Fundamentals of Mathematics

- Numbers: integers, rationals, reals; ordering. Recalls of plane trigonometry; complex numbers and their roots. Vectors and vectorial operations; straight lines and planes in space.
- Sequences and their limits, monotonicity, comparisons, indecision forms; Napier's constant "e". Series and convergence criteria.
- Functions of a real variable: limits, continuity, asymptotes; composite and inverse. Elementary functions and their graphs: powers and radicals, exponentials and logarithms, trigonometric functions and their inverse.
- Differential calculus in one variable: derivatives, maxima and minima, convexity, analysis of functions; Taylor's formula.
- Integral calculus in one variable: definite integral, primitives (by decomposition, substitution and by parts), relations between definite integral and primitives. Physical and geometrical applications; generalized integrals.
- Multivariable functions: partial derivatives, gradient, Hessian; optimization in two variables. Linear regression line.
- Ordinary differential equations: linear first order and separable; linear second order with constant coefficients. Initial conditions, existence and uniqueness theorem.