## 20410233 - ISTITUZIONI DI MATEMATICHE

The objective of this course is to give students an understanding of basic calculus as well as to enable them to approach problems from a mathematical perspective.
teacher profile | teaching materials

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.

Core Documentation

Marcellini-Sbordone Elementi di Matematica, Esercitazioni di Analisi Matematica

Reference Bibliography

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

Type of delivery of the course

Lessons + exercises.

Attendance

Following in person is highly recommended.

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. It is possible to bring notes and a NON graphing calculator. 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.

teacher profile | teaching materials

Programme

Numbers (natural, 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.

Core Documentation

Marcellini-Sbordone Elementi di Matematica, Esercitazioni di Analisi Matematica

Reference Bibliography

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

Type of delivery of the course

lesson + exercises

Attendance

Following in person is highly recommended

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. It is possible to bring notes and a NON-graphing calculator. 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.