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.

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.  

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy