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## MATHEMATICAL METHODS FOR THE ENGINEER

CODE 104742 2023/2024 6 cfu during the 2nd year of 8713 INGEGNERIA BIOMEDICA (L-8) - GENOVA 6 cfu during the 2nd year of 8719 INGEGNERIA INFORMATICA (L-8) - GENOVA 6 cfu during the 2nd year of 9273 INGEGNERIA ELETTRONICA E TECNOLOGIE DELL'INFORMAZIONE(L-8) - GENOVA MAT/07 Italian GENOVA 1° Semester This unit is a module of: AULAWEB

## AIMS AND CONTENT

### LEARNING OUTCOMES

The purpose is to acquire the knowledge of concepts and methods of calculus concerning functions of several variables, Fourier series, and functions of a complex variable.

### AIMS AND LEARNING OUTCOMES

Consistent with the lectures given by the teacher, the student is required to apprehend the concepts, mainly through the definitions and proofs of theorems. In addition the student has to manage the methods of calculus associated with the subjects developed in the course. The subjects involve: 1) differential and integral calculus for functions of several variables, line integrals and surface integrals. 2) Fourier series; proof and historical origin; calculus of Fourier coefficients of given functions. 3) functions of a complex variable; differentiable functions; Cauchy's integral formula, the fundamental theorem of algebra, residues, calcolus and applications.

Transverse competences on the learning method.

### TEACHING METHODS

The lectures are developed on the blackboard by the teacher; particular emphasis is given to the presentation of concepts, the mathematical developments, and the applications.

Working students or students who have special needs are advised to contact the teacher, at the beginning of the course, so as to establish methodologies consistent with the individual learning methods.

It is developed the skill on how to learn learning.

### SYLLABUS/CONTENT

Line integrals, surface integrals, multiple integrals. Differentiation of functions of several variables and of composite functions. Differential operators. Fourier series: Fourier theorem, calculus of Fourier coefficientsof a given function, series for functions with a generic period, historical origin (heat equation) and method of separation of variables. Differential calculus for functions of a complex variable: Cauchy-Riemann conditions, Cauchy theorem, fundamental theorem of algebra, residues and applications to the computation of integrals of functions of a real variable.

Lecture notes provided by the teacher.

## LESSONS

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

The exam consists of questions and answers in oral form. Students with learning disorders will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate, of the Engineering courses, in the committee for the Inclusion of Students with Disabilities.

The final vote is the average of the single votes obtained in the two moduli.

### ASSESSMENT METHODS

The assessment is based on the comprehension of concepts, technical skill in mathematical developments, and skill in solving appropriate exercises.

The final vote is the average of the single votes obtained in the two moduli.

### Exam schedule

Date Time Location Type Notes