35143 - Mathematical Methods for Engineering

Learning outcomes

The student acquires competences in advanced mathematical methods and tools, with applications to aerospace and mechanical engineering.

Course contents

Some hints on integration theory.

Complex analisys: introduction to holomorpphic function theory. Cauchy-Riemann conditions, null integral theorem, Cauchy integral formula, power serie, analytic functions. Zeros of analitic functions. Analytic extension. Tecnical lemmas. Laurent serie and classification of singularities.

Normed spaces. Hilbert spaces. Fourier series and applications.    Fourier transform: algebraic and differential property. Relationship with the convolution.

 Calculus of probability: combinatorics and discrete probability. Bayes law and conditional probability. Independent events.

Discrete and continuous random variable: expectancy, variance and covariance. Independent random variables. Some important discrete distributions: Bernoulli, Binomial, Geometrical, Poisson.

Some important real random variables: uniform,
Exponential, Normal. Hints on law of big numbers

Readings/Bibliography

Notes by the teachers. The notes will be made available to the students via the   institutional site.

Teaching methods

Lectures and public discussion of the exercises.

Assessment methods

Written test with exercises and oral test about theory.

The dates of the exams can be consulted on the AlmaEsami web platform of the University of Bologna.

Clarifications on the recording of the exam grade for those who have the  course MATHEMATICAL METHODS FOR ENGINEERING (6 CFU) as a module of the integrated course of NUMERICAL AND MATHEMATICAL METHODS FOR ENGINEERING (12 CFU)

If the MATHEMATICAL METHODS FOR ENGINEERING course (6 CFU) is one of the two modules that, together with NUMERICAL ANALYSIS (6 CFU), constitutes the integrated course of NUMERICAL AND MATHEMATICAL METHODS FOR ENGINEERING (12 CFU), the grade that will be recorded will be calculated with the arithmetic average of the single grades that the student has obtained in the two modules. It should be noted that the result of the average will be rounded to the nearest integer. Only if the resulting average is exactly equidistant between two integers, the grade will be obtained by rounding up to the next highest integer. Lastly, in order to obtain the "30 cum laude" final evaluation, the student must be in one of the two following cases:

- receiving "30 cum laude" in both modules;

- obtaining "30 cum laude" in one module and 30 in the other one.

Teaching tools

pdf files uploaded in the  institutional site, including notes and recording of the lessons

Links to further information

https://virtuale.unibo.it/course/view.php?id=19461

Office hours

See the website of Matteo Franca