Unit DIFFERENTIAL EQUATIONS
- Course
- Mathematics
- Study-unit Code
- 55A00088
- Curriculum
- Didattico-generale
- Teacher
- Tiziana Cardinali
- Teachers
-
- Tiziana Cardinali
- Hours
- 42 ore - Tiziana Cardinali
- CFU
- 6
- Course Regulation
- Coorte 2021
- Offered
- 2021/22
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/05
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Fixed point theory. Existence theorems for differential equations and inclusion equations.
- Reference texts
- I will use pieces of :
- L. C. PICCININI, G. STAMPACCHIA,G. VIDOSSICH, Equazioni differenziali ordinarie in R^n, Ed. Liguori, 1978.
- J.M. A. TOLEDANO, T. D. BENAVIDES, G.L. ACEDO, Measures of Noncompactness in Metric Fixed Point Theory, Birkhauser, 1997.
- L. GASINSKI, N. S. PAPAGEORGIOU. Exercises in analysis. Part 1. Problem Books in Mathematics. Springer, Cham, 2014.
- L. GASINSKI, N. S. PAPAGEORGIOU. Exercises in analysis. Part 2. Nonlinear analysis. Problem Books in Mathematics. Springer, Cham, 2016.
Some handouts in Italian will be supplied by the lecturer. - Educational objectives
- On successful completion of the course, students should be able to:
- to have a critical study about esistence of solutions local or global for problems involving differential equations or differential inclusions
- to organize the presentation in autonomy;
- to think critically and express mathematical concepts precisely in writing;
- to apply the knowledge gained in this course to other situations and disciplines;
- to communicate the mathematical knowledge acquired in the course;
- to read and understand texts of Differential Equations,
- to provide themselves a mathematical proof of simple statements.
- to know how to recognize correct demonstrations and identify incorrect reasoning;
- to apply knowledge and skills acquired in Differential Equations to analyze and handle novel situations in a critical way.
The competencies are set out in my view essential to a mathematician who wants to dedicate to teaching, as well as for a mathematician who is rather interested in research. - Prerequisites
- This course assumes that the student has a good working knowledge of Mathematical Analysis topics of a Bachelor Degree in Mathematics.
- Teaching methods
- Lectures (frontal hours) - exercise sessions - office hours.
The course consists into 42 hours of theory, together with different examples and counterexamples.
The aim of course is:
- to invite students to a critical approach to the study of existence of solutions of differential equations (by using examples and counterexamples in order to compare definitions and theorems)
- to show methods in order to obtain a solution for problems involving differential equations.
- to show methods in order to obtain the existence of a fixed point for a map.
Tutorial service is given in office hours. Customized support activities. - Other information
- Lecture hall in (see: http://www.dmi.unipg.it/didattica/corsi-di-studio-in-matematica/matematica-magistrale/orario-lezioni)
Attendance of the lectures is warmly recommended.
Tutorial service is given in office hours. Customized support activities.
The teacher will distribute educational materials (in Italian) useful for a better understanding of the course, in order to help and to let the students pass easily the exam. See: https://www.unistudium.unipg.it/unistudium/login/index.php
8 exams, see: web http://www.dmi.unipg.it/files/matematica/doc-magistrale/mate_calendarioesami_lm_iisem2019-2020
Examining board: T. Cardinali, I. Benedetti (A. Boccuto, R. Filippucci, P. Pucci, P. Rubbioni, A. Sambucini, E. Vitillaro).
The aim of course is to invite students to a critical approach to the study of existence of solutions of differential equations. Some exercises show methods in order to prove the existence of solutions for problems involving differential equations.
Some texts will be supplied by the lecturer in Italian language.
There is a Web page which contains this course description as well as other information related to this course, see:
https://www.unistudium.unipg.it/unistudium/login/index.php
Advice:
Don't miss class. Ask questions. Go to office hours as often as necessary.
You need to know the terminology used throughout this course. - Learning verification modality
- Examination with oral tests with the performance of some exercises. It consists of a discussion on three topics one of which divided into several questions and takes about 30 minutes.
If the student is interested, the oral exam can be divided into two partial exams.
The final exam is the student's opportunity to demonstrate everything he/she have learned in our time together.
In the final exam it is necessary that the student will need to know all definitions, theorems, proofs, examples and counterexamples introduced in the course. Moreover, the student will need to understand them, how they work, and more importantly whether they can be used or not.
Finally, the oral examination allows the teacher to verify the performance of the student and his/her ability to organize the presentation in autonomy.
It is possible to divide the oral examination in two parts: his subdivision is personalized, to be agreed with the teacher.
In the event that it is necessary according to the University regulations, the exams and partial exams could take place on the online platform.
Students with DSA certification must submit the same at least two weeks prior to the test.
Information on support services for students with disabilities and / or DSA see: http://www.unipg.it/disabilita-e-dsa - Extended program
- Fixed point theory. Existence theorems for problems involving differential equations or differential inclusions. Selections theorems for multimaps. Hints of applications to the existence of equilibrium points for deterministic or random abstract economies Hints of problems that can be studied with differential inclusions.