Course Details for A.Y. 2014/2015
Name:
Analisi Matematica III / Mathematical Analysis III
Basic information
Credits:
: Bachelor Degree in Mathematics 12 CFU (b)
Degree(s):
Bachelor Degree in Mathematics 2^{nd} anno curriculum Generale Compulsory
Language:
Italian
Course Objectives
The goal of this course is to provide a knowledge of the differential and integral calculus for
functions of several variables and of the theory of ordinary differential equations.
The student will also develop the ability of solving non trivial problems and exercises by applying
the techniques learned. The main concepts will be illustrated, if possible, by developing links with
the applications in physics and other sciences, and providing some background on the main
historical references.
Course Content
 Functions of several variables: continuity, differential calculus, Taylor expansions.
 Implicit functions e local inversion: Dini's theorem and implicit functions theorem.
Local inversion theorem.
 Optimization of functions of more variables.
 Measure and integration.
 Curves, curvilinear integrals and differential forms
 Surfaces and surface integrals.
 GaussGreen, Stokes and Divergence Theorem.
 Sequences of functions: point wise and uniform convergence. Uniform convergence and derivation and integration.
 Series of functions: point wise and uniform convergence. Uniform convergence and derivation and integration.
Power series. Taylor's series. Fourier series.
 Ordinary differential equations: local existence and uniqueness theorem. Linear homogeneous system. Wronskian matrix.
Exponential matrix. Linear systems of first order with constant coefficients. Linerar differential equations of order n. Autonmous systems. Stability of the critical points.
Liapunov method and linearization method.
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
variable and linear algebra contained in the courses of Matematematical Analysis 1 and Geometry 1.
Assessment Methods and Criteria
Written and Oral exam.
Textbooks
 C. D. Pagani, S. Salsa, Analisi Matematica , Zanichelli. (vol. 1,2)
Course page updates
This course page is available (with possible updates) also for the following academic years:
To read the current information on this course, if it is still available, go to the university course catalogue .
Course information last updated on: 03 marzo 2015, 16:33