- Docente: Alberto Parmeggiani
- Credits: 10
- SSD: MAT/05
- Language: Italian
- Moduli: Alberto Parmeggiani (Modulo 1) Loredana Lanzani (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Astronomy (cod. 8004)
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from Sep 23, 2022 to Dec 22, 2022
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from Sep 30, 2022 to Dec 23, 2022
Learning outcomes
At the end of the course the student is familiar with the fundamental notions of the differential and integral calculus for functions of several variables and with related arguments (differential equations, linear integrals, etc). Moreover the student is able to use classical tools from Mathematical Analysis in several different areas.
Course contents
Topology of R^n. Differential calculus for functions of several variables. Differentiable manifolds in R^n, constrained extrema. Differential equations and systems of differential equations. Curves in R^n, line integrals, differential forms (vector fields) closed and exact. Gauss, Green and Stokes's theorems. Multiple integrals in R^n. Fundamentals of Hilbert spaces.
Readings/Bibliography
the exposition of the arguments will follow the textbook:
-M. Bertsch - R. Dal Passo - L. Giacomelli, Analisi Matematica, McGraw-Hill.
Teaching methods
Lectures and exercices at the blackboard.
Assessment methods
The final exam consists of a written and oral exam, to be taken withing the same session. The written exam, of the duration of 3 hours, is related to the arguments developed during the course (notes are allowed, electronic devices are not allowed) the student will receive an evaluation: insufficient/sufficient/good/excellent, and a score. In case of the rating "insufficient" the student will have to repeat the written exam, in case of rating at least "sufficient", the student will be able to proceed to the oral exam.
The oral exam is aimed to verify the knowledge of the arguments explained in class during the course. The student is supposed to know all the definitions and also the proofs of some major theorems.
The final grade is based on the results obtained in both the written and the oral exams.
It is compulsory to sign up for the exam (both for the written and the oral exams) using AlmaEsami and, in case one is not able to take the exam, it is compulsory to remove one's name from the same list.
Office hours
See the website of Alberto Parmeggiani
See the website of Loredana Lanzani