27210 - Mathematical Analysis 1

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 instruments from Mathematical Analysis in several different areas.

Course contents

Real and complex numbers. The topology of the real line. Limits: of a sequence, of a function. Continuous functions and properties of continuous functions. Differential and integral calculus for real functions of one variable. Taylor polynomial. Generalized integral. Series (in R or C, of functions).

During the course we will solve several exercises.

Readings/Bibliography

The exposition will be following 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 thirtieths) ranging up to 24/30. 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. It consists of three questions. After the oral exam, the student will receive a score (greater than or equal to zero) up to 6/30.

The final grade is based on the results obtained in both the written and the oral exams and it is the sum of the two scores. The "laude" is obtained if the grade 30/30 is reached and an exact answer is given to a final question.

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.

The final grade may be rejected only once.

Students with learning disabilities or temporary or permanent disabilities: please contact the relevant University office promptly (https://site.unibo.it/studenti-con-disabilita-e-dsa/it ). The office will advise students of possible adjustments, that will be submitted to the professor for approval 15 days in advance. He/she will evaluate their suitability also in relation to the academic objectives of the course.

Office hours

See the website of Alberto Parmeggiani

See the website of Loredana Lanzani