Syllabus
Sequnces: properties (sequences bounded, increasin, decreasing), cauchy sequences, subsequence, limits, Cauchy condition, limit points. Series: introduction, properties, sum of series, convergence, tests (comparison, ratio, root, integral, Leibniz, Dirichlet, Abel, condensation), absolute and non-absolute convergence, rearrangement of series.
Sequencies and series of functions: pointwise and uniform convergence (Weierstrass test), statements on limits, continuity, derivatives and integrals, power series, properties, Taylor, Maclaurin series, expansion of basic elementary functions.
Annotation
Number sequences (revision). Number series.
Series with nonnegative terms, criteria of convergence. Alternating series, Leibniz criterion.
Absolute and nonabsolute convergence, rearrangement of series. Sequences and series of functions, pointwise and uniform convergence.
Power series, Taylor and Maclaurin series.