This is a full year course. Between the first and the second semester there will be a break, during which no lectures will be delivered. The first semester will be devoted to limits and differential calculus for functions of one real variable, while in the second semester integral calculus in one variable, functions of two variables and an introduction to differential equations will be dealt with.
The main objective is to supply the fundamentals of differential and integral calculus in one variable, differential equations and functions of several variables.
The main objective is to supply the fundamentals of differential and integral calculus in one variable, differential equations and functions of several variables. In particular, students are expected to develop the following skills: operations on limits and derivatives, study of functions of one variable, integral calculus, elementary study of level curves of functions of two varlables, resolution of simple differential equations of first order, resolution of linear differential equations of order n with constant coefficients.
Lectures (120 hours)
Real numbers, cartesian coordinates in a plane, functions of one real variable, monotonic functions, composition and invertibility of functions, elementary functions, supremum and infimum, limits of functions, limits of sequences, infinitesimal and infinite functions, continuous functions and their properties, derivatives, derivation rules, derivatives of elementary functions, sign of derivatives in the study of monotonicity and convexity, theorems of Fermat, Rolle, Lagrange, de l'Hospital, Taylor expansions and applications to critical points, definite and indefinite integrals, fundamental theorem of integral calculus, integral functions, improper integrals, real functions of two variables (domain, limits at a point and at infinity, continuity, partial and directional derivatives, differentiability and tangent plane, maxima and minima), linear first order differential equations with continuous coefficients, linear differential equations of order n with constant coefficients, separation of variables.
M. Bramanti, C. Pagani, S. Salsa: Analisi Matematica 1, Zanichelli (2008);
T. Zolezzi: Dispense di Analisi Matematica I, edizioni ERSU (anni 90);
P. Marcellini, C. Sbordone: Esercitazioni di matematica, Liguori (1988);
F. Buzzetti, E. Grassini Raffaglio, A. Vasconi: Esercizi di analisi matematica, Masson (1989);
M. Bertsch, R. Dal Passo: Elementi di analisi matematica, Aracne (2000).
M. Baronti, F. De Mari, R. Van der Putten, I. Venturi: Calculus problems, Springer (2016).
Ricevimento: At the end of lectures or by appointment. Students are suggested to enroll in AulaWeb, in order to be able to get information and news by the teachers about the course.
LAURA BURLANDO (President)
MAURIZIO CHICCO (President)
MARCO BARONTI
September 18, 2017
MATHEMATICAL ANALYSIS I
The exam consists of a written and an oral test. Furthermore, during the year, there will be two written tests. The students that will pass them, will be enabled to access directly the oral exam.
The written test is based on the resolution of problems similar to those carried out during the course. In such a test is proven the ability to perform problems relating to one variable or n variable functions, ordinary differential equations and integrals. In the oral exam is assessed the understanding of the concepts and reasoning skills acquired by the students.
Once the course has started, office hours for students will be decided for the period of lectures. Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teachers about the course.
