Basic Mathematics

1. Functions of one real variable – definition, domain and range, classification, graphs, 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.
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. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations.
5. The indefinite integral – definition and properties, basic integration rules, methods of integration: integration by substitution, integration by parts.
6. The definite integral – definition and properties, the Newton-Leibniz formula.