udents in their second year of licensure are the target audience for this course. Its goal is to give students a foundational understanding of differential calculus for functions of many variables, which is a need for any course in mathematics used in economics. It can be useful for students in their second year of a license in applied mathematics, technical sciences, or computer science, and for students in their second year of a preparatory school.
The required mathematical level is that of the first-year license: limits, continuity, derivation, limited developments, real and complex sequences, integrals, special functions, and ordinary differential equations.
The first chapter introduces the topology of $\mathbb{R}^{n}$, in particular the notions of distances, norms, opens, and closures in $\mathbb{R}^{n}$, which will be useful throughout this course for all the new tools covered. Chapter two deals with the functions of several variables. It focuses on the notions of limit, continuity, and the existence of partial derivatives. We also introduce the notion of differentiability of functions of several variables and vector functions. It is devoted to the study of free and bound extremums and to calculating a minimum and a maximum. We're interested in local inversion theorems and implicit functions. The final chapter is devoted to multiple integrals, with the following objectives: calculate double and triple integrals, surface area, and volume.
At the end of these chapters, you'll find a selection of sample exercises with answers, written in a progressive and detailed manner to enable students to familiarize themselves with new concepts and check that the essential points have been correctly assimilated.
- معلم: chafia laouar
This course serves as pedagogical support designed for second-year mathematics students under the L.M.D. system, covering the "Analysis 3" module. The course introduces key concepts in mathematical analysis, such as convergence of sequences and series, power series, and Fourier series. Each chapter includes exercises with solutions to help students understand the material.
The first chapter explains numerical series and infinite sums. The second chapter discusses simple and uniform convergence of function sequences and series. The third chapter focuses on power series, including finding the radius of convergence and series expansions. The fifth chapter covers Fourier series and their applications, while the last chapter explores generalized integrals
- معلم: Fares Bekhouche
This manuscript is intended for all second year of the mathematics license students and all those who want to acquire the basic concepts of finite-dimensional endomorphism reduction written in a clear and accessible style with many examples. The content of this manuscript also includes proofs of some results.
This is the Algebra 3 course taught at the university of Abbes Laghrror Khenchela.
The object of this work is to study some processes of linear algebra which allow to simplify the description of certain endomorphisms of a vector space, in particular of certain square matrices. It consists in finding and explaining a basis of the vector space made up of eigenvectors.
Certain parts can be admitted on first reading without harming a good assimilation of new notions. The matrix trigonalization technique is given in Jordan form, following a clear and simple algorithm. His difficult demonstration is completed by a series of exercises at the end of the chapter. The diagonalization of the matrices is done by hand, without using too theoretical notions.
The content of this manuscript also includes proofs of some results. On the other hand, the examples and the exercises proposed since, we can easily construct the characteristic polynomial of matrice so that their eigenvalues.
Note that each chapter is subdivided into several sections, each of which contains a basic concepts are presented at the beginning of each section, corrected exercises, and suggested exercises. The manuscript finally ends with a chapter that we remember some definitions and present without proof the classical results on square matrices that we need in this work, and present some examinations conducted at the University of Khenchela.
In fact, these lessons, which are based on square matrices, are a continuation study of Algebra 2 taught in the first year MI.
This polycopy is organized of four chapters ordered as follows:
Firstly, the chapter 1 is devoted to explaining and studying the construction of the ring of polynomials, where we introduce preliminary results and basic theories that will be useful in studying the Reduction of endomorphisms of finite-dimensional vector spaces.
- معلم: lamia Djebara