Learning objectives
To provide the basic knowledge about implicit functions, sequencs and series of functions, ordinary differential equations.
Prerequisites
Mathematical Analysis I and Mathematical Analysis 2, 1° module.
Course unit content
Implicit functions. The inverse function Theorem. Extremum problems with side conditions.
Sequences and series of functions. Pointwise and uniform convergence. Total convergence of series of functions. Power series. Taylor series. Fourier series.
Ordinary differential equations (ODE). The Cauchy problem. Local existence and uniqueness theorem. Extension of the solutions. Solutions of some type of first order ODE. Linear equations.
Full programme
Implicit functions. The inverse function Theorem. Extremum problems with side conditions.
Sequences and series of functions. Pointwise and uniform convergence. Total convergence of series of functions. Power series. Taylor series. Fourier series.
Ordinary differential equations (ODE). The Cauchy problem. Local existence and uniqueness theorem. Extension of the solutions. Solutions of some type of first order ODE. Linear equations.
Bibliography
M. Fusco, P:Marcellini, C. Sbordone, Analisi Matematica due, ed. Liguori.
M: Bramanti, C.D. Pagani, S.Salsa, Analisi matematica 2, ed. Zanichelli
Teaching methods
Oral lessons with check of understanding.
Assessment methods and criteria
Written and oral examination
Other information
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2030 agenda goals for sustainable development
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