Professor
Chiara GiacomoniCollaborator
Micaela FedeleLearning objectives
The course aims to provide the tools to achieve adequate knowledge of the concepts that underlie mathematical analysis and to develop and consolidate calculation skills. Particular attention has been paid to the choice of significant examples, sometimes drawn from applied sciences, others from more common applications, in order to stimulate logical-deductive aptitudes.
Course content
Main topics: basic notions of set theory; introduction to logic; real numbers, axiom of completeness; complex numbers; elements of topology, accumulation points, Bolzano-Weierstrass theorem, Cantor's theorem; elementary functions, behavior of the function and interpretation of the graphs, injective, surjective and bijective applications, inverse, increasing and decreasing functions, composite function, monotone function; limit of a function, properties of the limit, continuity of a function, Weierstass theorem, intermediate value theorem, discontinuity; derivatives, analytical and geometric meaning of the derivative, fundamental theorems of differential calculus, Fermat's theorem, Rolle's theorem, Lagrange's theorem; applications of derivatives, inflection points, asymptotes; Taylor's formula, local and global extrema; Riemann integral, necessary and sufficient conditions for the existence of the Riemann integral, integration by parts and by change of variable, fundamental theorem of integral calculus. Complex numbers. Combinatorics.
Prerequisites
Basic mathematical knowledge acquired from high school such as: first and second degree algebraic equations and inequalities, powers, exponentials, logarithms and trigonometric functions. These topics will be taken up again in the pre-course held every year before the start of the course.
Bibliography
Teacher's handouts
– Mathematical Analysis by Bertsch, Dal Passo, Giacomelli – Mcgraw-Hill
– Mathematics Exercises – 1st volume part one – P. Marcellini, C. Sbordone – Liguori Editore
– Mathematics exercises – 1st volume part two – P. Marcellini, C. Sbordone – Liguori Editore
Teaching methods and tools
Lectures in the classroom and exercises carried out with the aid of computer projections.
Assessment methods and criteria
The exam consists of two tests, written (2 or 3 hours) and oral (40 minutes). You can access the oral test only if you have passed the written one.
