Algebra 1. Complex numbers. 2. Vectors and vector spaces; Matrix equations. 3. Systems of linear equations; Matrix notation; Solving linear systems; Introduction to linear transformations. 4. Matrix algebra; Operations with matrices; Determinants; Eigenvalues and Diagonalisation. Orthogonality - Scalar product and modulus - Singular value decomposition. Calculus 5. Real numbers and functions; Real functions; Operations with functions. 6. Successions and series; Limit of a succession; Indeterminacies. 7. Differential calculus; Limit of a function; Continuity. 8. Derivatives; Taylor developments; Numerical approximations; Graphical representation of functions. 9. Integral calculus; Primitives; Integration by parts; Fundamental theorem of calculus; Riemann integral; Properties of the integral. 10. Geometric applications of integrals. 11. Improper integrals.

Classroom lectures. Face-to-face classes: reduced (workshops, seminars, case studies). Student individual work. Final exam. Seminars and lectures supported by computer and audiovisual aids. Practical learning based on cases and problems, and exercise resolution. Individual and group or cooperative work with the option of oral or written presentation. Individual and group tutorials to resolve doubts and queries about the subject.