Real numbers, complex numbers. Real functions. Continuity. Derivatives. Graphical study of functions. Fundamental theorem of the calculus. Sequences. Taylor formula. Differential equations (just an introduction).
Solution of linear systems, Gauss' elimination method. Rank of a matrix and number of free parameters in the space of the solutions of linear systems. Eigenvalues and eigenvectors, reduction of a symmetric matrix to a diagonal form.
Elements of algebra: groups and abelian groups, rings, fields.
Introduction of the fundamental mathematical concepts, that are essential to describe the physical phenomena and those in chemistry, in a quantitative way.
KNOWLEDGE AND UNDERSTANDING:
Introduction to linear algebra and to basics of calculus, both differential and integral. APPLYING KNOWLEDGE AND UNDERSTANDING:
Development of the abilities in problem solving, in a mathematical framework.
Acquiring of the rigorous way to proceed (in a mathematical framework) that is typical in the scientific method.
Ability in explaining, in a coherent way, logical arguments.
Development of the ability in formulating hypotheses and in verifying them.