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Teacher
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NATALINI PIERPAOLO
(syllabus)
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.
(reference books)
A. Laforgia, Equazioni differenziali ordinarie, Accademica editrice
A. Laforgia, Successioni e serie di funzioni, Accademica editrice
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Università Roma Tre