Foundations of mathematics

Course objectives

General objectives. Learning the basic notions of differential and integral calculus. Specific objectives. Knowledge and understanding: Learn the theory and the tools of the mathematical analysis of real functions of one variable. In particular, the concepts of limits, convergence, and differential and integral calculus. Applying Knowledge and understanding: To be able to solve classical problems in analysis, such as, making a qualitative plot of the graph of a function, finding maxima and minima of a function in one variable, computing the area under the graph of a function via the solution of definite integrals, solving simple ordinary differential equations. Making judgments: To be able to carry out a mathematical deduction and to write it in the form of a proof. Communication skills: To be able to appropriately use the mathematical language and the related notions, as well as to autonomously develop and express a mathematical reasoning. Learning skills: Learning the method for approaching a scientific topic, recognizing the critical aspects and trying to give an appropriate explanation in an autonomous manner as well as in collaboration with the professor and other students.

Channel 1
SAVERIO SALZO Lecturers' profile

Program - Frequency - Exams

Course program
Logic. Theorems and proofs. -The real numbers, bounded sets, sup, inf, completeness. -The complex numbers. -Real functions of one real variable. Standard functions (affine, quadratic, powers, exponentials, logarithmic, trigonometric): definition, properties and graph. -Limits of sequences and functions -Derivatives and the Taylor polynomial -Integrals -Series of numbers -Ordinary differential equations
Prerequisites
Basic set theory and algebra. First and second degree equations and inequalities. Rational equations and inequalities. Linear, quadratic, exponential, logarithmic, trigonometric, root functions, and equations and inequalities involving them.
Books
BERTSCH M.; DALL'AGLIO A.; GIACOMELLI L. . EPSILON 1. PRIMO CORSO DI ANALISI MATEMATICA. Mc Graw Hill Bramanti, Pagani, Salsa. Analisi Matematica 1. Mc Graw Hill Bertsch, Dal Passo, Giacomelli. Analisi matematica. Mc Graw Hill
Frequency
Mandatory course but presence is not registered.
Exam mode
The following aspects will be considered towards the final evaluation of the written exam: (1) the logic followed by the student for the solution of the problems; (2) the correctness and the soundness of the solutions of the problems; (3) how compatible are the solutions to the problems of the exams in accordance to the knowledge and the ability the student has received along all the lectures. (4) the ability to write correctly in Italian (or English if the exam is in English) A further oral exam is not mandatory and it is at teacher discretion or in some specific cases. The evaluation of the oral exam will consider the following aspects: (1) the ability to elaborate a correct and clear answer to the questions raised and (2) the readiness of the student in answering the questions (3) How the student is able to infer genuine new knowledge from the topics covered during the lectures.
Lesson mode
Theory and practice classroom
SAVERIO SALZO Lecturers' profile
Channel 2
NICOLA GALESI Lecturers' profile

Program - Frequency - Exams

Course program
Logic. Theorems and proofs. -The real numbers, bounded sets, sup, inf, completeness. -The complex numbers. -Real functions of one real variable. Standard functions (affine, quadratic, powers, exponentials, logarithmic, trigonometric): definition, properties and graph. -Limits of sequences and functions -Derivatives and the Taylor polynomial -Integrals -Series of numbers -Ordinary differential equations
Prerequisites
Basic set theory and algebra. First and second degree equations and inequalities. Rational equations and inequalities. Linear, quadratic, exponential, logarithmic, trigonometric, root functions, and equations and inequalities involving them.
Books
BERTSCH M.; DALL'AGLIO A.; GIACOMELLI L. . EPSILON 1. PRIMO CORSO DI ANALISI MATEMATICA. Mc Graw Hill Bramanti, Pagani, Salsa. Analisi Matematica 1. Mc Graw Hill Bertsch, Dal Passo, Giacomelli. Analisi matematica. Mc Graw Hill
Frequency
Mandatory course but presence is not registered.
Exam mode
The following aspects will be considered towards the final evaluation of the written exam: (1) the logic followed by the student for the solution of the problems; (2) the correctness and the soundness of the solutions of the problems; (3) how compatible are the solutions to the problems of the exams in accordance to the knowledge and the ability the student has received along all the lectures. (4) the ability to write correctly in Italian (or English if the exam is in English) A further oral exam is not mandatory and it is at teacher discretion or in some specific cases. The evaluation of the oral exam will consider the following aspects: (1) the ability to elaborate a correct and clear answer to the questions raised and (2) the readiness of the student in answering the questions (3) How the student is able to infer genuine new knowledge from the topics covered during the lectures.
Lesson mode
Theory and practice classroom
NICOLA GALESI Lecturers' profile

Program - Frequency - Exams

Course program
Logic. Theorems and proofs. -The real numbers, bounded sets, sup, inf, completeness. -The complex numbers. -Real functions of one real variable. Standard functions (affine, quadratic, powers, exponentials, logarithmic, trigonometric): definition, properties and graph. -Limits of sequences and functions -Derivatives and the Taylor polynomial -Integrals -Series of numbers -Ordinary differential equations
Prerequisites
Basic set theory and algebra. First and second degree equations and inequalities. Rational equations and inequalities. Linear, quadratic, exponential, logarithmic, trigonometric, root functions, and equations and inequalities involving them.
Books
BERTSCH M.; DALL'AGLIO A.; GIACOMELLI L. . EPSILON 1. PRIMO CORSO DI ANALISI MATEMATICA. Mc Graw Hill Bramanti, Pagani, Salsa. Analisi Matematica 1. Mc Graw Hill Bertsch, Dal Passo, Giacomelli. Analisi matematica. Mc Graw Hill
Frequency
Mandatory course but presence is not registered.
Exam mode
The following aspects will be considered towards the final evaluation of the written exam: (1) the logic followed by the student for the solution of the problems; (2) the correctness and the soundness of the solutions of the problems; (3) how compatible are the solutions to the problems of the exams in accordance to the knowledge and the ability the student has received along all the lectures. (4) the ability to write correctly in Italian (or English if the exam is in English) A further oral exam is not mandatory and it is at teacher discretion or in some specific cases. The evaluation of the oral exam will consider the following aspects: (1) the ability to elaborate a correct and clear answer to the questions raised and (2) the readiness of the student in answering the questions (3) How the student is able to infer genuine new knowledge from the topics covered during the lectures.
Lesson mode
Theory and practice classroom
  • Lesson code10606834
  • Academic year2024/2025
  • CourseComputer and System Engineering
  • CurriculumInformatica
  • Year1st year
  • Semester1st semester
  • SSDMAT/09
  • CFU9
  • Subject areaMatematica, informatica e statistica