|
| Instructor:
Elisabetta Rocca Office: C4, Mathematical Department Telephone: 0382985688 E-mail: elisabetta.rocca@unipv.it Office hours: online by appointments by e-mail. Schedule: 11-13 room C7 The lessons will start on October 3rd All the informations on the course are on Kiro. Course Objectives: The course is an introduction to some basic elements of ordinary differential equations and dynamical systems. Programme: Ordinary differential equations: Basic definitions, examples and properties. First order linear equations and separation of variable method. The Cauchy problem. Existence and uniqueness: the Peano's theorem, the Cauchy-Lipschitz theorem. Linear systems, exponential matrix, higher linear orders ODEs with constant coefficients. Boundary problems. The Bernoulli and homogeneous equations. Qualitative study of solutions of Cauchy problems. Asymptotic behaviour and stability of dynamical systems. Examples. The linearization method. Suggested Reading Material: M.W. Hirsch, S. Smale. Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, 1974. C.D. Pagani, S. Salsa, Analisi Matematica, Volume 2, Zanichelli, 2006 (Italian). H. Ricardo. A modern introduction to differential equations. Elsevier. Notes of Fabio Bagagiolo on ODEs. Final Exam: The exam will be written. The students have one our time. The written exam consists of two questions. The first one is intended to verify the capability of applying formulas of resolutions of ODEs, without the need for a deep understanding. The second one of medium difficulty and more theoretical-oriented, is intended to verify comprehension of the subjects. The written exam of Advanced Mathematical Methods for Engineer is held concurrently with the written exam of Numerical Methods in Engineering Sciences, as well as the optional oral exam, and the results of both parts determine the evaluation for [510810] - ADVANCED MATHEMATICAL AND NUMERICAL METHODS FOR ENGINEERS. Oral exam is not compulsory. However, students who got an overall (Adv.Math.Meth.+Num.Meth.) positive grade in the written part (i.e., at least 18/30) might choose to take an oral exam. The oral exam covers the topics presented during the lessons of both courses: Advanced Mathematical Methods for Engineer and Numerical Methods in Engineering Sciences. The oral exam can change the grade in any direction: a poor oral part might end up in a failed exam. For students that chose the basic written exam for the part of Numerical Methods in Engineering Sciences, the maximum grade obtainable can never exceed 24/30. Some previous written exams Written tests 2022/2023: 23.07.2023 The Text Solutions 27.06.2023 The Text Solutions 24.01.2023 The Text Solutions 23.02.2023 The Text Solutions Written tests 2021/2022: 25.01.2022 The text Solutions 24.02.2022 The text Solutions 28.06.2022 The text Solutions Written tests 2020/2021: 23.02.2021 The text Solutions 26.01.2021 The text Solutions Written tests 2019/2020: The text of 24.01.2020 Written tests 2018/2019: 31.01.2019 The text Solutions 13.02.2019 The text Solutions 18.03.2019 (appello straordinario) The text Solutions 18.06.2019 The text Written tests 2017/2018: 06.02.2018 The text Solutions 20.02.2018 The text Solutions 26.06.2018 The text Solutions Written tests 2016/2017: 31.01.2017: The text Solutions 20.02.2017: The text Solutions 21.06.2017: The text Solutions Other sources Previous years exams and material
|
Elisabetta
Rocca