Differentiation of one-variable functions: tangents and derivatives, rules of differentiation, chain rule, higher-order derivatives.
Continuity and differentiability, Taylor's formula, intermediate-value theorem, De L’Hôpital’s Rule.
Single-variable optimization: local and global extrema, stationary points and first-order condition, simple tests for extreme points, extreme points for concave and convex functions, second-order derivative and convexity, inflection points, study of the graph of a function, asymptotes.
Sequences and series; convergence criteria; geometric series.
Sequences and series in financial mathematics.
Integration: the definition of integral and its geometrical interpretation; primitives and indefinite integrals, fundamental theorems of integral calculus.
Rules and methods of integration: immediate integrals, integration of rational functions, integration by parts, integration by substitution.
Integration in economics: continuous compounding and discounting, present values.
Linear algebra: vector spaces, bases and dimensions; matrices and their properties; systems of equations, existence of solutions.
