Real numbers. Sequences of real numbers and their limits. Functions of one real variable: limits, continuity, differentiability. Integration theory for functions of one real variable. Series
Knowledge acquired:
The course aims to provide the basic concepts of differential and integral calculus for function of a real variable. Study of sequences and series of real numbers, will be treated.
Competence acquired:
Find the proof of simple statements concerning functions of one real varibles, sequences and series. Computation of: limits, derivatives, integrals, study of sequences and series of real numbers.
Skills acquired (at the end of the course):
Students will be able to correctly carry out the exercises and deal with Physic basic concepts by means of appropriate analytical tools.
Prerequisites
Courses to be used as requirements (required and/or recommended)
Courses required: None
Courses recommended: Pre-course
Frequency of lectures, practice and lab:
Strongly recommended
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 375
Hours reserved to private study and other indivual formative activities: 219
Contact hours for: Lectures (hours): 75
Contact hours for: Laboratory (hours): 0
Contact hours for: Laboratory-field/practice (hours): 75
Seminars (hours): 0
Stages: 0
Intermediate examinations: 6
Further information
Office hours:
Tuesday, from 14.30
Type of Assessment
Written (eventually substituted by intermediate examinations) and oral test.
Course program
Retrieve and complements the real numbers. Sequences of real numbers. Limits of sequences. Real functions of a real variable and their limits. Continuous functions and their properties. Differential calculus and applications. Fundamental theorems of calculus. Taylor's formula and applications. Study of functions: maximum and minimum; monotony; concavity, convexity and inflection points, asymptotes. Indefinite integrals, and calculation of the primitive of a function. Definite integrals: definition and main properties, applications to Geometry and Physics. Fundamental theorems of integral calculus. Integration techniques and calculation of integrals. Improper integrals. Numerical series, convergence criteria for positive series and series with terms of arbitrary sign.