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 several exercices.

Readings/Bibliography

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

- M. Bertsch - R. Dal Passo - L. Giacomelli, Analisi Matematica, McGraw-Hill (this book contains both Analysis 1 and 2, and is very well organised).

- C.D. Pagani - S. Salsa, Analisi Matematica 1, Masson, Milano

Concerning the exercises, the teacher will make available on IOL different tests of the past years, with the solutions or traces of the solutions. If desired, students can also practice the following books:

- M. Bramanti- Esercitazioni di Analisi Matematica 1, Esculapio.

- Salsa - Squellati Esercizi di Analisi matematica 1, Zanichelli

 

Teaching methods

Lectures and exercices given by the teacher. All the work done in class is immediately made available on the platform Virtuale (ex-IOL).

Assessment methods

Written test followed (if appropriate) by oral test. The written part last 3 hours if in person, less if performed online.

The written test in passed with a mark not less than 15/30.

The oral test is intended to verify the knowledge of the arguments explained in class. The student is supposed to know all the definitions and also the proofs of some major theorem.

The final mark is based on the results obtained in both the written and the oral tests.

 

Teaching tools

All the lectures given by the teacher are made available online on the platform Virtuale (ex-IOL).

Links to further information

http://www.dm.unibo.it/~tesi/

Office hours

See the website of Maria Carla Tesi

See the website of Alberto Parmeggiani