27210 - Mathematical Analysis 1

Learning outcomes

At the end of the course the student acquires the fundamental notions of differential and integral calculus for functions of one variable, and related topics. The student is able to manage classical instruments of Mathematical Analysis useful for related disciplines, such as physics and astronomy.

Course contents

Real and complex numbers. Metric spaces (basic theory): continuity. Elementary functions. Differential and integral calculus for real functions of one variable. Sequences and series. Taylor's series. Forier's series (basic theory). During the course we will solve a number of exercices.

Readings/Bibliography

The notes of Prof Venni, to which the course is largely inspired, will be made available on the platform Virtuale (ex-IOL), as a pdf file. These notes are sufficient for the preparation of the exam.

However, the exposition of the arguments will follow the textbook:

-M. Bertsch - R. Dal Passo - L. Giacomelli, Analisi Matematica, McGraw-Hill.

Remark: this textbook contains both Analysis 1 and 2, and will be the reference textbook for Analysis 2. However, students may use any good Analysis textbook, which contains the arguments of the course (which are standard).

As regards the exercises, some past exams will be made available on IOL. However, students are eoncuraged to use any exercise textbook that deals with the arguments in the program.

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 Maria Carla Tesi