Syllabus
0. Taylor polynoms, convergence of Taylor series, forms of remainders, series for elementary functions, rules for Taylor polynoms, use for computing. 1.
Integral of real functions of one variable: indefinite integral (antiderivative), definite integrals (Riemann and Newton), calculation of integrals (by parts, substitution, integration of rational and similar functions), convergence of definite integrals. 2. Applications of integrals: integral criterion for convergence of series, area between curves, volumes of solids, length of plane curves, area of surfaces of revolution, moments and centers of mass. 3.
Diferential equations: existence theorems, separation of variables, linear differential equations, systems of linear differential equations, applications of differential equations in geometry, physics and elsewhere, stability of solutions. 4. Functions of more variables: limits, continuity, partial derivatives, polar and spherical coordinates, theorems on continuous functions and implicit functions, maxima and minima, integrals, examples of partial differential equations.
Annotation
The second part of a four-semester course in calculus for bachelor's program Financial Mathematics.