This course provides students with basic concepts of real functions in a single variable, and concepts of ends and continuity. It also addresses the rules of differentiation. This course aims to develop the student's ability to determine the types of real, compulsory and non-compulsory functions, to chart them, to determine the scope, extent and reverse functions of them, to determine the existence of the end, as well as to know the continuity of the functions and to determine whether they are derivable. The course also aims to enhance students' skills in drawing curves using preferential concepts and demonstrations, through scheduled training and the diversity of evaluation methods. The rapporteur focuses on understanding real functions in a single and derivative variable and its applications that help him to understand the behaviour of multiple functions in his future study.