Analysis 2 : Course & exercises ; Bachelor’s Degree in Mathematics and Computer Science (LMD) First Year, Semester 2

Abstract

This manuscript presents Analysis 2, which provides the fundamental tools and results of mathematical analysis across its three chapters. It is a continuation and complement of Analysis 1. Chapter 1 explores limited developments, focusing on Taylor and Maclaurin develop- ments for approximating functions. Chapter 2 introduces the Riemann integral, emphasiz- ing its de nition, properties, and applications to calculating areas and primitives. Finally, Chapter 3 addresses ordinary di erential equations (ODEs), where we study methods for solving rst and second order linear ODEs and more other types of di erential equations modeling real world phenomena. Each chapter is followed by solved exercises to help students assimilate the course. This course aims to provide technical skills and conceptual understanding, thus laying a solid foundation for further study and practical applications in mathematics and related elds. The content of this course is primarily intended for rst-year undergraduates in the Bachelor of Mathematics and Computer Science (LMD) program, as well as computer engineering students. However, this course may also be useful for students in various scienti c and technical elds, such as physics, chemistry, biology, and economics, who require a solid foundation in mathematical analysis. We hope this manuscript will serve as an e ective teaching resource, supporting stu- dents in their regular attendance and diligent preparation for tutorials