NUMERIC SETS
Sets and logic: operations between sets, logical operations, properties of operations, De Morgan laws, predicates and propositions, syllogisms and tautologies. Natural numbers, relative integers, factorial of n, binomial coefficients and their properties, Newton's formula, combinatorial calculus. Induction principle. Rational numbers, real numbers and their properties. Highs and lows, upper and lower extremes.

ELEMENTARY FUNCTIONS
Radicals, powers, logarithms, rule properties, power and property functions, exponential functions and properties, logarithmic functions and properties, trigonometric functions and properties, hyperbolic functions and properties, exponential, logarithmic and trigonometric properties and inequalities. Composite and inverse functions, inverse trigonometric functions, inverse hyperbolic functions

LINEAR ALGEBRA
Vector spaces on R ^ n. Canonical vectors, dependence with linear independence. Bases and size. Scalere product and vector product. Matrices: transposed, symmetric matrix, sum and matrix difference, product for a scalar, produced rows by columns and its properties. Determinant: calculation through the Laplace formula and its properties. Characteristic of a matrix. Calculation of the inverse matrix. Linear systems: resolution of n * n systems with Cramer's rule. Homogeneous systems. Matrix representation of linear transformations. Image and core of a transformation. General rectangular systems. Rouché-Capelli theorem. Eigenvalues and eigenvectors (outline).

GEOMETRY
Parametric and Cartesian and vector equations of lines and planes. Normal color. Scalar product, vector product, mixed product. Transformation of the coordinate system by translation and rotation. Transformation from Cartesian to polar coordinates. Conics, classification of conics. Degenerate conics.

COMPLEX NUMBERS
Representation of a complex number in algebraic, geometric and trigonometric form; opposite, reciprocal, conjugate, and module of a complex number; property; operations between complex numbers; De Moivre's formula; exponential representation and Euler formulas; n-th roots and their graphic interpretation; algebraic equations in C.

SUCCESSION
Convergence and divergence, comparison theorems, operations with limits, indeterminate forms, monotony, Neperian number and remarkable limits.

SERIES
Succession of partial sums, series with positive terms, harmonic and geometric series, necessary condition of convergence, criterion of comparison, of relationship, of root, of asymptotic comparison. Telescopic series. Series with alternate sign, absolute convergence, Leibniz criterion.

LIMITS AND CONTINUITY FOR FUNCTIONS OF A REAL VARIABLE
Concept of function, domain, subject, codomain, operations between functions, composition, equality and disparity. Compound functions. Limits and properties. Notable limits. Asymptotic estimates. Continuity and theorems on continuous functions Monotony, maxima and minima. Asymptotes. Graphs of elementary functions.

DERIVATIVES
Incremental ratio, Geometric interpretation of the derivative. Derivative of elementary functions. Rules of derivation. Angular points, cusps, bent to vertical tangent. Derivative of the composite function. Derivative of the inverse function. Limit of derivative and derivability. Rolle's theorem, Cauchy. Lagrange or average value theorem.
Applications of derivatives: critical and inflection points, monotony, concavity and convexity. The theorem of de l'Hopital. Study of the graph of a function.
The concept of differential. Differential and linear approximation. The "or small" symbol. Applications to the calculation of limits. Taylor-MacLaurin formula with Peano remainder and with Lagrange remainder. Taylor-MacLaurin series development of functions. Approximate solution of an equation with the Newton method. Approximate solution of an equation with the secant method (outline).

INTEGRAL
Integral as a limit of sums. Definition of integral. Classes of integrable functions. Integral properties. Integral average theorem, fundamental theorem of integral calculus, primitives and calculation of indefinite and definite integrals. Immediate integrals for decomposition, for replacement. Integration of rational functions. Integration by parts. Integration of trigonometric functions. Integration of irrational functions. Generalized integrals (outline). Differential equations with separable variables. Initial conditions.