Mathematics I, Analysis and Algebra
Résumé de section
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These lessons are intended for first-year students in the Material Sciences department, following the curriculum provided by the ministry for the Mathematics course in the first year of Algebra and Mathematical Analysis. This course is divided into two parts over two semesters, where students study Mathematics 1 in the first semester and Mathematics 2 in the second semester. This subject is a fundamental course belonging to the core unit, which has a coefficient of 3 and a credit of 6. The grade for this subject is calculated as 33% based on the total score of the coursework and 67% based on the score of the final exam for each semester.
These lessons can be foundational for the first year and preparatory for the second year, serving as a starting point for further training in calculus, matrices, and solving differential equations. The lessons are written in a clear and simple manner to encourage students to learn the basic principles and concepts of algebra and mathematical analysis, in an attempt to simplify the definitions and explanations for differentiation, integration, and differential equations, which require describing physical, chemical, or other phenomena and knowing specific things about these phenomena, observations, or samples.
In these lessons, we have carefully integrated examples and exercises. Some of the exercises can be found on various websites, which we have reviewed and translated into Arabic. This work is divided into two parts, the first of which is dedicated to algebra and the second to mathematical analysis in each semester. At the end of each chapter, we address a series of solved exercises that help to deepen and consolidate the concepts.
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We will try to explore the properties of sets, without focusing on a specific example. We will quickly discover that the relationships between sets are no less important than the sets themselves, and this will be the concept of the application (or function) between two sets.
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[1] Allab, K. Eléments d'analyse : fonction d'une variable réelle O.P.U., 1986.
[2] Azouly, E., Avignant, J. Auliac, G. Les mathématiques en Licence, 1ère. Tome 1: Cours+ exos, MIAS. MASS. SM, Ediscience (Dunod pour la nouvelle édition) Paris 2003.
[3] Azouly, E., Avignant, J. Auliac, G. Les mathématiques en Licence, 1ère. Tome 2: Cours+ exos, MIAS. MASS. SM, Ediscience (Dunod pour la nouvelle édition) Paris 2003.
[4] Azouly, E., Avignant, J. Auliac, G. Problèmes Corrigés de mathématiques , DEUG MIAS/SM, Ediscience (Dunod pour la nouvelle édition) Paris 2002.
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[6] Baba-Hamed. C, Benhabib. K, Algèbre. Rappel de cours et exercices avec solutions. O.P.U., 1990.
[7] Bayart, F. Bibmath.net, https://www.bibmath.net
[8] Chambadal, L. Exercices et problèmes résolus d'analyse : mathématiques spéciales. Bordas, 1973.
[9] Exo7 Cours et exercices de mathématiques, http://exo7.emath.fr/un.html
[10] Godement, R. Cours d'algèbre. Hermann, 1966.