Learning objectives
Provide the basic tools of Mathematical Analysis
Prerequisites
No
Course unit content
Real analysis, functions of one variable, sequences, series
Full programme
Integrals
Partitions of an interval; Riemann sums; Riemann integral; integrability of monotonic functions and of continuous functions;
integral mean; fundamental theorem of integral calculus; primitives; integration by parts; integration by substitution; integration of rational functions.
Improper integrals; convergence of the integral, absolute convergence,comparison tests. Integral test for positive valued series.
Asymptotic expansions
Landau symbols; Taylor's theorem; explicit formula of the remainder; Mac Laurin expansion of elementary functions; Taylor's series
Complements
Bolzano-Weirstrass theorem, compactness in the real line; Cauchy sequences; upper and lower limits;
uniform continuity.
Complex numbers.
Definitions, operations, complex plain, polar form, root extraction.
Differential equations
Nomenclature: order, linear and nonlinear; first examples; solutions of linear first order equations; solution of separable differential equations; constant coefficients linear differential equations.
Bibliography
E. Acerbi, G. Buttazzo: Primo corso di Analisi Matematica, Ed. Pitagora, 1997.
E. Acerbi, G. Buttazzo: Analisi matematica ABC, Ed. Pitagora, 2000.
M. Bramanti, C.D. Pagani, S. Salsa: Analisi Matematica 1, Ed. Zanichelli, 2008.
M. Giaquinta, L. Modica, Analisi Matematica 1, vol. 1 & 2, Ed. Pitagora, 1998.
E. Giusti, Analisi matematica vol.1, Ed. Boringhieri, 2002
Teaching methods
classroom lectures and classroom exercises
Assessment methods and criteria
written and oral examination
Other information
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