AIMS AND CONTENT

LEARNING OUTCOMES

This course completes the basic concepts of mathematics and consists of three main parts. Analysis of functions of several variables: line integrals, differentiation of function of several variables, Taylor's formula, multiple integration, surface integrals. Functions of a complex variable: derivative, Cauchy-Riemann conditions and Cauchy's theorem, fundamental theorem of algebra, residues and application to integrals. Fourier series: function series, Riemann-Lebesgue lemma, Fourier's theorem (sine-cosine form), complex Fourier series.

AIMS AND LEARNING OUTCOMES

The aims and the learning outcomes deal with both the mathematical developments (definitions, consequences, applications) and the usage of the known mathematical tools for the solution of practical problems. The exam consists of both written and oral parts. 

TEACHING METHODS

The lectures are given by writing directly on the blackboard and deriving step-by-step the mathematical developments. The lectures give both theoretical developments and applications.

Students who hold valid certificates relating to Specific Learning Difficulties (SLD), disabilities or other educational needs are invited to contact the lecturer and the school’s disability liaison officer at the start of the course to agree on any teaching arrangements which, whilst respecting the course objectives, take into account individual learning styles.

The contact details for the university’s disability liaison officer are available at the following link: https://unige.it/commissioni/comitatoperlinclusionedeglistudenticondisabilita.

SYLLABUS/CONTENT

The course consists of three parts. Functions of several real variables: continuity, differentiability, Taylor's formula, Gauss-Green formulae, multiple integrals, line integrals, surface integrals. Functions of a complex variable: differentiability, Cauchy-Riemann conditions, integration, Cauchy's theorem, fundamental theorem of algebra, residues. Fourier series: series of  functions, Riemann-Lebesgue lemma, Fourier theorem, sine-cosine and complex forms.  

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes on the whole content of the course are provided.  

TEACHERS AND EXAM BOARD

Exam Board

MAURO GAGGERO (President)

ROBERTUS VAN DER PUTTEN

ANGELO MORRO (President Substitute)

LESSONS

LESSONS START

https://easyacademy.unige.it/portalestudenti/index.php?view=easycourse&_lang=it&include=corso

Class schedule

The timetable for this course is available here: Portale EasyAcademy

FURTHER INFORMATION

Students with valid certifications for Specific Learning Disorders (SLD) may request accommodations for exams at least 7 days prior to the exam date by filling out the “accommodation request form” (available via online services at https://modulionline.unige.it/richiesta-adattamenti# no-back), which will be automatically forwarded by the system to the instructor in charge of the course and to the faculty liaison for students with disabilities and SLDs in their School/Department.

The student will receive a copy of their request.