- Docente: Daniele Ritelli
- Credits: 6
- SSD: MAT/05
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Statistical Sciences (cod. 9222)
Learning outcomes
By the end of the course the student knows the fundamentals of the theory of ordinary differential equations, including existence and uniqueness; the major results in the theory of stability; the class of differential equations solvable in closed form; the change of variable method and the Lie symmetry theory; the family of linear equations of second order with variable coefficients and their connections with the special functions theory.
Course contents
General Theory.
Preliminary tools: sequences and series of functions: uniform convergence and passage to the limit.
Existence and Uniqueness with the Lipschitz condition. Existence without the Lipschitz condition. Some global properties of solutions. Dependance on data. Nonuniqueness. Approximate solutions.
Solvable differential equations by means of elementary techniques
Equations of first order: separable equations, homogeneous equations, linear equations, exact equations, integrating factor, Bernoulli equation, Riccati equation.
Equations of second and higher order: linear homogeneous differential equations, non homogeneous equation, variation of parameters.System of linear differential equations with constant coefficients
Linear second differential equation with variable coefficients
Preliminary to the series solution
Solution at an ordinary point
Solution at a singular point
Hypergeometric equation
Bessel equation
Readings/Bibliography
Lecture notes prepared by the instructor.
https://www.dropbox.com/s/0997axbwlzb0vu5/Edos18.pdf?dl=0
A First Course in Ordinary Differential Equations
Analytical and Numerical Methods
Authors: Hermann, Martin, Saravi, Masoud
Chapters 1, 2, 4, 5
ISBN 978-81-322-3527-9
Teaching methods
Lessons ex Cathedra. Homework which will be discussed in the classroom
Assessment methods
Written exam with occasional in-course tests. The written examinations detects the capability of the student to solve differential equations giving detailed explanations about the techniques employed in the process. The oral examination is optional: concerns the proofs of theorems exposed during the course.
Teaching tools
Tablet used as a blackboard
Links to further information
https://www.dropbox.com/s/0997axbwlzb0vu5/Edos18.pdf?dl=0
Office hours
See the website of Daniele Ritelli