Real powers, modulus, roots.
Polynomials. Elements of combinatorics and binomial theorem.
Cartesian and parametric equations. Sums and products of vectors.
Linear systems. Matrices and determinants. Independence, bases. Projections. Matrix of an operator. Eigenvectors.
Complex numbers. Euler Formula. Complex roots.
Functions and graphs. Invertible functions.
Convergent sequences and series.
Theorems about limits. Properties of continuous functions.
Differentiation. Mean value Theorem. If the sign of f' is constant
in an interval, then f is monotonic in that interval.
f'' and convexity. Criteria for maxima and minima in stationary points.
Definite and indefinite integrals. Fundamental Theorem of Calculus.
Integration by change of variables and by parts.
Examples of improper integrals.