Maths1 : Analysis and Algebra1 ; For students of the common core sciences of matter

Abstract

This mathematics course goes beyond certain developments within the strict frame-work of the program usually covered in the first year of the undergraduate cycle ofhigher education. We wanted to make it a reference document that engineering stu-dents can use in the rest of their studies to deepen or review the notions of algebra oranalysis used in the teaching of applied mathematics for the master’s degree.In this work, we have endeavored to give precise definitions and present rigorous rea-soning without, however, seeking exhaustiveness. Furthermore, as far as possible, wehave sought to motivate the concepts introduced and to illustrate them with examples,remarks and warnings in order to make learning more dynamic.This manuscript constitutes the essential part of Analysis 1 and Algebra 1 whichI gave first year LMD science of matter. We will enhance the course with applicationsand motivations from physics and chemistry.It covers the essential elements of set theory, applications and relationships, internallaws, an introduction to general algebra such as groups, rings, fields. It then addressesthe real functions of a real variable, in particular the notion of limit, its properties, thenotion of continuity and differentiability of functions and finally we study the usualfunctions, these functions appear naturally in solving simple problems, especially thosedealing with real-world topics in physics. It also covers an introduction of vector spacesgiven in the last chapter. We then formalize the abstract and fundamental concept inlinear algebra as well as that of linear