Linear vector spaces.

Matrices and determinants, systems of linear equations, Gaussian elimination.

Bilinear and quadratic forms, positive and negative definiteness.

Basic theory of functions of several variables, metric, limits, continuity.

Partial derivatives and total differential, operators grad, div, rot.

Multidimensional integral. Exchange of limits and integrals, derivatives and integrals.

Number series, convergence and divergence, absolute and non-absolute convergence, Taylor series.

Ordinary differential equations and their systems, basic methods, Bernoulli and Euler equations, equations in the form of total differential, solving equations using series.

The second semester of the four-semester course on Applied Mathematics. Basics of linear algebra and matrix calculus.

Differential and integral calculus of functions of several variables. Ordinary differential equations.