Series; ordinary differential equations; integrals transforms (Laplace, Fourier); functions of more variables.
teacher profile teaching materials
2nd order differential equations: Theorem of existence and uniqueness (without demonstration); Linear equations; The general solution of the homogeneous; Wronskiano and its properties; A method for obtaining a homogeneous equation solution, knowing another; homogeneous differential equations with constant coefficients: Real and distinct roots, real and coincident roots, complex and conjugated roots; Further results on homogeneous equations; The equation is not homogeneous; The method of changing the parameters; The method of indefinite coefficients.
Sequences and series of functions; Punctual and uniform convergence; Criterion of Wierstrass; Uniform convergence and continuity; Convergence and Integration; Uniform convergence and derivation; Power Series; Convergence properties; Criteria for the search for the convergence radius; Integration and derivation of power series; Taylor Series; The binomial series; Evaluation of some integrals through power series; Fourier series.
Integration by series of second order differential equations.
Laplace's transformation; Demonstration property; Transformations of integral and derivative; Solutions to Some Cauchy Problems; The convolution integral; Additional applications.
Functions of multiple variables: generality, limits and continuity; Partial derivatives; Extreme values (classification of critical points); Lagrange multipliers.
A. Laforgia, Successioni e serie di funzioni, Accademica editrice
Programme
First order differential equations: Separate variable equations; Linear equations; Bernoulli's equation. The theorem of existence and uniqueness (without proof) for first order differential equations.2nd order differential equations: Theorem of existence and uniqueness (without demonstration); Linear equations; The general solution of the homogeneous; Wronskiano and its properties; A method for obtaining a homogeneous equation solution, knowing another; homogeneous differential equations with constant coefficients: Real and distinct roots, real and coincident roots, complex and conjugated roots; Further results on homogeneous equations; The equation is not homogeneous; The method of changing the parameters; The method of indefinite coefficients.
Sequences and series of functions; Punctual and uniform convergence; Criterion of Wierstrass; Uniform convergence and continuity; Convergence and Integration; Uniform convergence and derivation; Power Series; Convergence properties; Criteria for the search for the convergence radius; Integration and derivation of power series; Taylor Series; The binomial series; Evaluation of some integrals through power series; Fourier series.
Integration by series of second order differential equations.
Laplace's transformation; Demonstration property; Transformations of integral and derivative; Solutions to Some Cauchy Problems; The convolution integral; Additional applications.
Functions of multiple variables: generality, limits and continuity; Partial derivatives; Extreme values (classification of critical points); Lagrange multipliers.
Core Documentation
A. Laforgia, Equazioni differenziali ordinarie, Accademica editriceA. Laforgia, Successioni e serie di funzioni, Accademica editrice
Type of delivery of the course
Theoretical frontal lessons and guided exercises. In the case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities will be implemented. In particular, the following methods will apply: each lesson will be transmitted on the Moodle portal through pdf files often integrated with commented ppt files.Type of evaluation
Written exam with 4 exercises on the whole program. It to be done in two hours. In the event of an extension of the health emergency from COVID-19, all the provisions governing the methods of student assessment will be implemented. In particular, the following procedures will be applied: Remote written exam transmitted on the Moodle portal with 2 exercises on the whole program to be carried out in 1 hour. Oral exam at a distance through the Teams software. teacher profile teaching materials
Type of evaluation
Written exam with 4 exercises on the whole program. It to be done in two hours. In the event of an extension of the health emergency from COVID-19, all the provisions governing the methods of student assessment will be implemented. In particular, the following procedures will be applied: Remote written exam transmitted on the Moodle portal with 2 exercises on the whole program to be carried out in 1 hour. Oral exam at a distance through the Teams software.