ANALYSIS III:Intended to the students of second year Bachelor in Mathematics

Abstract

These notes constitute the core of the semester-long course in Analysis III o¤ered to second-year students in the Mathematics LMD program. They may also be useful for second-year students in the physics program as well as for students in the common engineering core. This course consists of ve chapters: the rst is dedicated to numerical series, the second to sequences and series of functions, and the third to power series, particularly important for the study of functions of complex variables. Fourier series, which are useful in the third year, especially in problems governed by parabolic equations, constitute the fourth chapter. Finally, the last chapter addresses the convergence of integrals and is complemented by an introduction to integrals dependent on one or more parameters. We hope that our dear students will derive greater bene t from these notes.