Linear Algebra: An algebraic vector, basic terms. A matrix, the rank of a
matrix, elementary treatments of a matrix. Systems of linear equations. A
determinant, determinant properties. Foundations of the matrix calculus.
The Real-Valued Function of a Real Variable: Definition, the domain of
definition, the range of values, the graph of a function. Properties of
functions. Inverse, composite functions. Basic elementary functions. The
sequence of real numbers and the limit of the sequence. The limit of a function
at a point. The continuity of a function.
The Derivation of a Function: Derivation definition and the geometric
significance of the derivation. The derivation of basic elementary functions.
Derivation Applications: A tangent and a normal. Monotony. Local and absolute
extreme values of a function. Convexity, concavity, inflection points.
Asymptotes. The behaviour of a function.
The Differential Calculus of Functions of Several Variables: The definition of
functions of two and several variables, the domain of definition. The partial
derivations of the first and higher orders.
The Indefinite Integral: An indefinite integral and a primitive function.
Basic formulas. Integration by parts. The method of substitution.