# CALCULUS 2B cod. 1007196

2° year of course - Second semester
Professor
Alessandra LUNARDI
Analisi matematica (MAT/05)
Field
Formazione teorica
Type of training activity
Characterising
56 hours
of face-to-face activities
6 credits
hub:
course unit
in ITALIAN

## Learning objectives

The object is to supply the students with knowledge and understanding of sequences and series of functions, ordinary differential equations and systems.
Amain aim is to give them the competence to treat and apply these instruments.
Objects of the course are also : judgement independence, strong written and oral communication skills, learning ability, in accordance with the specific objects of the mathematics degree.

## Prerequisites

Mathematical Analysis I and Mathematical Analysis 2A

## Course unit content

Sequences and series of functions.
Ordinary differential equations and systems.

## Full programme

Sequences and series of functions. Pointwise and uniform convergence. Total convergence of series of functions. Power series and Taylor series.
Ordinary differential equations (ODE) and systems of ODE. The Cauchy problem. Local existence and uniqueness theorem. Extensions of the solutions. Qualitative study of solutions and continuous dependence on the initial data. Solutions of some type of first order ODE. Linear equations and systems with constant coefficients.

## Bibliography

M. Fusco, P:Marcellini, C. Sbordone, Analisi Matematica due, ed. Liguori.
M. Bramanti, C.D. Pagani, S.Salsa, Analisi matematica 2, ed. Zanichelli.
G. Prodi, Lezioni di Analisi Matematica II, ed. Tecnico Scientifica.

## Teaching methods

The teaching consists in frontal lessons where both theoretical and applicable aspects are expounded. The exercises are worked out with the collaboration of the students and are programmed in order that students can solve autonomously the problems arising from the theoretical lessons.

## Assessment methods and criteria

The final exam consists in a written test followed by an oral discussion. In both the tests the student has to demonstrate knowledge, comprehension and to be able to connect knowledge and comprehension about the subjects of the course.
The written test consists in some open questions.
The marks, ranging from 0 to 30, will be attributed considering the accuracy of the exposition and the operating methods.
The test will be considered sufficient if the average of the total amount of the written and oral tests is greater or equal to 18.

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