Témata výkladu zpracovaných v podobě multimediálních studijních opor:
1. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations.
2. Functions of one real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing), inverse functions, composition of functions.
3. The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval.
4. An introduction to the differential calculus – slope of a tangent line at a point, derivative, equation of a tangent line and normal line to a curve at a point, techniques of differentiation, higher order derivations, l´Hospital´s rule.
5. Course of a function – local and global extrema, intervals of monotonicity, points of inflection, convexity, concavity, asymptotic lines.
Problems are solved offline (individually, under the supervision of a tutor with the aid of supportive materials).
1. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations.
2. Functions of one real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing), inverse functions, composition of functions.
3. The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval.
4. An introduction to the differential calculus – slope of a tangent line at a point, derivative, equation of a tangent line and normal line to a curve at a point, techniques of differentiation, higher order derivations, l´Hospital´s rule.
5. Course of a function – local and global extrema, intervals of monotonicity, points of inflection, convexity, concavity, asymptotic lines.
Problems are solved offline (individually, under the supervision of a tutor with the aid of supportive materials).