Mathématiques

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    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.
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    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.
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    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
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    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
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    MATHEMATICS 1 : First Semester For first year university students in matter sciences and related disciplines
    (Faculty of sciences, 2024-02) Khemis , Rabah
    Mathematics can be deemed as the language of science and technology due to the fact that the mathematical concepts and tools form integral parts of the vocabulary of several scholars working in various fields. For this, a knowledge of some basic mathematical concepts and techniques is crucial for an increasing number of university courses for a wide range of scientific disciplines such as mathematics, physics, chemistry, computer sciences, engineering and life sciences. Indeed, for physics and chemistry, mathematics has always been, and still is, one of the core tools since it promotes rigorous thinking, problem solving ability and help in expressing ideas, formulating theories, modelling and also getting a better understanding of a broad range of phenomena that appear almost in every facet of our lives. The red thread of this course which can be considered as a first step towards further learning in mathematics, is to introduce some basic mathematical concepts that are assumed to be mastered by students in chemistry and physics. Most of them are presented in their simplest but rigorous forms so that students that take their first steps in the university can easily understand them especially those with little background in mathematics and often no motivation to learn more. This course is not proof-based but it provides a scaffolded approach to learning main ideas and notions that will be required for applying mathematics in physics and chemistry. Whist it has been geared primarily towards first year students at the universities whose speciality is precisely matter sciences, the actual audience may be all students studying mathematics at the university whatever their speciality. Students are assumed to have a little prior knowledge especially knowledge of high school mathematics which should be a sufficient prerequisite. Furthermore, an acquaintance with some basic concepts of mathematical logic and some types of mathematical proof is an element of the knowledge required for this module. The content here is divided into two main parts: The first part that is made up of three chapters, deals with analysis whereas the second one is algebra. The first three chapters cover a collection of topics such as sets, relations and functions while the other three chapters focus on groups, rings, fields, vector spaces and linear transformations Finally, it is our aspiration that this course will greatly simplify the work of the students and will also be a helpful resource for them - including those struggling with their mathematics.
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    Optimisation sans Contrainte اﻷﻣﺜﻠﻴﺔ دون ﻗﻴﻮد
    (كلية العلوم, 2022) ساسي ، ﻓﺎﺗﺢ
    لطالما اقترنت النمذجة الرياضياتية لمختلف الظواهر الفيزيائية والإشكاليات اليومية بلغة نظرية تسمى اليوم بالأمثلية أوالأمثَلة، و التي ظهرت بظهور الإنسان منذ القدم من خلال ممارساته اليومية، وقد اقترن بروزها كمجال بحث فعلي بأعمال كل من نيوتن ، لاغرونج ،كوشي و أولر في القرن18 ، وتطورت بتطور علوم الحاسوب وظهور البرمجة العددية لتشمل بعد ذلك جميع المجالات. إن المبدأ العام للأمثلية يتمثل في استخدام عدة طرق تحليلية وعددية لايجاد الحلول المثلى لمسألة معينة، هذه الأخيرة ترتكز على تابع متعدد المتغيرات غالبا وفي بعض الأحيان يكون مرفقا ببعض الشروط أو القيود، كما أن الحلول تختلف دقتها من طريقة لأخرى فلكل طريقة خوارزمية ذات خطوات و هوامش خطأ مختلفة. اختصارا يمكن القول . الأمثلية = عين النقطة الحدية الصغرى(وفي بعض الحالات العظمى ) لدالة معينة.
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    مبادئ المنطق وطرق البرهان الرياضي - مطبوعة دروس
    (كلية العلوم, 2022) بوهالي ، كلثوم
    الرياضيات والمنطق علمان متداخلان كل منهما يبرهن على صحة الاخر لذا كان تطورهما متلازما. لا يمكن تعلم موضوع في الرياضيات غير منطقي، وبالتالي المنطق الرياضي هو فرع من فروع الرياضيات يهتم باستخدام الرموز المنطقية )أدوات الربط( وهي رموز يتم بواسطتها ربط العبارات يبعضها البعض للحصول على عبارات منطقية جديدة ونستخدم في المنطق الرياضي جداول خاصة تعرف باسم جداول الحقيقة )الصحة( وهي تهدف إلى إثبات صحة قضية ما أو عدم صحتما وهي الطريقة الحسابية الأسهل والأضمن لإيجاد قيم الحقيقة للعبارة الرياضية وكلها تعبر عن المنطق الجملي.