Faculté des Sciences

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Algebra 1 : Mathematical logic , Set theory ,Mappings ,Binary relations , Algebraic structures , Polynomial rings
(Faculty of Sciences, 2025) SACI , Fateh
This course is designed primarily for first-year students in Mathematics and Computer Science under the LMD system. The primary goal is to develop a fundamental understanding and skills necessary for working with mathematical expressions, equations, and functions. This comprehensive course provides a solid foundation in key mathematical concepts, covering logic, set theory, binary relations, mappings, algebraic structures, and rings of polynomials. It starts with Chapter 1: Logic Concepts, where students learn about logical operators, quantifiers, and proof methods. Chapter 2: Sets introduces set theory, including set operations and applications. Chapter 3 : Binary Relations explores reflexive, symmetric, transitive, and equivalence relations. Chapter 4: Mappings delves into injective, surjective, and bijective functions. Chapter 5: Algebraic Structures covers groups, rings, and fields, while Chapter 6: Rings of Polynomials focuses on the structure and applications of polynomial rings, particularly in algebraic geometry. This progression equips students with the foundational knowledge required for advanced mathematical studies.
Analyse Numérique Cours et Exercices
(Faculté des sciences, 2023) Nasri , Nassima
L'analyse numérique a commencé bien avant la conception des ordinateurs et leur utilisation quotidienne que nous connaissons aujourd'hui. Les premières méthodes ont été développées pour essayer de trouver des moyens rapides et efficaces de s'attaquer à des problèmes soit fastidieux à résoudre à cause de leurs grande dimension (systèmes à plusieurs dizaines d'équations par exemple), soit parce qu'il n'existe pas de solutions explicites connues même pour certaines équations assez simples en apparence. Dés que les ordinateurs sont apparus, ce domaine des mathématiques a pris son en vol et continue encore à se développer de façon très soutenu. Les applications extraordinairement nombreuses sont entrées dans notre vie quotidienne. Nous pouvons téléphoner, communiquer par satellite, faire des re- cherches sur internet, regarder des films où plus rien n'est réel sur l'écran, améliorer la sécurité des voitures, des trains, des avions, connaitre le temps qu il fera une semaine à l'avance,...et ce n'est qu'une toute petite partie de ce qu'on peut faire. Le but de ce polycopié est s'initier aux bases de l'analyse numérique et il est destiné aux étudiants de la deuxième année licence en mathématiques en espérant qu'il éveillera leurs intérêts et leurs inspirations.
Applied statistical hydrology course
(Faculty of Sciences, 2024) Hebal , Aziz
Precipitation includes all meteoric waters that fall on the surface of the earth, both in liquid and solid forms (drizzle, sleet, hail), and deposited or occult precipitations (dew, frost, hoarfrost...) caused by temperature or pressure changes. The most commonly used precipitation measurement devices are: – Pluviometers; – Pluviographs; – Snow gauges; – Radars. Point analysis concerns the series of measurements from a given point, i.e., a single station. From a series of point measurements, two types of graphs can be constructed: the rainfall height curve and the hyetogram.
Cours : Chimie Des Produits Naturels A Activité Biologique : Master II , Chimie Organique.
(Faculté des Sciences, 2021) Boudermine , Sihem
La nature et sa biodiversité offre des molécules biologiquement actives. Cette biodiversité très riche va conduire à une diversité chimique et structurale d’autant plus importante. Des substances sont étudiées par les biologistes qui les utilisent dans leurs recherches pour déterminer et certaines de ces substances deviendront même des médicaments. Les substances naturelles offrent des potentialités considérables comme : - Molécules d’intérêt pharmacologique, agronomique et cosmétique. -Marquent l’identité d’une espèce, familles ou genres donc des outils moléculaires pour l’exploration du monde vivant.
