Syllabus
1. Taylor polynomial (a) Basic properties (Taylor polynomial, Lagrange form of a residue). (b) Taylor polynomials of elementary functions
2. Primitive functions (a) Basic properties (arithmetic, substitution theorems, integration per partes) (b) Integration of rational functions (c) Some special substitutions
3. Definite integral (a) Newton's integral (calculation methods, substitutions, per partes) (b) Riemann integral (definition, relation between Newton's and Riemann integral) (c) Convergence of the Newton integral (comparison criterion) (d) Applications of definite integral (e) Riemann-Stieltjes integral (definition, relation between Riemann-Riemann-Stieltjes integral)
4. ODE (a) 1st order (Separated variables, homogeneous, kinear, applications) (b) 2nd order (Linear, constant coefficients)
5. Functions of several variables I (a) basic concepts in R ^ n (closed and open sets, continuity) (b) partial derivatives
Annotation
The second part of a four-semester course in calculus for bachelor's program Financial Mathematics.