78139 - 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

The teaching course is divided into two modules:

- MODULE concerning some METHODS OF MATHEMATICAL ANALYSIS:

Main topics:

- Metric and Hilbert spaces. The L^2 space (outline).

- Elements of holomorphic functions (Cauchy theorems and Residue Calculus).

- Fourier series (convergence theorems: L^2 and pointwise).

- Laplace transform (application to linear EDO resolution).

- Fourier transform in L^1 (and an introduction to the L^2 case).

- (ONLY if time remains): Hints on the method of characteristics for linear first-order PDE's.

- MODULE concerning the CALCULUS of PROBABILITY:

- Introduction to probability theory. Elements of combinatorics. Events and probability space. Definition, axioms and basic properties of probability. Conditional probability. Bayes law, chain rule for events. Independent events.

- Random variables. Partition and distribution functions. Moments of distributions. Expectation and variance. Special distributions. Joint and marginal distributions. Independent random variables. Dependence and conditional distributions. Chain rule for random variables.

- Law of large numbers and central limit theorem. 

Readings/Bibliography

- MODULE on Complex Analysis and Transforms:

G.C. Barozzi, Matematica per l'informazione, Zanichelli

For the exercises - IMPORTANT:
See the pdf files published on the website IOL (Insegnamenti online); if the student carefully solves these exercises, he/she will not need further texts.

- MODULE concerning the CALCULUS of PROBABILITY:

1) https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf

2) Schwarzlander, H., Probability concepts and theory for engineers, John Wiley & Sons, 2011. ISBN 978-0-470-74855-8

Further most specific material (possibly: slides of the lessons, examples and exercises) will also be provided by the teacher through the shared digital area at IOL - Insegnamenti online.

Teaching methods

Both modules involve theoretical lessons, accompanied by the solution of exercises designed to help the student to become familiar with the mathematical tools introduced during the lessons.

Assessment methods

At the end of the course ONLY the written test is scheduled.

During each of the six written exams, the student can take (at his own choice) the written test of one or both modules. An hour and a half is provided for each module. The final grade will be the sum of the scores obtained on the two modules (expressed in the maximum score of 16, per module). Once the sufficiency is obtained on both modules, the student can register his/her grade on his/her electronic career. A sufficient grade on the single module remains valid during the six written exams.

Number of exams: Three exams in the winter session (January-February). Three exams in the summer session (one in June; one in July; one in September).

Exam registration: The student must register for the written exam through the "Alma Esami" website. Those who do not enroll in the written tests CANNOT take the exam. Attention: the registration form usually closes several days before the test!

Teaching tools

Sheets of exercises will pe published on the IOL website, for each module.

Office hours

See the website of Andrea Bonfiglioli

See the website of Claudio Giorgi