# MATHEMATICAL ANALYSIS

OVERVIEW

The course is a standard introduction to Calculus: differential and integral calculus in one variable, some differential equations, differential calculus in two variables. The various topics will be presented mainly via examples and intuitive justifications; in some cases formal proofs will be given. Exercise sessions are very important for the course.

## AIMS AND CONTENT

LEARNING OUTCOMES

The course aims at giving the basic tools of calculus. At the end of the course, students will understand the basic concepts of mathematical analysis and will be able to solve some problems using such tools. Another goal of the course is to train students in rigorous thinking.

AIMS AND LEARNING OUTCOMES

The aim is to provide some fundamental tools of Mathematical Aalysis, to improve the students' attitude toward rigorous reasonig and and to teach students how to solve some problems using the notions studied in the course.

At the end of the course the student must know the fundamental results of the differential calculus in one and two variables and of the integral calculus in one variable. Moreover, the student must know how to apply such notions to solve the exercises, and must be able to apply such notions in other courses that use them.

PREREQUISITES

The standard curriculum of the Italian scuole medie superiori

Teaching methods

Traditional: theory lessons, exercises sessions, support by tutors; exercises for independent training are given to students.

SYLLABUS/CONTENT

Differential calculus in one variable (limits, continuity, derivatives, Taylor formula, study of functions). Integral calculus in one variable (primitives, definite integrals and areas, improper integrals, study of integral functions). Differential equations (separation of variables, linear equations of first order, linear equations with constant coefficients). Differential calculus in two variables (limits, continuity, partial derivatives, level curves, tangent lines and planes, max, min and hessian matrix).

RECOMMENDED READING/BIBLIOGRAPHY

F.Parodi, T.Zolezzi - Appunti di Analisi Matematica - ECIG Genova

M.Baronti. F.De Mari, R.Van der Putten, I.Venturi - Calculus Problems - Springer Italia 2016.

## TEACHERS AND EXAM BOARD

**Ricevimento:** On appointment; take directly an appointment with the professor or write to perelli@dima.unige.it

## LESSONS

Teaching methods

Traditional: theory lessons, exercises sessions, support by tutors; exercises for independent training are given to students.

LESSONS START

When the first year starts.

## EXAMS

Exam description

Two intermediate written exams (end of first and second semester), final written and oral examination. If students pass both intermediate written exams, the arithmetic mean of the results can be taken as result for the written exam in the summer sessions (June - July - September). If both such intermediate written exams are passed with success, their arithmetic mean can be used as the final mark of the course.

Assessment methods

Evaluation of the output from written and oral exams; the goal of the course is reached if the student is able to solve exercises of the same level as those proposed during the exercises hours of the course, and if the student knows the fundamental contents of the course.

## FURTHER INFORMATION

Students are recommended to follow all lectures, exercises sessions and tutors hours.