Course reminder and solved exercises in Analysis 2:intended for first year Mathematics and Computer Science students

Abstract

The aim of this course is to bridge the gap between the knowledge of analysis accumulated in high school and the fundamentals that will form one of the pillars of mathematical analysis training in the bachelor’s degree. Given that recruitment to the first year of analysis is fairly heterogeneous, it seems a good idea to start by recalling the basic notions that will be used throughout this course, so as not to lose anyone along the way. Where necessary, at the start of each chapter, we’ll remind you of what you’re supposed to know by the end of the course. As far as possible, we’ll also try to provide the essential results of each chapter on a single page, so as to summarize the knowledge you need to master in order to move on to the next chapter. We will provide as many examples and figures as necessary afin order to achieve a better understanding of the course. We’ll also try to point out the pitfalls that everyone can fall into, either through inattention or poor mastery of the course. This course brings together the notes from the analysis module dedicated to first-year students in the mathematics and computer science stream. It includes limited developments, Reiman integrals and ordinary differential equations. The general idea behind the first chapter is to To handle Limited development, you first need to know a few basic rules. These rules all have a name afin order to identifier them right away, so you know what you’re talking about. A bit like a map, this lets us know what we’re seeing, where we’re going and how we’re getting there. Let’s start with the simple, familiar rules. In the second chapter we give the notion of a Reiman’s integral in Analysis. Darboux’s sums. They are introduced and studied in this chapter. Further, we give the different methods for calculating integrals For the last chapter: we study two types of Ordinary differential equations.An ordinary differential equation ofn order, an ordinary differential equation of 1st order and 2nd order. They are introduced and studied in this chapter. Further, we give the different methods and types to solve this type of an ordinary differential equation Each chapter is followed by a list of exercises, usually illustrating a point made earlier. It goes without saying that these exercises complement the course.