Cours de la théorie des semi groupes d'opérateurs linéaires
(Faculté des Sciences, 2023) Leulmi ,Soumya
La plus part des phénomènes dans la nature peuvent être reformulé et modélisé sous forme d'une équation différentielle (ordinaire ou aux dé- rivées partielles, inclus les conditions au bord) ou d'un systèmes d'équations différentielles. Une vaste classe de ces équations peuvent être écrite sous forme d'un problème d'évolution : du(t) dt = Au(t) + f(t); t > 0: u(s) = u0: Dans le cas où f(t) = 0, s = 0 et A est une application Lipchitzienne le théorème de Cauchy-Lipchitz -Picard rend un grand service à résoudre ce problème et la solution sera donnée par la formule : u(t) = eAtu0: Mais dans le cas où A est non borné, alors A est non Lipchitzienne, donc on peut pas appliquer le théorème de Cauchy-Lipchitz-Picard. L'idée serait de définir pour une classe d'opérateurs non nécessairement bornés un objet mathématique qui donne l'existence et l'unicité. La théorie des semi groupes d'opérateurs linéaires trouve dans les espaces de Banach une résolution dans le cas où A est non borné.
Cours Statistiques Expérimentales : 3 année Licence (LMD) , Spécialité amélioration de la production animale
(Faculté des Sciences, 2024) Benatmane , C
Les statistiques expérimentales jouent un rôle essentiel dans la conception et l'analyse des expériences agricoles. Elles permettent de garantir la validité des résultats et d'interpréter les données de manière rigoureuse. Voici les principaux concepts et méthodes associés aux statistiques expérimentales dans le contexte de l'agriculture : - Essais randomisés : Chaque traitement est attribué de manière aléatoire pour éviter les biais. - Blocs randomisés : Les essais sont organisés en blocs pour contrôler les variations non contrôlées (par exemple, la qualité du sol). - Plans factoriels : Étudier plusieurs facteurs simultanément pour observer les interactions entre eux.
Cours sur Espaces vectoriels normés : Pour la 3iéme Année Licence Mathématiques - Semestre 5.
(Faculté des Sciences, 2025) Khelili , Besma
Ce polycopié pédagogique, intitulé " Les espaces vectoriels normés " , est le fruit de plusieurs années d'enseignement des matières Analyse 1-3, Topologie et Algèbre linéaire. Il est destiné aux étudiants de L3 en licence de mathématiques et a été dispensé à l' université 20 août 1955 de Skikda entre 2018 et 2025. Ce cours introduit les concepts fondamentaux des espaces normés et des espaces de Hilbert , qui jouent un rôle clé en analyse fonctionnelle. Ce manuscrit constitue un guide complet visant à aider les étudiants à développer une compréhension approfondie de ces espaces, de leurs propriétés et de leurs applications. L' étude de ce sujet leur fournit une base rigoureuse pour la recherche et les applications mathématiques avancées dans divers domaines scientifiques. Il se décline en trois chapitres, chacun étant suivi d'une série d'exercices. Nous commençons par un rappel des concepts fondamentaux des espaces vectoriels et de leurs sous-espaces, qui forment le cadre général des structures algébriques utilisées en mathématiques. Ensuite, dans le chapitre 1, nous introduisons la notion de norme sur un espace vectoriel, en définissant la norme, la distance et en présentant divers exemples d'espaces vectoriels normés. Il explore l' équivalence des normes et les boules, essentielles pour l' étude de la convergence et de la continuité. Des concepts topologiques fondamentaux, tels que la limite, les ouverts, les fermés, l' adhérence et l' intérieur, sont abordés, ainsi que les ensembles et fonctions bornés. Enfin, la dernière partie traite des espaces de Banach, caractérisés par leur complétude, en introduisant les suites de Cauchy et en illustrant leurs propriétés par des exemples concrets. Le deuxième chapitre étudie les applications linéaires continues et la continuité dans les espaces vectoriels normés. Il traite des formes linéaires, de la dualité topologique et des propriétés des espaces de dimension finie. Des exercices pratiques illustrent ces concepts Le troisième chapitre est consacré aux espaces de Hilbert, qui jouent un rôle central en analyse fonctionnelle en raison de leur structure géométrique riche et de leurs nombreuses applications. Il commence par l' introduction du produit scalaire, qui permet de définir une distance et d' étudier les propriétés géométriques des espaces vectoriels. L'étude se poursuit avec les espaces préhilbertiens complets, où l' on introduit les notions essentielles d orthogonalité et de projection orthogonale. Le théorème de