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) The book is available in the library
Modesti P. - Salinelli E. - Vignati M., Matematica generale, Esercizi e Complementi, Giappichelli, 1997 (solo esercizi) The 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).
Further informations can be found in the web page of the course at the URL:
https://eco.dir.unipmn.it/
Teaching methods
Lessons and exercises.
Examination
A compulsory written exam with exercises and theoretic questions, and an optional oral exam.