ID:
500541
Duration (hours):
60
CFU:
6
SSD:
ANALISI MATEMATICA
Year:
2025
Overview
Date/time interval
Primo Semestre (29/09/2025 - 16/01/2026)
Syllabus
Course Objectives
Learn how to work in the complex framework, evaluate integrals of holomorphic functions, manipulate power and Fourier series, adopt the point of view of signal theory, calculate and operate with Fourier, Laplace and Zeta transforms, solve simple ordinary differential equations with constant coefficients, understand convolutions.
Course Prerequisites
Differential and integral calculus for scalar and vector functions, matrices and linear transformations, sequences and series, power series in the real line, complex numbers, polar coordinates.
Teaching Methods
The course is divided into lessons (on the blackboard, integrated with transparencies), exercises on the blackboard and laboratory activities. During the lessons, the main results, their scope of validity, their mutual relationships, and the most relevant applications are presented and discussed. Exercise hours are aimed at acquiring the main calculation techniques and the most elaborate strategies for solving problems, in the context of the theoretical results already acquired. Part of the exercises is also aimed at solving the exam topics from previous years.
Assessment Methods
The exam consists of a written test. The written test is divided into two parts. The first part consists in solving five problems, in which it is necessary to apply an articulated solution strategy, in any case discussed during the exercise hours. The second part is of a more theoretical nature and concerns the knowledge of the main results presented in class and the understanding of the relationships between them. This second part consists of five problems as well. The overall grade is the average of the grades obtained in the individual parts; written tests in which each part has achieved a rating of less than 16 points are not considered acceptable. If a student who passes the written exam wishes to improve her/his overall grade, she/he may take an oral exam.
Texts
G.C. Barozzi, Matematica per l'Ingegneria dell'informazione. Zanichelli 2004. F. Bagarello, Metodi matematici per fisici e ingegneri. Zanichelli 2019. M. Codegone, L. Lussardi. Metodi Matematici per l'Ingegneria. Zanichelli 2021. M. Giaquinta, G. Modica. Note di Metodi Matematici per Ingegneria Informatica. Pitagora, Bologna. F. Tomarelli - Esercizi di Metodi Matematici per l'Ingegneria - CLU.
Contents
Complex functions Manipulation of complex numbers Rational, exponential, and trigonometric functions, logarithms Power series Conplex derivatives, olomorphic functions, Cauchy-Riemann conditions Line integrals, Cauchy theorem, , analyticity of olomorphic functions Singularities, Laurent series, residue formula Evaluation of integrals, Jordan lemma The language of signals Continuous and discrete signals. Basic operations on signals: sum and linear combinations of signals, traslation and rescalings. Scalar products and norms. Z trasform Definition and simple examples Simple applications to difference equations Fourier series Periodic signals, trigonometric and exponential functions, Fourier series. Pointwise and energy convergence, Gibbs phenomenon. Parseval identity Applications Fourier Transform Definition of Fourier transform, relationships with Fourier series, elementary properties Riemann-Lebesgue lemma Inversion theorem for piecewise regular functions Plancherel identity, Fourier transform for L^2 functions Laplace transform Definition, links with the Fourier transform, main properties Inversion of Laplace transform, residue and Heaviside formula Application to simple ordinary differential equations Convolution Definition and simple example of convolutions Links with Fourier and Laplace transform Simple applications to differential and integro-differential equations
Course Language
Italian
More information
Students in the categories identified by the project on innovative teaching will have the opportunity to hold receptions even at special times.
Degrees
Degrees
ELECTRONIC AND COMPUTER ENGINEERING
Bachelor’s Degree
3 years
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