représentation de Riesz est également abordé, illustrant l importance de la dualité dans ces espaces. Une section d' exercices est incluse pour consolider ces concepts fondamentaux. Ensuite, le chapitre se focalise sur les systèmes orthogonaux et les bases hilbertiennes, en introduisant les concepts de systèmes orthogonaux et orthonormaux. Le procédé d'orthonormalisation de Gram-Schmidt est présenté comme un outil essentiel pour construire des bases orthonormées. Les inégalités de Bessel et de Parseval sont étudiées en détail, suivies de l'égalité de Parseval, qui met en évidence le lien entre les séries orthogonales et la structure des espaces de Hilbert. Enfin, une attention particulière est portée aux systèmes orthonormés complets dans des espaces concrets, avec une application directe aux séries de Fourier. La base hilbertienne trigonométrique est introduite, illustrant l' utilité des espaces de Hilbert en analyse de Fourier. La majorité des exemples sont extraits des références [1 - 23]. Pour compléter l 'étude , une série d exercices et de travaux dirigés est proposée, couvrant des sujets variés, pour approfondir la compréhension et maîtriser les outils mathématiques abordés dans ce cours.
Course General Biodiversity Intended for L3 Biology and Ecology of Aquatic Environments students
(Faculty of Sciences, 2025) BOUDEFFA , Khaled
Biodiversity encompasses all living organisms and the ecosystems that host them, as well as the complex interactions that connect them. It is both the result of a long evolutionary process and a key factor in maintaining the ecological balance of our planet. Understanding biodiversity, its components, and the threats it faces is now a major challenge for the conservation of ecosystems and the sustainable management of natural resources. This general biodiversity handbook aims to provide a comprehensive overview of the fundamental concepts related to biological diversity. It explores the different levels of biodiversity (genetic, species, and ecosystem diversity), the evolutionary mechanisms that shape it, and the main anthropogenic pressures contributing to its decline. By highlighting the importance of biodiversity in ecological balance and ecosystem services, this document serves as an educational tool to raise awareness about the necessity of its conservation. Designed for students, researchers, and environmental science enthusiasts, this material provides a foundation for reflection and learning. It is based on recent scientific data and concrete examples to illustrate both the richness and fragility of life on Earth. May this handbook serve as a resource to better understand the complexity of the living world and encourage a more responsible and respectful approach to nature.
Course Handout Acoustic : 3rd year Licence (LMD) Sector Physic Specialty Materials Physic
(Faculty of Sciences, 2025) HADEF , Zakaria
This handout of the acoustics course was written for 3rd year students in the Physics of Materials License who are preparing, as part of the L.M.D. reform, a License in the field of "Material Sciences". It complies with the official program. It was written with the aim of providing a work and reference tool covering the knowledge required of them. The manuscript is composed of five chapters, the first is mainly devoted to reminders on oscillations and resonance. The second chapter is reserved for understanding sound and sound sources. The properties of the acoustic wave are detailed in the third chapter. Medical diagnosis by ultrasound was studied in the fourth chapter. The last chapter is devoted to the presentation of the role of sound waves in prospecting and industry. Although this manuscript has been prepared with the greatest care, it obviously remains improvable. I thank in advance anyone who sends me remarks or comments
Course handout Degradation and conservation of ecosystems (DCE) : Ineeded for master 2 of Applied Microbiology students
(Faculty of Sciences, 2025) BOUCETTA , Sabrine
The structure of ecosystem is generally a description of an environment’s organisms and physical features. This includes the amount and distribution of energy in the environment. Now let you have some very easy discussion about the structure of ecosystem in brief : a) Abiotic components: abiotic components are the inorganic and organic components present in the air, water and soil, either they remain in the abiotic phase or they are absorbed by plants and thus entered the biotic phase. The biotic organism after their death and decay they are returned back to the nature.
