714-0560/02 – Mathematics for Bachelors I ()

The function of one real variable. The limit of a function, the continuity of a function. The derivation of the function of one variable. Derivations of higher orders. Monotony, local extremes, convexity, concavity, inflexion, asymptotes. The derivation of a parametrically defined function. Linear algebra. Determinants. Arithmetic vectors, operations. Matrices, the rank of a matrix, operations with matrices. Systems of linear algebraic equations. Solid analytic geometry. Geometric vectors. The scalar, vector, triple products and their applications. Analytical expressions of a plane and a line in space. Integral calculus. The primitive function and the indefinite integral of the function of one real variable, basic integration methods – substitution, by parts. The definite integral, applications. The differential calculus of functions of two variables. The domain of definition. Partial derivations of the first and higher orders. Extremes of functions of two variables. Implicitly defined functions. Ordinary differential equations. 1st order differential equations, kinds of solution. Separable, homogenous and linear equations. 2nd order linear equations with constant coefficients.