Textbooks: Marcellini, Sbordone, "Elementi di Analisi Matematica uno", Liguori editore, 2002
Marcellini, Sbordone, "Esercizi di Matematica", primo volume, Liguori editore, 2009.
Knowledge acquired: The course intends to give to students the fundamental concepts of differential and integral calculus for real function in one real variable: continuity, differentiability, polynomial approximation, Riemann's integral and fundamental theorem of integral calculus. The "continuous" point of view is joined to the "discrete" with the study of sequence and numeric series concepts.
Competence acquiredKnowledge of fundamental issues of calculus: limit, derivative, Taylor polynomial, antiderivatives, Riemann's integral, series and generalized integrals.
Skills acquired (at the end of the course):At the end of the course the student learns how to apply the tools of calculus to the study of functions of one real variable, the research of maxima and minima, function approximation, evaluations of areas and volumes.
Courses to be used as requirements (required and/or recommended)Courses required: NoneCourses recommended: None
Frequency of lectures, practice and lab: Highly recommended
Teaching toolsUniFi E-Learning: http://e-l.unifi.it
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 300
Hours reserved to private study and other indivual formative activities: 192
Contact hours for: Lectures (hours): 108
Contact hours for: Laboratory (hours): 0
Contact hours for: Laboratory-field/practice (hours): 0
Seminars (hours): 0
Intermediate examinations: 12
Wednesday, from 2 pm to 3 pm in her office (room n. 6 in the basement of Maths Department) during classes. By appointment in when the course is finished.
Type of Assessment
Written exam: the written test contains 5 exercises about the course. The written exam is passed if the grade is at least 16/30.
A part of the written examination can be tested during intermediate session in February. In that case the written exam consists in 3 exercises on the second part of the course.
Oral exam: it takes place in the same session of the written exam. It is an oral examination on the theory of the course with small exercises to test the correct application of the theory.
Real numbers: definition and properties. Upper and lower bound of a set. Number sequences: limit definition, limit uniqueness, comparison theorems, undetermined forms, and remarkable limits. Neper's number. Functions in one real variable: definitions of domain, codomain, injectivity, surjectivity, invertibility. Odd, even and periodic functions. Continuous functions: definition and main theorems (Weierstrass, theorem of zeros and intermediate values). Derivatives: definition and main theorems (Fermat, Rolle, and Lagrange). Taylor's formula. Antiderivatives and integration methods. Riemann's integrals. Fundamental theorem of calculus. Area of plane regions and volume of solids. Improper integrals. Numerical series.