Course Details
Name:
Analisi Matematica C / Mathematical Analysis C
Basic information
Credits:
Bachelor Degree in Mathematics: 6 Ects (b)
Degree(s):
Compulsory 2^{nd} year Bachelor Degree in Mathematics curriculum Generale
Language:
Italian
Course Objectives
The goal of this course is to provide a knowledge of series of functions (in particular power series and Fourier series), the theory of ordinary differential equations and the theory of Lebesgue measure in R^n.
The student will also gain the ability of solving non trivial problems and exercises by applying
the techniques learned. The main concepts will be illustrated, if possible, introducing links with
the applications in physics and other sciences, and providing some background on the main
historical references.
Course Content
 Series of functions: pointwise and uniform convergence.
Continuity, differentiation and integration of series.
Power series. Taylor series.
 Fourier series: Bessel inequality, pointwise and uniform convergence, integration term by term.
 Ordinary differential equations: uniqueness, local existence and extension of the solution of the Cauchy problem. Qualitative behaviour of the solutions of Cauchy problems and exact solution of some differential equations.
Linear first order systems and linear equation of order n .
. Autonmous systems: stability of the critical points, Liapunov method and linearization method.
 Lebesgue measure in R^n: measure of open and close sets, outer and inner measure, Lebesguemeasurable sets. Properties of the Lebesgue measure and comparison with PeanoJordan one.
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should

have deep knowledge of basic properties of differential and integral calculus for vector valued functions.

have knowledge and understanding of differential calculus and ordinary differential equations theory

understand and explain the meaning of complex statements using mathematical notation and language;

understand differential and integral calculus for functions of several variables and of the theory of ordinary differential equations and their connections and
be aware of potential applications in other fields.

demonstrate skill in mathematical reasoning and ability to conceive a proofs.

demonstrate capacity for reading and understand other texts on related topics.
Prerequisites and Learning Activities
The student must know the basic notions of numerical sequences and series, functions of one and several
variables and linear algebra contained in the courses of Mathematical Analysis A, Mathematical Analysis B , Geometry A
and Geometry A.
Teaching Methods
Language: Italian
Lectures and exercise sessions.
Assessment Methods and Criteria
Written and Oral exam.
Textbooks
 C. D. Pagani, S. Salsa, Analisi Matematica. Zanichelli. (vol. 2)
Course page updates
This course page is available (with possible updates) also for the following academic years:
Course information last updated on: 27 luglio 2019, 12:55