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81854 - Mathematical Analysis 1B

Academic Year 2022/2023

                
                        Docente:
                        Giovanni Cupini
                    
                        Credits:
                        7
                    
                        SSD:
                        MAT/05
                    
                        Language:
                        Italian
                    
                        Moduli:
                        
                            Giovanni Cupini
                            (Modulo 1)
                        
                            Giovanni Dore
                            (Modulo 2)
                        
                        Teaching Mode:
                        
                                    Traditional lectures (Modulo 1)
                                
                                    Traditional lectures (Modulo 2)
                                
                            Campus:
                            Bologna
                        
                            Corso:
                            First cycle degree programme (L) in
                            Mathematics (cod. 8010)

                            Teaching resources on Virtuale

Learning outcomes

At the end of the course, the student deepens the basic knowledge of mathematical analysis, identifying it as a unique and creative central science. He has knowledge of the concept of integral and generalized integral of real functions of a real variable and of a number series. It is able to study real functions of a real variable. In particular, the student knows how to apply this knowledge to the solution of simple practical problems, posed by pure and applied sciences.

Course contents

Local extrema.

Convex functions. Convexity criterion. Graphing functions of one real variable.

Riemann integral for functions of one real variable. Fundamental theorems of integral calculus. Antiderivatives. Application of integral calculus: first order linear differential equations.

Improper integrals. Numerical series.

Metric spaces. The n-dimensional Euclidean real space.

Readings/Bibliography

Some teaching material will be uploaded on the web site "Virtuale" [https://virtuale.unibo.it/]

To study in depth the topics of the course, students can consult the following books.

Theory:

E. Lanconelli, Lezioni di Analisi Matematica 1, ed. Pitagora

P. Marcellini - C. Sbordone: Analisi Matematica 1, ed. Liguori

E. Giusti, Analisi Matematica 1, ed. Boringhieri

Exercises:

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

P. Marcellini - C. Sbordone: Esercitazioni di Matematica, volume 1, parte seconda, ed. Liguori

E. Giusti, Esercizi e complementi di Analisi Matematica, volume 1, ed. Boringhieri

Teaching methods

Lessons and exercises in the classroom.

Assessment methods

The examination consists of a preliminary written test and an oral one.

The written test consists of five exercises related to the arguments of the course in 2 hours and 30'. In order to participate to the written test the student must register at least four days before the test through AlmaEsami [https://almaesami.unibo.it/]. The written test is passed with a minimum score of 15 out of 30.

The written test remains valid for the oral exam in the same examination period.

The test about the theory follows the written test; it 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 them.

Office hours

See the website of Giovanni Cupini

See the website of Giovanni Dore