1. Introduction: sets, numbers, the real line, absolute value, intervals, mathematical induction.
2. Sequences: convergence, limits, indeterminate forms, introduction to series.
3. Functions, limits and continuity: elementary functions, algebraic operations and composition, inverse function, limits, continuity, intermediate value theorem.
4. Differentiation: derivative, algebraic operations and chain rule, Rolle's theorem, mean value theorem, L'Hôpital's rule, extrema, convexity, derivative of an inverse function, polynomial approximation, Taylor's theorem.
5. Integration: Riemann's integral, properties, fundamental theorem of calculus, integration by parts, changes of variables, improper integrals.
6. Series: series of non-negative terms, alternating series, absolute and conditional convergence, convergence tests, power series, radius of conergence, Taylor series.