AIMS AND CONTENT

LEARNING OUTCOMES

The aim of this teaching is to introduce to the rigorous treatment of analysis while developing the methods of differential and integral calculus in the context of real functions of one real variable, with the purpose of acquiring logical rigor, attaining a good command of calculus, and knowing the main proof techniques.

AIMS AND LEARNING OUTCOMES

The expected learning outcomes are that the student knows how to handle the basic tools of analysis and calculus. It is expected that the student has understood proofs and knows how to set up and write demonstrations of simple statements.

TEACHING METHODS

Traditional: blackboard.

SYLLABUS/CONTENT

1. The  indefinite integral. Integration techniques.  Integration of elementary functions.  Integration by parts and by substitution.  Integration of rational functions. 

2. The Riemann integral. Definition and properties of the definite integral. Integrability of continuous and monotonic functions. The oriented integral. The integral mean theorem. Relations between derivation and integration: integral functions, the fundamental theorem of calculus and its consequences. Improper integrals. Convergence criteria. 

3. Series.  Geometric and telescopic series. Convergence. Series with non negative terms: comparison, root and ratio criteria; condensation, order and integral tests.  Alternating series and Leibniz' theorem.

4. Differential equations. Separation of variables. Linear first order equations Second order linear equations with constant coefficients.

RECOMMENDED READING/BIBLIOGRAPHY

A.Bacciotti, F.Ricci - Analisi Matematica I - Liguori Editore

M. Baronti, F. De Mari, R. van der Putten, I. Venturi - Calculus Problems, Springer, 2016

Further readings will be posted on the web page (AULAWEB)

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Lessons will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written test and an oral test.

Students enrolled in the course of study in Physics are not required to study the proofs of the theorems that will be the object of learning during the second semester.

Students with a certified DSA, disability or other special educational needs are advised to contact the lecturer at the beginning of the course in order to agree on teaching and examination methods that, while respecting the teaching objectives, take into account individual learning methods and provide suitable compensatory tools.

ASSESSMENT METHODS

Written tests. 

1. Two intermediate written tests will be given during the course of the year. If a student obtains an average mark greater than or equal to 18/30 and if he or she obtains at least 15/30 in both, the average of the two marks counts as the written test and takes its place.

2. A written test with a mark of 17/30 or higher gives access to the oral test.

3. If a student hands in a written test, any written tests handed in previously are deemed to have been cancelled.

The written test will include several exercises on the topics of the program to assess the student's ability to critically use the tools learnt during the course.

Oral tests. During the oral test, the committee questions the entire syllabus. In particular, knowledge of the definitions of the main concepts, and of the statements an

FURTHER INFORMATION

Teaching style: in presence.

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.