integration, Series tests, Taylor expansion.

Affiliation:

Professor of Mathematics and Numerical Analysis, Faculty of Engineering, Zagazig University, Egypt.