66877 - Calculus

Academic Year 2022/2023

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Information Science for Management (cod. 8014)

Learning outcomes

At the end of the module, the student is acquainted with the fundamental notions concerning differential and integral calculus of functions of one variable.

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. Sequences.
  • Limits. Continuous functions and their properties.
  • Differential calculus: derivatives, Taylor formula and function study.
  • Integral calculus: the fundamental theorem, primitives; integration rules.

Readings/Bibliography

  • E. Lanconelli, Lezioni di Analisi Matematica 1, Pitagora.
  • M. Bramanti, C.D. Pagani, S. Salsa, Analisi matematica 1, Zanichelli.
  • M. Bertsch, A Dall’Aglio, L. Giacomelli, Epsilon 1 Primo corso di Analisi Matematica, McGrawHill.

Teaching methods

  • Lectures.
  • Discussion of solving exercises.

Assessment methods

In order to pass the exam of the integrated course Mathematical Analysis - Linear Algebra on must pass the exam on each of the two parts; the grade of the integrated course is the mean of the grades of the two parts.

The examinations of Mathematical Analysis consists of a 2- hour written test consisting of two parts:

  • a first one will propose some exercises;
  • a second one will ask questions about the theory (definitions, theorem statements, examples, counterexamples, proofs).

The written test aims at verifying the knowledge of the theory and the ability of applying it. Justification of the steps followed in carrying out the proposed questions is required. The use of books, notes or calculators is not allowed.

The examination is passed if the grade of both parts is greater than 8/16 and if the sum of the two is greater than 18/32. The final grade is the sum of the grades in each part (with an evaluation of more than 30 is achieved cum laude).

In case the written test is passed, the student can ask to also take an elective oral test. This one has to be taken in the same exam period (winter, summer, fall) as the written part.

Teaching tools

Tutoring and office hours.

Additional materials will be available on the course Virtual page.

Office hours

See the website of Maurizio Casali