Numerical Analysis I
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Date
2026
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University Hassiba Benbouali of Chlef
Abstract
Numerical analysis is a fundamental branch of applied mathematics that focuses on the
design, analysis, and implementation of algorithms to obtain approximate solutions to
mathematical problems when exact solutions are difficult or impossible to determine. In
a context where exact computation is often replaced by numerical values, a rigorous study
of errors, stability, and the accuracy of the methods used becomes essential.
This Numerical Analysis 1 course material, intended for second-year undergraduate
(LMD) mathematics students, aims to provide the theoretical foundations and practical
tools necessary to understand and master the basic methods of numerical computation.
It is structured into five chapters, each addressing a key area of numerical analysis and
supported by examples and exercises designed to encourage progressive learning.
Chapter 1: Numerical Errors
This chapter introduces the concepts of numerical errors, particularly truncation and
rounding errors, decimal notation of approximated numbers, and absolute and relative
error analysis. These notions are crucial for evaluating the reliability of numerical results.
Chapter 2: Solving Algebraic Equations
This chapter deals with the solution of algebraic equations, presenting iterative methods
such as the bisection method, the fixed-point method, and the Newton-Raphson method,
with particular attention paid to convergence and error estimation.
Chapter 3: Interpolation and Approximation
This chapter is dedicated to interpolation and approximation. It covers the Lagrange
and Newton interpolation methods, the study of interpolation errors, and least-squares
approximation techniques for fitting data.
Chapter 4: Numerical Differentiation
This chapter focuses on numerical differentiation, particularly useful when the function
in question is only known through discrete data points.
Chapter 5: Numerical Integration
This chapter addresses numerical integration, discussing classical methods such as the
rectangle rule, trapezoidal rule, and Simpson’s rule, with emphasis on their accuracy and
applications.
This educational resource seeks to combine mathematical rigor with the practical aspects of numerical computation, while fostering in students a critical approach to interpreting numerical results. It provides an essential introduction to numerical analysis and
prepares students for more advanced modules in their mathematics curriculum.
Description
Intended for students of Second Year LMD Mathematics Degree (L2)
Faculty of Exact Sciences And Informatics
Department of Mathematics