Programme

Numbers (naturali, integers, rationals, reals). Functions, their graphs. Injective, monotone, periodic functions. Composition and inversion of functions. Interpretation of the graph of a function. Elementary functions. Sequences and limits. Examples. Operations on limits, sum product and composition. Orders of magnitude. Some notable limits. Continuous functions. Differentiable functions. Geometric interpretation of the derivative. Derivative of elementary functions. Derivative of the product, sum, composition of functions. Second derivatives. Maxima and minima. Rolle and Lagrange theorems. Monotone functions. Theorem de l'Hopital. Taylor formula. Primitives and basic properties. Integration by parts and substitution. Rational functions. Riemann integrability. Differential equations. Vector spaces. Matrices and linear systems.

Core Documentation

Marcellini-Sbordone: Elementi di Calcolo,
Marcellini-Sbordone: Esercitazioni di Matematica

Reference Bibliography

Benedetto, Degli Espositi, Maffei: Matematica per le scienze della vita

Type of delivery of the course

Lessons + exercises.

Type of evaluation

The exam consists of a written test and an oral confirmation interview. The written test focuses on carrying out exercises of a similar type to those seen in class. The oral exam is used to verify the knowledge of the bases of mathematical reasoning as well as of the definitions used in carrying out the exercises.