# 28410 - Differential Equations 1

### Course Unit Page

• Teacher Angelo Favini

• Credits 6

• SSD MAT/05

• Language Italian

• Course Timetable from Feb 18, 2019 to May 24, 2019

## Learning outcomes

At the end of this course, students knowthe fundamentals of the theory of ordinary differential equations.They can apply their knoledges to solve various types of problems, like periodic movements, evolution of the species, radioactive  decay.

## Course contents

Cauchy problem. Systems  of differential equations.Differential equations of higher order.Some nonlinear equations.Linear differential equations in R and in C. Nonlinear differential equations. Some applications to Physics, chemical reactions, population growth, electrical circuit.Boundary-value problems. Equilibrium points. Lyapunov theorem.

• B.Pini,  Secondo corso di Analisi Matematica, Parte II, ed.CLUEB, Bologna, 1972.
P.D. Ritger, N.J. Rose, Differential equations with applications, ed. McGraw-Hill,New York, 1968.
E.A. Coddington, An introduction to ordinary differential equations, ed. Prentice-Hall, Englewood Cliffs, N.J., USA, 1961.
E.A. Coddington, N. Levinson, Theory of ordinary differential equations, ed.McGraw-Hill, New York, USA, 1955.
E. Hille, Lectures on ordinary differential equations, ed. Addison-Wesley, Reading, USA, 1969.
• C.Chicone, Ordinary differential equations with applications, ed.Springer, New York, 1999
• A.Ambrosetti, Appunti sulle equazioni differenziali ordinarie, Springer, 2012.
• C.Parenti, A.Parmeggiani, Algebra lineare ed equazioni differenziali ordinarie, Springer, 2010.

## Teaching methods

The course consists of lessons where there are presented the basic elements of ordinary differential equations, system of ordinary differential equations and differential equation of higher order. Much attention is devoted to the linear case and wide treatment is addressed to the qualitative analysis of autonomous equations of the second order. Special relevance is given also to the stability solutions. Several lectures are devoted to resolutions of exercises and problems from applied sciences illustrate the theoretical presentation.

## Assessment methods

Assessment method consists in an oral examination that wants to verify the degree of knowledge of the program of the course. The further aim of the proof is to verify the knowledge of the general methods of ordinary differential equations.

## Office hours

See the website of Angelo Favini