- Docente: Angelo Favini
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
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.
Readings/Bibliography
- 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