Course program
One-variable functions: basic definitions, graphs and elementary functions (linear, quadratic, polynomial, rational, irrational, power, exponential, logarithmic, absolute value). Odd and even functions. Composite functions. Inverse functions. Limits and continuity. 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.
