Real numbers. Sequences and function. Limits of sequences and function. Elementary functions. Continuous functions. Differentiable functions and their properties. Local maxima and minima. Graphics of functions. Taylor's formula. Riemann's integral. Integrability of continuous functions. Newton-Leibniz Formula. Antiderivatives. Numerical series. Improper integrals.
Knowledge acquired: The course intends to give the fundamental concepts of differential and integral calculus for real function in one real variable: continuity, differentiability, polynomial approximation, Riemann’s integral, fundamental theorem of integral calculus and differential equation of simple resolution. The “continue” point of view is joined to the “discrete” with the study of sequence and numeric series concepts.
Competence acquired:Knowledge of fundamental issues of calculus: limits, derivatives, Taylor polynomials, antiderivatives, Riemann's integrals, 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.
Teaching Methods
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 individual formative activities:
Contact hours for: Lectures (hours): 120
Contact hours for: Laboratory (hours):
Contact hours for: Laboratory-field/practice (hours):
Seminars (hours): 0
Stages: 0
Intermediate examinations: 9
Further information
Office hours:
Monday 1.30 pm to 3.00 pm and by appointment
Type of Assessment
Written test followed by an oral test
Course program
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.