Course handout Industrial Microbiology : Intended for 3rd year Microbiology students
(Faculty of Sciences, 2025) BOUCETTA , Sabrine
This industrial microbiology handout is intended for 3rd-year Microbiology degree students and is divided into two parts. The first part enables students to acquire a basic knowledge of the subject, through the study of the three main players in industrial microbiology: industrial microorganisms, industrial fermenters and industrial culture media. After acquiring the basic notions, the second part of the subject will discuss the various products of industrial fermentation, which are (i): microbial biomass: generally used as a source of proteins of unicellular origin, (ii): the industrial production of certain primary metabolites represented by amino acids, organic acids and biogases, and (iii) the industrial production of certain secondary metabolites represented by antibiotics, polysaccharides and vitamins. The teaching method used in this course is based on the use of simple and basic language, supported by examples. In addition, and in order to make the content more accessible to students, many illustrations in the form of simplified diagrams, photos and summary tables have been used. As a result, it is always encouraging and motivating to receive corrections, advice and recommendations from our teaching and research colleagues.
Course Handout of "Plant Biology 1" Intended for First-Year Engineering Students in Agronomic Sciences
(Faculty of Sciences, 2025) SOUILAH , Nabila
Plant biology is a broad discipline that encompasses all aspects of plant life, both aquatic and terrestrial, including their morphologies, modes of reproduction (sexual and asexual), adaptations to various environments, and the mechanisms enabling sustainable interactions (such as parasitism and symbiosis) (Campell et al., 2008). The living world consists of an immense collection of organisms in constant evolution. It is divided into two biotic groups (prokaryotes and eukaryotes) and six kingdoms: Archaea, Eubacteria, Protists, Fungi, Animals, and Plants (Margulis & Schwartz, 1988; Raven et al., 2013).
Course Handout on Technology of Agri-Food Industries (T.I.A.A. 1 and T.I.A.A. 2) : For the use of third-year undergraduate students in Agri-Food Science and Quality Control
(Faculté des Sciences, 2025) LAIB , Imen
This handout is intended for third-year undergraduate students in Food Science and Quality Control, as part of the TIAA1 and TIAA2 courses. It has been designed to support students in learning the fundamentals of food science and technology, with a focus on dairy products, the sugar industry, fats and oils, beverages, cereal products, fruits and vegetables, as well as meat products. The food industry is a complex and ever-evolving sector where mastering processing techniques, understanding the properties of raw materials, and managing quality are essential challenges. This document aims to provide students with a solid and structured foundation to understand the various food industry sectors, addressing the technological, microbiological, and nutritional aspects of food products. The objectives of this handout are as follows: to convey fundamental knowledge about raw materials and processing techniques, to facilitate the learning of quality control methods, to develop a global perspective on food industry sectors through concrete examples and case studies, and to prepare students for professional challenges by training them to meet the demands of the food industry market.
