Metodi matematici 1 - 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





Educational aims

The course aims at introducing the student to the basic notions of calculus together with the basic techniques and applications.


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 set 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, semielasticity, elasticity, 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.


Prerequisites

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

Course Texts

Textbooks:
Margarita S. - Salinelli E., MultiMath-Matematica Multimediale per l’Università, Springer-Verlag Italia, 2004 (teoria ed esercizi) This book is available in the library
Modesti P. - Salinelli E. - Vignati M., Matematica generale, Esercizi e Complementi, Giappichelli, 1997 (solo esercizi) This book is available in the library
D’Ercole R., Precorso di Matematica, Pearson, 2011 (math refresher, available as
e-book on the math refresher site). This book is available in the library

Further information can be found in the web page of the course at the URL:

https://eco.dir.unipmn.it/


Teaching methods

Lectures and tutorials.


Examination

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