Professor
Chiara GiacomoniCollaborator
Luca CambriaLearning outcomes
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 contents
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 algebraic equations and inequalities of first and second order, power, exponential, logarithmic and trigonometric functions. These topics are resumed in the pre course that is held every year before the beginning of the course.
Reading/Bibliography
Teacher’s notes: - Analisi Matematica di Bertsch, Dal Passo, Giacomelli – Mcgraw-Hill - Esercitazioni di Matematica - XNUMX° volume parte prima – P. Marcellini, C. Sbordone – Liguori Editore - Esercitazioni di Matematica - XNUMX° volume parte seconda – P. Marcellini, C. Sbordone – Liguori Editore
Teaching methods
Lectures in the classroom and exercises carried out with the aid of computer projections.
Assessment methods
The exam consists of two parts, written (2 or 3 hours) and oral (40 minutes). Admission to the oral test is allowed only to who already passed the written test.