- Real and complex numbers.
- Sequences and series of numbers.
- Functions of one real variable: continuity, differentiability, Taylor formula, Riemann integral.
- Sequences and series of functions: pointwise and uniform convergence; differentiability and integrability term by term.
- Power series, elementary functions.
- Improper Riemann integral, functions defined by integrals (Euler integrals).
Algebra and Geometry
- General notions about some algebraic structures: groups, rings, fields.
- General properties about polynomials with real and complex coefficients.
- Finite dimensional vector spaces over real and complex numbers: base and dimension.
- Linear transformations and matrices; eigenvalues, eigenvectors, diagonal form and applications.
- Quadratic forms. Plane and solid analytical geometry: lines, planes, conics, quadrics.