34605 - Mathematical Methods for Energetics (Graduate Course)

Learning outcomes

The class is to give the essentials on the mathematical method of widest use in modeling energy systems: analytic functions; main integral transforms (Fourier, Laplace); PDE's; probability and 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