The course aims to provide students with the fundamentals of differential and integral calculus for real functions, first of one and then of several variables.
It focuses on maxima and minima, the theory and applications of integrals (single and multiple), and introduces advanced tools for the study of curves, ordinary differential equations, and curvilinear and surface integrals.
Mathematical Analysis I. Fundamentals of functions of a real variable: definitions of limit, continuity, and differentiability, together with their main properties.
The course, in order to achieve the expected objectives, mainly takes place through lectures. There are also practical based lessons, guided exercises with teacher support, and exam simulations with the aim of stimulating a critical thinking together with an autonomous the approach to problem solving.
The exam consists of a written test followed by an oral examination. During the written test, students are required to provide the complete solution of some exercises. The allotted time for the written test is two hours. The evaluation of the written test is expressed on a 30-point scale. The student passes the written test if the overall score is not lower than 15/30. Once the written test has been passed, the student is entitled to take the oral examination only in the same exam session in which the written test was passed.
The written test assesses the students’ critical skills on the topics covered during the course, as well as the methodological rigor of the solutions proposed in response to the questions.
The oral examination consists of a discussion on the topics included in the course syllabus. It evaluates the student’s ability to communicate, using appropriate scientific language, the acquired knowledge, as well as the ability to explain the theoretical aspects underlying the various types of exercises contained in the written test. The score of the oral examination will be assigned according to the following grading criteria:
C. Canuto, A.Tabacco, Mathematical analysis 2, Ediz. MyLab. Pearson 2023
P. Marcellini, C. Sbordone, N. Fusco, Analisi Matematica Due, Zanichelli 2020.
In the first part of this course we provide the student with the basic notions of differential calculus for real functions of several real variables and we focus on maxima and minima for those functions.
Next, we develop the main topics regarding integral calculus: we start with functions of a real variable and then we pass to multiple integrals.
Subsequently and gradually, we will move on to targeted in-depth studies that will allow the deal with complex problems inherent to curves, ordinary differential equations, curvilinear and surface integrals.
