Mathematical Analysis I - a.y. 2016/2017
Period (Year/Semester): I/I
Required/expected prior knowledge: Nothing.
Ferdinando Farroni - Classe A-E Fuorigrotta
Vittorio Coti Zelati - Classe F-R Fuorigrotta
Francesco della Pietra - Classe S-Z Fuorigrotta
Francesco Chiacchio - Classe A-I San Giovanni a Teduccio
Cristina Trombetti - Classe J-Z San Giovanni a Teduccio
Provide the basic concepts, in view of the applications, of the infinitesimal, differential and integral calculus for real functions of a real variable; to acquire adequate logical formalization capacities and deliberate operational skills.
Tables of contents:
Real numbers. Complex numbers. Elementary functions in the real field. Equations and inequalities. Limits of real functions of a real variable: limits and their properties, operations with limits and indeterminate forms, infinitesimals and infinities, calculation of limits. Continuous functions: properties and main theorems. Differential calculus for real functions of a real variable: differentiable functions and geometric meaning of the derivative, the differential, main theorems of differential calculus, relative and absolute extrema, monotonicity criteria, convex and concave functions, study of the graph of a function, Taylor's formula. Indefinite integrals: primitive and integration rules. Integral calculus for continuous functions in a compact interval: main properties and theorems, area under the graph of a function, the fundamental theorem of calculus, calculation of definite integrals. Numerical sequences and series, geometric series, harmonic series.
Lectures and exercises.
Textbooks and learning aids:
P. Marcellini – C. Sbordone, Analisi Matematica 1 – Editore Liguori.
P. Marcellini – C. Sbordone, esercitazioni di Matematica Parte 1 e Parte 2 - Editore Liguori.
M. Bramanti – C.M. Pagani – S. Salsa, Analisi Matematica 1 – Editore Zanichelli.
Note e dispense pubblicate sul sito docente. Raccolta dei compiti di esame.
Assessment will be written (multiple choice tests, open questions and numerical exercises) and oral.