1.Functions of one real variable – definition, domain and range,
classification, graph, even and odd functions, monotonic functions
(strictly increasing, strictly decreasing). Inverse functions.
2.The limits of functions – properties of limits, limits to infinity,
one sided limits, definition of continuity, continuity on an interval,
sequences, limits of sequences.
3.An introduction to the derivate – 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.
4.Additional applications of derivative – extreme values of
a continuous function, intervals of increase and decrease,
the second-derivative test for concavity, the second-derivative
test for relative extreme, asymptotes.
5.Linear algebra – matrices, addition and multiplication
of matrices, determinant, the inverse of the matrix,
matrix equations.
6.Linear algebra – system of linear equations, Gauss
elimination method.
classification, graph, even and odd functions, monotonic functions
(strictly increasing, strictly decreasing). Inverse functions.
2.The limits of functions – properties of limits, limits to infinity,
one sided limits, definition of continuity, continuity on an interval,
sequences, limits of sequences.
3.An introduction to the derivate – 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.
4.Additional applications of derivative – extreme values of
a continuous function, intervals of increase and decrease,
the second-derivative test for concavity, the second-derivative
test for relative extreme, asymptotes.
5.Linear algebra – matrices, addition and multiplication
of matrices, determinant, the inverse of the matrix,
matrix equations.
6.Linear algebra – system of linear equations, Gauss
elimination method.