This module deals with some issues of Mathematical Analysis with the aim to complete the basic learning and introduce some theoretical tools used in engineering science.The main topics concern with the theory of vector fields, the Fourier's analysis and the functions of a complex variable.
The module aims to introduce the basic methods for the following topics in Mathematical Analysis: 1) Path and surface integration for vector fields, differential operators. 2) Fourier series and applications. 3) Functions of one complex variable, integration, computation of residues and applications.
This module aims to provide the student with the knowledge of the following mathematical conceps:
1) Integration of differential forms. Vector flux, divergence, curl and their properties for vector fields.
2) Orthogonal functions, Fourier series and applications.
3) Functions of one complex variable and integration on a path in the complex plane. Computation of residues, Fourier and Laplace transforms and applications.
The main learning outcomes consist of technical skills about the following issues:
Evaluation of maxima and minima under constrains. Integration of differential forms. Vector calculus and use of differential operators. Fourier series expansions and applications to differential equations. Integration on the complex plane and evaluation of residues. Applications of Fourier and Laplace transforms.
Basic knowledge on linear algebra and differential calculus are required as prerequisites. In particular, the student must be familiar with the analysis of functions of one and more variables, series of functions, and ordinary differential equations.
Lectures on the theoretical contents, examples and exercises.
First part: Maxima and minima with constraints. Vector analysis: Differential forms and path integrals, vector fields, circulation, flux, divergence and Stokes theorems.
Second part: Fourier series and applications
Third part: Functions of a complex variable. Analytic functions and McLaurin series. Residue theorem and application to improper integrals. Fourier Transform and applications. Laplace transform.
Ricevimento: By appointment
MAURIZIO ROMEO (President)
CLAUDIO ESTATICO
ANGELO MORRO
September, 17, 2018
A written test on tecnical skills (the required result must be greater or equal to 18/30). This is a prerequisite for an oral exam concerning theoretical issues.
The written test is intended to verify technical skills about the following points: 1) Computation of maxima and minima with constraint, 2) Computation of field lines or potentials for vector fields, 3) Fourier series expansion of a periodic function and its application to numeric series, 4) Evaluation of improper integrals by residues or derivation of Laplace transforms
The objective of the spoken exam is to verify the student's knowledge about theoretical concepts. The student is required to state and prove theorems, showing to be aware of formulas and notations adopted.
