Numerical Analysis I
| dc.contributor.author | MEZOUAGHI Abdelheq | |
| dc.date.accessioned | 2026-06-15T10:04:13Z | |
| dc.date.available | 2026-06-15T10:04:13Z | |
| dc.date.issued | 2026 | |
| dc.description | Intended for students of Second Year LMD Mathematics Degree (L2) Faculty of Exact Sciences And Informatics Department of Mathematics | |
| dc.description.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. | |
| dc.identifier.uri | https://dspace.univ-chlef.dz/handle/123456789/2476 | |
| dc.language.iso | en | |
| dc.publisher | University Hassiba Benbouali of Chlef | |
| dc.title | Numerical Analysis I | |
| dc.type | Working Paper |
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