Functions of several variables II (implicit function theorem, free and bounded extrema).
Sequences and series of functions (uniform convergence of series of functions, power series).
Introduction to measure theory (measurable representations, abstract Lebesgue integral, Lebesgue measure on R ^ n).
Multidimensional integral (Fubini's theorem, Substitution theorem, contents of shapes and volumes of bodies).
Swap integral order and limits, integral and series, or integral and derivative.
Gamma function and Beta function.
Lebesgue-Stieltjes integral.
The third part of a four-semester course in calculus for bachelor's program Financial Mathematics.