Course in Numerical methods For Engineers and scientists
(Faculty of sciences, 2024) SELMANI , WISSAME
The course on numerical methods in mathematics for engineers is a fundamental aspect of engineering education, designed to equip students with tools to solve complex mathematical problems using computational techniques . This course bridges the gap between theoretical concepts and real-world applications by teaching algorithms and strategies to approximate solutions for mathematical models that are otherwise challenging or impossible to solve analytically. Throughout the course, students delve into numerical techniques such as root finding, interpolation , numerical integration, differential equations, and matrix computations.They learn how to apply these methods using programming languages like Maple, MATLAB,Python,or others, gaining hands-onexperience in implementing algorithms and analyzing the accuracy and efficiency of their solutions Understanding numerical methods iscrucial for engineers as it enables them to simulate, model, and solve problems encountered in various engineering disciplines.It empowers them to tackle real-world challenges where analytical solutions may be impractical or unavailable,allow- for accurate predictions,design optimizations,and informed decision-making in engineeringing projects. This course aims to expose the different digital methods for level technicians L2 university. This document contains six(06)chapters and the objectives collectively aim to equipeng ineering students with a robust foundation in numerical methods, preparing them to tackle intricate engineering problems using computational tools and mathematical techniques
Course of : MATHEMATICS 3
(Faculty of sciences, 2024) BENDIB , EL OUAHMA
The aim of this course is to provide general training in numerical series and integral calculus for second-year science and technology students, and to know a new mathematical tools. This course provides the fundamental concept of numerical series, multiple integrals, improper integrals, differential equation and how to use Fourier transform and Laplace transform for solving some differential equations
DYNAMICAL SYSTEMS 1 First semester : For first-year Master’s degree students
(Faculty of Sciences, 2025) Boulfoul , Amel
This course book serves as an introduction to dynamical systems, focusing on ordinary differential equations (ODEs), their stability, periodic solutions, and bifurcations. It is aimed at students in mathematics, particularly those in the first year of their Master’s degree. The book is structured into five main chapters, each addressing important aspects of dynamical systems. The first chapter, Preliminaries of Ordinary Differential Equations, begins with a review of differential systems, followed by their classification, and linear differential systems, including homogeneous and nonhomogeneous cases. The second chapter, General Theory of ODEs, introduces the fundamental aspects of ordinary differential equations, initial value problems, and solutions. It includes key existence and uniqueness theorems, different proof methods, and examples. Additionally, the continuation of solutions and maximal intervals of existence are discussed in detail. The third chapter, Stability in Linear and Nonlinear Systems, explores the concept of stability, starting with linear systems and extending to nonlinear systems. It covers important tools such as Lyapunov’s method and the analysis of conservative and dissipative systems, which are fundamental for understanding system behavior over time. In the fourth chapter, Periodic Solutions and Their Stability, we delve into the nature of periodic solutions, limit cycles, and their stability. Concepts such as Poincar´e maps, Bendixson’s and Dulac’s criteria, and the Poincar´e-Bendixson theorem are explored, offering a deep understanding of the behavior of dynamical systems in the long term. Finally, the fifth chapter, Introduction to Local Bifurcations, introduces the v concept of bifurcation, focusing on one-dimensional and two-dimensional systems. Key bifurcations, including saddle-node, pitchfork, transcritical, and Hopf bifurcations, are explored, laying the foundation for further study and applications in complex systems. In this book, my objective was to collect the most important definitions, information, and tools from the most significant references such as [[12], [14], [15], [10], [5]], and the references therein, to help students focus on the essential notions of dynamical systems. Throughout the book, a formal and clear approach is taken, with numerous examples and illustrations. The topics covered are foundational for the study of dynamical systems and provide the necessary tools to tackle more advanced subjects in mathematical modeling, control theory, and applied mathematics. It is my hope that this book serves as a learning resource for students and a reference for those seeking to deepen their understanding of dynamical systems
Electronics Components : Intended for Master 2 physics of materials
(Faculty of Sciences, 2025) Gacem , Amel
Electronic components are the basic building blocks of electronic circuits, essential for controlling and manipulating electrical signals. Key components include resistors, which regulate current flow; capacitors, which store and release energy; diodes, which allow current to flow in one direction; transistors, used for amplification and switching; and inductors, which store energy in a magnetic field. These components work together in circuits to perform specific functions, such as signal processing, power management, and data transmission, forming the foundation of modern electronic devices like smartphones and computers. This document is a course support for electronic components intended for students in the Master 2 in Physics of Materials, who wish to deepen their knowledge in the subject. This document aims particularly to support the personal work of the student and to make the professor's work more effective. The aim behind this course is to simplify the essential ideas contained in this course and to make them didactically simpler. Consequently, the emphasis will be placed on physical explanations, demonstrations, and examples when they are essential for the students' good understanding. In the context of this course, we are mainly interested in presenting the content of the subject of electronic components in accordance with the official program. The program is structured in the form of four chapters; these chapters allow the main concepts of electronic components to be introduced in a simple way. The first chapter, entitled Diodes, is devoted to presenting basic notions on semiconductors as an introduction and more mainly to the in-depth study of PN junction diodes, their polarization, their modeling and their different functions. The second chapter, entitled Transistors, will be dedicated to the study of the different types of junction and field effect transistors, their operating principle, their characteristics and their polarization in static and dynamic regime. The third chapter, entitled Transistor Amplifiers ; is devoted to examining their operation, their equivalent diagrams, their main electrical characteristics and their applications in modern technology. The last chapter deals with the different types of feedback in positive or negative amplifiers and their general properties. the study of their influence on gain fluctuations and input and output impedances in electrical circuits. A large number of bibliographic references have been used to develop this document. Each chapter is preceded by the main part of a course followed by assessment questions with their indicators. I hope that this handout will serve as a valuable working tool for level License and Master in physics and electronics students.
