Metodi matematici I A e B - eng

MATHEMATICS 1

Course A – Prof. Ernesto Salinelli
Course B – Prof. Francesca Centrone

Course Code: E0252
Subject code: SECS-S/06
8 ECTS – 64 hours
Location: Novara



Language: Italian
Brief description:
Numerical sets. Real functions of one real variable: definition and properties, operations, differential calculus, antiderivatives and their applications.

Course Texts:
•    Margarita S. - Salinelli E., MultiMath-Matematica Multimediale per l’Università, Springer-Verlag Italia, 2004 (theory and exercises)
•    Salinelli E., Esercizi svolti di Matematica, Giappichelli, 2015 (exercises)
•    D’Ercole R., Precorso di Matematica, Pearson, 2011 (math refresher, available as e-book on the math refresher platform)

Educational aims
The course aims at introducing the student to the basic notions of calculus useful for the applications in business and economics.

Prerequisites
Elementary set theory, numerical sets, equations and inequalities, analytic geometry.

Teaching methods
Lectures and tutorials.

Other information
An online math platform is available for the refresh of the prerequisites.
On the web page of the course at the URL: https://eco.dir.unipmn.it/ any useful information on the course and supplementary didactic resources can be found.

Examination
A compulsory written exam with exercises and theoretic questions, and an optional oral exam.

Content of the Course:
Quick refresh of the prerequisites.
The set of the real numbers, the real line, intervals. Introduction to the topology of the real line.
Ordered sets on the real line, g.l.b., l.u.b., maximum and minimum of a set.
Real functions of one real variable: definition, elementary functions, operations among functions, injective, surjective and bijective functions, invertibility, monotonicity, concavity and convexity, extrema of a function.
Limits and continuity: definitions and basic theorems.
Differential calculus in one variable. Definitions: difference quotient, derivative, tangent line. Derivatives of elementary functions, differentiation rules. Higher-order derivatives.
Some theorems of differential calculus. Applications of differential calculus to computation of limits, monotonicity and convexity study, and determination of extrema.
Introduction to the antiderivatives and their applications: definition, elementary integrals, linearity of integration, integration by parts. Application to the computation of definite integrals.