Mathematics 1
Course program objectives (competences):
Students should acquire the above knowledge at a level that they can use when adopting the
course programs for which they are a prerequisite. Mastering the above contents among
students should improve logical thinking and reasoning, as well as advance
abstract thinking and in general the types and qualities of thinking.
Course program content:
The concept of a sequence. Convergent sequences, properties. Monotone sequences. Cauchy sequences. Basic properties
of real functions. Elementary functions. Limit of a function at a point, continuity. Points of
interruption, classification. The concept of a derivative, properties. Derivation of an inverse, complex and implicit function.
Higher-order derivatives. Differentials of a function. Basic theorems of differential calculus.
L'Hôpital's rule. Taylor's formula. Monotonicity and local extrema of a function. Convex functions. Tangent equation. Inflection points, asymptotes and graphs. Application of derivatives. Concept of primitive function and indefinite integral. Change of variables. Partial integration. Integration of some classes of functions. Concept of definite integral, properties. Relationship between definite and indefinite integral. Change of variables and partial integration. Application of definite integral. Cartesian rectangular coordinate system in space. Scalar and vector quantities. Projection of a vector on an axis. Operations with vectors. Linear dependence and linear independence of vectors. Projection theorems. Decomposition of vectors into components. Scalar product. Coordinate form of a scalar product. Vector product. Coordinate form of a vector product. Mixed product of vectors. Coordinate form of a mixed product. Transformation of Cartesian rectangular coordinates Differential equations, Differential equations with decomposition of variables, Homogeneous differential equations, linear differential equation of the first order, Bernoulli's equation.
Learning methods: Oral presentation method, problem-based teaching method.
