- Docente: Domiziano Mostacci
- Credits: 6
- SSD: ING-IND/18
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Energy Engineering (cod. 5978)
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from Sep 16, 2024 to Dec 20, 2024
Learning outcomes
At the end of the course, the student has acquired competences on the mathematical tools of widest use in modeling energy systems, and more generally in treating problems in Physics. More specifically, the pupil is able to make us of: analytic functions; Fourier series; Fourier and Laplace integral transforms; PDE's. He/She will be acquainted with probability calculus: laws, random variables, main distributions and densities; including basic notions of statistics.
Course contents
Complex Analysis:
Complex numbers - their meaning and their representations; complex functions of complex variables, holomorphic and analytic functions; extension of the main real functions to the complex field (exponential, trigonometric, hyperbolic, logarithmic).
Complex integration; Cauchy formula, Cauchy theorem; series in the complex field: Taylor and Laurent series; singularities.
Residue theorem and applications to integration; integrals of multivalued functions.
Integral transforms - Fourier transforms, Laplace transforms; problem solution through transforms.
Differential equations:
Partial differential equations (PDE) - Linear, semilinear, quasilinear 1st order PDEs. Principal 2nd order PDEs: parabolic, hyperbolic, elliptic PDEs; diffusion/heat equation, wave equation; equations with the Laplace operator (Laplace, Poisson, Helmolttz equations)
Probability and statistics:
The laws of probability; Random variables and vectors; Main distributions/densities. Basics of statistics
Readings/Bibliography
Teacher's notes; G. Spiga: “Problemi matematici della fisica e dell'ingegneria”, pub. Pitagora, Bologna 1985
Teaching methods
Lectures; practical excercises.
Assessment methods
Written assignements. Oral final. The student will be required to show good understanding of the basic principles and prove capable to apply them to simple practical problems.
Teaching tools
Transparencies, projector, lecturers. Instructro's notes will be available on line (at present on http://campus.unibo.it/), and students are asdvised to print them out and bring them to class. The same material will be made available also at the copy center on the 1st floor of the Old Engineering bdg., just next to the school library.
Office hours
See the website of Domiziano Mostacci