16953 - Mathematics 1

Learning outcomes

At the end of the course, the student possesses basic knowledge of complex numbers, differential and integral calculus for functions of a real variable, and real and complex linear algebra of finite-dimensional spaces.

Course contents

• Outlines of set theory and basic logic
• Sets of numbers: natural, integer, rational and real numbers, topology of R
• Functions of one real variable: operations, properties, elementary functions
• Limits. Continuous functions and their properties.
• Differential calculus: derivatives, Taylor formula and function study
• Integral calculus: the fundamental theorem, primitives; integration by substitution, by parts
• Improper integrals: definition and possible behaviors
  

Readings/Bibliography

• Marco Bramanti Carlo Domenico Pagani Sandro Salsa
  Analisi matematica 1 (2014)
  con elementi di geometria e algebra lineare

• Sandro Salsa Annamaria Squellati
  Esercizi di Analisi matematica 1
  Seconda edizione (2023)

Teaching methods

• Lectures

Assessment methods

In order to pass the exam of the integrated course Calculus - Linear Algebra one needs to pass the exam on each of the two parts; the grade of the integrated course is the average of the grades of the two parts.

The two modules are "independed" so one can take the two exams in any order.

The assessment for Calculus consists of a written exam of 2 hours related to the topics developed during the course. Notes are not allowed, electronic devices are not allowed with the exception of a scientific calculator.

It is compulsory to sign up for the exam using AlmaEsami and, in case one is not able to take the exam, it is compulsory to remove one's name from the same list.

Students with SLDs or temporary or permanent disabilities: it is recommended that they contact the relevant University office in good time (https://site.unibo.it/studenti-con-disabilita-e-dsa/it ). The office will propose any possible accommodations to the students concerned; these must in any case be submitted, at least 15 days in advance, to the approval of the course instructor, who will assess their appropriateness also in relation to the learning objectives of the course.

As regards assessment of learning, the use of AI is prohibited. Any use constitutes a violation of academic integrity.

Teaching tools

Additional material (exercises, notes) will be available on the course "Virtuale" page.

Office hours

See the website of Laura Galli

See the website of Stefano Francaviglia