FUNCTIONS WITH ONE VARIABLE B
Learning outcomes of the course unit
Provide the basic tools of Mathematical Analysis
Course contents summary
Complex numbers. Definitions, operations, complex plain, polar form, root extraction.
Sequences. Mathematical induction; real and complex sequences;
limit of a sequence; subsequences; Cauchy sequences; monotonic sequences;
Neper's number; sequences defined by recurrence relation; upper and lower limits;
Bolzano-Weirstrass theorem, compactness in the real line. Uniform continuity.
Series. Convergence criteria: comparison tests, ratio test, root test; absolute convergence;
rearrangements; alternating series; examples: geometric series, harmonic series, power series.
Improper integrals; convergence of the integral, absolute convergence,
comparison tests. Integral test for positive valued series.
J. Cecconi, G. Stampacchia, Analisi Matematica 1, LIGUORI, 1974.
E. Giusti, Analisi Matematica 1, BORINGHIERI, 1983.
E. Acerbi, G. Buttazzo, Primo corso di Analisi Matematica, Pitagora editrice, Bologna (1997)
Teaching method: classroom lectures and classroom exercises
Assessment method: written and oral examination