81853 - ANALISI MATEMATICA 1A

Learning outcomes

At the end of the course, the student will acquire the basic knowledge of mathematical analysis as a central science, useful and creative. He should master the concepts of limit, continuity, differentiability and integrability for functions of a real variables. In particular, students will be able to apply this knowledge to the solution of simple practical problems posed by the pure and applied sciences.

Course contents

Ordered set. Axiomatic notion of real numbers and n-th arithmetic roots. Exponential function in Q. Sequences of real numbers. Cauchy sequences. Exponential functions and logarithm. Complex numbers and circular functions. Limits for real functions of a real variable. Metric spaces. Continuous functions. Derivatives. Higher order derivatives. Taylor formula. Maxima and minima.

Readings/Bibliography

E. Giusti: Analisi Matematica 1, Ed. Boringhieri

E. Lanconelli: Analisi Matematica 1, Ed. Pitagora

Alternatively, the student may use also:

Mariano Giaquinta, Giuseppe Modica, Analisi Matematica 1: funzioni di una variabile, Ed. Pitagora.

Carlo Domenico Pagani, Sandro Salsa, Analisi matematica 1, Ed. Zanichelli 2015

R.Beals, Analysis: An introduction, ed. Cambridge University Press.

M.Bertsch, R. Dal Passo, Elementi di Analisi Matematica 1, Aracne ed.

In general, the student may use any good textbook of Mathematical Analysis which contains the arguments of the program. The student will check with the professors the validity of the chosen alternative textbook depending on the program.

Teaching methods

Lectures and exercises given by the teacher in the classroom using the blackboard.

Assessment methods

The exam will consist of

1) a written part organized in two steps: a basilar  theoretic part that must be successfully passed in order to be admitted to the subsequent steps. After that, there will be a second written text consisting of 3/4 exercises, that will receive 4 possible rates: poor, almost fair, fair, good, excellent. If the rate is "poor" the student must repeat the written exam. In order to sustain the written test the student must register through AlmaEsami [https://almaesami.unibo.it/] .

The written test remains valid f

2) Otherwise, he can proceed to the second part of the exam, the oral exam, within the same session. The oral test mainly concerns the theoretical aspects of the course. The student must show to know the concepts explained during the course (in particular definitions, theorems and their proofs) and how to connect with each other.

During the second written exam the student can use books or notes. Electronic devices of any kind are forbidden.

Office hours

See the website of Bruno Franchi

See the website of Alberto Parmeggiani