To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.
Curriculum
scheda docente
materiale didattico
- Existence and uniqueness theorems (Gronwall's lemmas; Picard's theorem, Peano's theorem).
- Existence intervals and maximal solutions.
- Dependence on initial data and parameters.
2. Qualitative analysis of some simple EDO classes. Phase space.
3. Linear systems with constant coefficients. Exponential of matrices and Jordan's normal form theorem.
4. Linear systems with variable coefficients. Solution spaces. The Wronskian.
6. Periodic solutions and Fourier series.
7. Hamiltonian systems and celestial mechanics (introduction)
Shair Ahmad and Antonio Ambrosetti, Differential Equations. A first course on ODE and a brief introduction to PDE
Series: De Gruyter Textbook De Gruyter | 2019 DOI: https://doi.org/10.1515/9783110652864
Programma
1. General theory:- Existence and uniqueness theorems (Gronwall's lemmas; Picard's theorem, Peano's theorem).
- Existence intervals and maximal solutions.
- Dependence on initial data and parameters.
2. Qualitative analysis of some simple EDO classes. Phase space.
3. Linear systems with constant coefficients. Exponential of matrices and Jordan's normal form theorem.
4. Linear systems with variable coefficients. Solution spaces. The Wronskian.
6. Periodic solutions and Fourier series.
7. Hamiltonian systems and celestial mechanics (introduction)
Testi Adottati
Gerald Teschl: Ordinary Differential Equations and Dynamical Systems , Graduate Studies in Mathematics Volume 140, American Mathematical Society, 2011Shair Ahmad and Antonio Ambrosetti, Differential Equations. A first course on ODE and a brief introduction to PDE
Series: De Gruyter Textbook De Gruyter | 2019 DOI: https://doi.org/10.1515/9783110652864
Bibliografia Di Riferimento
[T] Ordinary Differential Equations and Dynamical Systems (Graduate Studies in Mathematics). AMS. by Gerald Teschl (Author). ISBN-13: 978-0821883280 [D] Demidovich, B.P., Esercizi e problemi di Analisi Matematica, Editori Riuniti, 2010Modalità Erogazione
Lectures (about thirty-six hours) and exercises (about twentyfour hours). All the program material will be explained in class. The lessons / exercises will include a continuous dialogue with the students: the feedback from the students during the course is a fundamental tool for the success of the course itself. In the event of an extension of the health emergency from COVID-19, all the provisions (of the State and of the Roma Tre University) that regulate the methods of carrying out the educational activities will be implemented. In particular, distance lessons may be needed.Modalità Frequenza
In class. Possibility of online/recorded lectures, if necessary.Modalità Valutazione
The evaluation is based on a written test (explicit solutions of ODE's, qualitative analysis, etc.) and an oral exam concerning the content of the course. In the case of an extension of the health emergency from COVID-19, all the provisions (of the State and of the Roma Tre University) that regulate the methods of student assessment will be implemented. In particular, distance assessments may be necessary and in this case the oral evaluation will be preceded by a preliminary written test which is an integral part of the oral examination.
scheda docente
materiale didattico
- Existence and uniqueness theorems (Gronwall's lemmas; Picard's theorem, Peano's theorem).
- Existence intervals and maximal solutions.
- Dependence on initial data and parameters.
2. Qualitative analysis of some simple EDO classes. Phase space.
3. Linear systems with constant coefficients. Exponential of matrices and Jordan's normal form theorem.
4. Linear systems with variable coefficients. Solution spaces. The Wronskian.
6. Periodic solutions and Fourier series.
7. Hamiltonian systems and celestial mechanics (introduction)
Shair Ahmad and Antonio Ambrosetti, Differential Equations. A first course on ODE and a brief introduction to PDE
Series: De Gruyter Textbook De Gruyter | 2019 DOI: https://doi.org/10.1515/9783110652864
Mutuazione: 20410469 AM430 - EQUAZIONI DIFFERENZIALI ORDINARIE in Matematica LM-40 CHIERCHIA LUIGI
Programma
1. General theory:- Existence and uniqueness theorems (Gronwall's lemmas; Picard's theorem, Peano's theorem).
- Existence intervals and maximal solutions.
- Dependence on initial data and parameters.
2. Qualitative analysis of some simple EDO classes. Phase space.
3. Linear systems with constant coefficients. Exponential of matrices and Jordan's normal form theorem.
4. Linear systems with variable coefficients. Solution spaces. The Wronskian.
6. Periodic solutions and Fourier series.
7. Hamiltonian systems and celestial mechanics (introduction)
Testi Adottati
Gerald Teschl: Ordinary Differential Equations and Dynamical Systems , Graduate Studies in Mathematics Volume 140, American Mathematical Society, 2011Shair Ahmad and Antonio Ambrosetti, Differential Equations. A first course on ODE and a brief introduction to PDE
Series: De Gruyter Textbook De Gruyter | 2019 DOI: https://doi.org/10.1515/9783110652864
Bibliografia Di Riferimento
[T] Ordinary Differential Equations and Dynamical Systems (Graduate Studies in Mathematics). AMS. by Gerald Teschl (Author). ISBN-13: 978-0821883280 [D] Demidovich, B.P., Esercizi e problemi di Analisi Matematica, Editori Riuniti, 2010Modalità Erogazione
Lectures (about thirty-six hours) and exercises (about twentyfour hours). All the program material will be explained in class. The lessons / exercises will include a continuous dialogue with the students: the feedback from the students during the course is a fundamental tool for the success of the course itself. In the event of an extension of the health emergency from COVID-19, all the provisions (of the State and of the Roma Tre University) that regulate the methods of carrying out the educational activities will be implemented. In particular, distance lessons may be needed.Modalità Frequenza
In class. Possibility of online/recorded lectures, if necessary.Modalità Valutazione
The evaluation is based on a written test (explicit solutions of ODE's, qualitative analysis, etc.) and an oral exam concerning the content of the course. In the case of an extension of the health emergency from COVID-19, all the provisions (of the State and of the Roma Tre University) that regulate the methods of student assessment will be implemented. In particular, distance assessments may be necessary and in this case the oral evaluation will be preceded by a preliminary written test which is an integral part of the oral examination.