# MATHEMATICS

## AIMS AND CONTENT

LEARNING OUTCOMES

The aim of this course is to provide a practical working tool for students where rigorous Calculus is needed. The main focus is on the study of functions of one real variable (continuity, derivative, maxima/minima, integration) and a brief introduction to multivariable calculus (oriented towards finding maxima/minima). The last part of the course is oriented towards basic ordinary differential equations (for example separation of variables, linear first-order, and constant coefficients ODE).

AIMS AND LEARNING OUTCOMES

The aim of this course is to provide a practical working tool for students where rigorous Calculus is needed. The main focus is on the study of functions of one real variable (continuity, derivative, maxima/minima, integration) and a brief introduction to multivariable calculus (oriented towards understanding the objects and finding maxima/minima). The last part of the course is oriented towards basic ordinary differential equations.

Teaching methods

During the course theory and example classes will be given. During theory classes, definitions, theorems and main proofs will be given, with lots of examples and exercises. In the example classes, exercises will be discussed and solvedwith the class, aiming to a ameliorate the calculus skills of the students.Nicola FUSCO, Paolo MARCELLINI, Carlo SBORDONE, Lezioni di analisi matematica 1

SYLLABUS/CONTENT

Definitions and first examples of functions; continuity, derivability and theorems about them, study of maxima/minima, integration. Definitions and examples of functions of two variables: various representations. Continuity and differentiability for multivariable functions. Maxima/minima. Ordinary differential equations: separation of variables, constant and nonconstant linear differential equations

RECOMMENDED READING/BIBLIOGRAPHY

Nicola FUSCO, Paolo MARCELLINI, Carlo SBORDONE, Lezioni di analisi matematica 1

## TEACHERS AND EXAM BOARD

**Ricevimento:**
The teacher is available for explanations one afternoon a week.

Exam Board

VICTOR LOZOVANU (President)

MATTEO SANTACESARIA

ELEONORA ANNA ROMANO

ALESSANDRO DE STEFANI

SIMONE DI MARINO (President Substitute)

## LESSONS

Teaching methods

During the course theory and example classes will be given. During theory classes, definitions, theorems and main proofs will be given, with lots of examples and exercises. In the example classes, exercises will be discussed and solvedwith the class, aiming to a ameliorate the calculus skills of the students.Nicola FUSCO, Paolo MARCELLINI, Carlo SBORDONE, Lezioni di analisi matematica 1

LESSONS START

Lectures will begin in September: 6 weekly hours

## EXAMS

Exam description

The exam will consist of a written part and an oral part. The oral part is accessible only if the score in the written test is higher or equal to 14.

Assessment methods

During the written test, the student will solve exercises mainly concerning limits, integrals, study of functions (possibly of more than one variable) and ordinary differential equations. During the oral examination student must highlight critical analysis, skills and ability to apply the concepts learnt to solve easy exercises, possibly some (guided) applications to the real world.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

08/06/2021 | 09:00 | GENOVA | Scritto + Orale | |

12/07/2021 | 09:00 | GENOVA | Scritto + Orale | |

01/09/2021 | 09:00 | GENOVA | Scritto + Orale |