Syllabus
Differential equations - existence and uniquity, methods of solutions of first order differential equations (separation of variables method and variation of constant method for linear ones) and second order equations (undetermined coefficients method), thair applications.
Series - tests for convergence (comparison, ratio, root, Leibniz, Abel, Dirichlet tests), absolut convergence, sums of series.
Sequences and series of functions - uniform convergence of sequences and series, tests (Weierstrass, Abel, Dirichlet tests), power series, power series expansion of basic functions, application for calculation of limits.
Annotation
Differential equations, methods of solution, linear differential equations of 1st and 2nd order, series and its convergence, sequences and series of functions, uniform convergence, power series.