Épidémiologie : Cours destiné aux étudiants 3ème année licence toxicologie
(Faculté des Sciences, 2025) Gabli , Zahra
L’épidémiologie permet de recueillir, interpréter, utiliser l’information sur les problèmes de santé . Ses objectifs sont la promotion de la santé et la réduction des problèmes de santé. - aborder des problèmes de santé au niveau de population. - Déterminer la fréquence et la distribution d’un phénomène de santé dans la population. - Identifier les causes de ce phénomène. - Évaluer la qualité des méthodes de diagnostic. - Effectuer la surveillance des maladies et Mesuré l’efficacité d’une intervention destinée à modifier son évolution.
GENETICS : Course for 2nd year Biological Sciences, Marine and Continental Hydrobiology students
(Faculty of Sciences, 2025) Boulechfar , Safia
The course of Genetics is specifically designed for 2nd year Biological Sciences and Marine and Continental Hydrobiology students. The overall aim of this course, is to provide a clear, comprehensive, rigorous, and balanced introduction to fundamental genetics. It is a guide to help students to: • understand the basic concepts of genetics • be able to make connections between the main concepts of genetics • apply the concepts and the principles to solve problems of several types during tutorial sessions, such as single-concept exercises that require application of definitions or the basic principles of genetics, and quantitative problems that call for some numerical calculation. The course comprises 11 chapters. Chapter 1 presents information about the genetic material including DNA and RNA structures, DNA replication, organization of DNA in chromosomes. Chapter 2 deals with cell cycle and cell divison. Chapter 3 covers the principles of inheritance including Mendel’s laws, independent and linked genes, X-linked inheritance. Chapter 4 deals with ordered tetrad analysis. Chapter 5 describes the mechanisms of genetic transfer between bacteria. Chapters 6 and 7 deal with topics in molecular genetics including transcription, translation and mutations. It is worth-mentioning that chapter 7 combined two chapters (genic mutations and chromosomal mutations) into just one chapter, which is mutations. Chapters 8 and 9 focus mainly on the structure of genes and control of gene expression in both prokaryotic and eukaryotic oganisms. Chapter 10 presents extrachromosomal genetics. Chapter 11 deals with some basic concepts of population genetics.
Geology course elements , 1st year Common Core L1: Natural and life sciences
(Faculty of Sciences, 2024) BOUDRIES , Amel
The objective of the geology instruction is to instill fundamental knowledge of the major phenomena shaping the Earth, demonstrating that the Earth is a dynamic planet with processes that we aim to comprehend. The general geology module primarily seeks to position geology within the natural sciences and underscore its relevance to biological requirements. In the first part of this module, students will be introduced to basic concepts concerning the fundamental understanding of the Earth's structure through various investigative methods. The second part will cover notions related to external phenomena (erosion and alteration) influencing changes in topography, and finally, structural geology in connection with internal and external geodynamics. The module will also explore the stratigraphic scale of geological times based on various methods of geochronological dating.

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