This is the webpage for Part 2 (Modulo 2) of the course Mathematical Methods M, taught by Andrea Petracci during the 1st semester of the academic year 2025/26. Part 1 (Modulo 1) of this course is taught by Nicola Arcozzi.
The course is part of the Master's Degree Programs in Telecommunications Engineering and in Electronic Engineering at the University of Bologna.
The official class webpage is available here.

Notices. Andrea Petracci will not give lecture on Friday the 19th of December 2025.
The upcoming exam calls are: January 12th, January 28th, February 12th.

Contacts. If you want to contact me, please write to:
a [dot] petracci [at] unibo [dot] it
Make sure to use your institutional mail address (@studio.unibo.it), otherwise your message might end up in my spam folder.

Schedule and venues. Always refer to the official timetable available here.

Office hours. Read the bottom of my institutional page

Material. This file contains a summary of the lectures (with bibliographical references) and some suggested exercises.
A note about about linear recurrence sequences can be found here.
A note about region of convergence of power series, aboutregion of convergence of Laurent series and about the Z-transform can be found here here.
Some examples of mock exams:
Mock exam 1
Mock exam 2

Rules for participation in the exam. (All of this refers only to Part 2 taught by Andrea Petracci.) There will be six exam sessions (also called "calls" or "appelli") during the 2025/26 academic year: three calls between January and February 2026, one call in June 2026, one call in July 2026, and one call in September 2026. The exam grade is expressed as an integer between 0 and 30. The minimum passing grade is 18.
Registration for the exam: in order to participate in any exam call, registration on AlmaEsami is mandatory. Registration must be completed according to the procedures and deadlines specified on the AlmaEsami website. Students who are not properly registered on AlmaEsami will not be allowed to take the exam.
Publication of results: a few days after the written exam, the results will be published on AlmaEsami. Grades will be communicated exclusively through AlmaEsami.
Review of the written exam: after the publication of the results, students may review their written exam and discuss the grading in person. The review will take place in my office (I9) at the Department of Mathematics, Piazza di Porta San Donato 5. The date and time of the review session will be announced together with the publication of the results.
Acceptance or refusal of the grade: From the day the results are published, if your grade is at least 18, you have two working days to make a decision. Within these two working days, you must choose one and only one of the following mutually exclusive options.

• Option 1 - acceptance of the grade. You accept the grade obtained. You do not need to communicate anything to me. After two working days from the publication of the results, the grade will be automatically finalised, i.e. the grade is definitive and irreversible. After accepting the grade, you may not attend further exam sessions. After accepting the grade, you may not attempt to improve it. Accepting the grade means accepting it permanently and without any possibility of change.
• Option 2 - refusal of the grade. You do not accept the grade obtained. You must send me an email explicitly stating that you refuse the grade. This email must be sent within two working days from the publication of the results. If the grade is refused, it is permanently cancelled. A refused grade is treated as if it never existed. To pass the exam, you must take the exam again in a later call. Once the grade is refused, only future exam results will count. For example, if in a later call you obtain a lower grade, that lower grade will be valid and binding, even if it is worse than the refused one.

Rules during the exam. (All of this refers only to Part 2 taught by Andrea Petracci.)

• Time available: 120 minutes.
• Allowed materials: one single A4 sheet with handwritten personal notes, and/or a basic (and practically unnecessary) non-programmable calculator.
• Prohibited materials: any additional notes, books, graphic or programmable calculators, mobile phones, tablets, laptops, smartwatches, or any device capable of communicating with the outside world (including earbuds or headphones). Any such device, if brought to the exam, must be switched off and stored inside a closed bag or backpack placed away from the candidate's desk. Possession of any prohibited device during the exam will result in immediate expulsion from the exam and formal reporting.
• Access to the exam room requires showing a valid university ID card with photograph. The ID card must remain visible on the desk for the entire duration of the exam.
• You do not need to rewrite the text of the questions. You do not need to submit this instruction sheet.
• Scoring: The total number of points available is 35. If x is the number of points obtained, the final grade will be the minimum between x and 30.