Mathematical analysis 1

Dr. Slagana Brsakoska, Professor

MSc Stevo Gjorgjiev, Assistant

Course content:

Real numbers.

Sets of real numbers and their basic characteristics. Complex numbers.

Vector spaces.

Polynomials (real and complex).

Eigenvalues ​​and eigenvectors.

Scalar products.

Arrays: Array boundary; Cauchy criterion; Weierstrass theorem; Countability and Continuum.

Functions: Limit of a function; Continuity; Inverse function; Decomposing rational fractions; Elementary functions; Basic limits.

Differential calculus for functions of one independent variable: Derivative and differential of first and higher order; Derivative of complex and inverse function; Lopital's Rule; Extremes; Examining and drawing functions; Taylor's formula; Application.

Multidimensional space. Vector space. Euclidean space. Standard space; Derivative of a vector function; Elements of differential geometry in plane and space.

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