1. Linear algebra – Euclidean space, matrices, addition and multiplication of
matrices, determinant.
2. Linear algebra – the inverse of the matrix, matrix equations, input-output
analysis. System of linear equations, Gauss elimination method.
3. Functions of one real variable – definition, domain and range,
classification, graphs, even and odd functions, monotonic functions (strictly
increasing, strictly decreasing), inverse functions.
4. The limit of function – properties of limits, limits to infinity, one sided
limits, definition of continuity, continuity on an interval, sequences, limits
of sequences.
5. An introduction to the derivation – 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.
6. Higher order derivations, l´Hospital´s rule.
7. 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.
matrices, determinant.
2. Linear algebra – the inverse of the matrix, matrix equations, input-output
analysis. System of linear equations, Gauss elimination method.
3. Functions of one real variable – definition, domain and range,
classification, graphs, even and odd functions, monotonic functions (strictly
increasing, strictly decreasing), inverse functions.
4. The limit of function – properties of limits, limits to infinity, one sided
limits, definition of continuity, continuity on an interval, sequences, limits
of sequences.
5. An introduction to the derivation – 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.
6. Higher order derivations, l´Hospital´s rule.
7. 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.