B006801 - REAL ANALYSIS I

Italian

Programme (short version for Diploma Supplement): Real numbers. Numeric sequences. Limits of functions. Continuous functions. Derivatives. Taylor’s formula. Antiderivatives and Riemann’s integrals. Improper integrals.

Textbooks: Marcellini, Sbordone, "Analisi Matematica uno", Liguori editoreMarcellini, Sbordone, "Esercitazioni di Matematica", first and second book, Liguori editore. (exercises book)

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: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): 96
Contact hours for: Laboratory (hours): 0
Contact hours for: Laboratory-field/practice (hours): 0
Seminars (hours): 0
Stages: 0
Intermediate examinations: 12

Friday, from 12.30 to 14 in her office (room n. 6 in the basement of Maths Department)

Exam modality: Written and oral.

Course Contents (detailed programme): Real numbers: definition and properties. Upper and lower bound of a set.Numeric 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).Antiderivatives and integration methods. Riemann's integrals. Fundamental theorem of calculus.Areas of plane regions and volumes of solids. Taylor's formula.Improper integrals. Numerical series.