The teaching aims to provide the mathematical skills indispensable for the language of science, presenting basic concepts and methodologies of algebra and mathematical analysis.
With this teaching the student will acquire the following competences:
Frontal lecture.
Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sara Ferrando (sara.ferrando@unige.it), the Department’s disability liaison.
Preliminaries: Recollactions on numeric sets and arithmetic calculus, properties of real and complex numbers. Elementary set theory: union, intersection and applications. Functions of a real variable, their graph and properties. Elementary functions: polynomials (finding roots and factoring), trigonometric functions, exponential functions and logarithm.
Linear algebra: solutions of linear systems using the Gauss algorithm, geometrical aspects (intersection of two lines in the plane). Matrices: product, determinant, rank.
Functions of a real variable: Domain of definition, image, composition, graph.
Limits: Definitions, properties, elementary limits and calculation rules, asymptotes.
Continuous functions: Definition, elementary properties, existence of zeros, global maxima and minima.
Derivable functions: Definition, geometric interpretation, derivatives of elementary functions and calculation rules, successive derivatives and Taylor polynomials. Use of derivatives in studying the graph of a derivable function: tangent lines to the graph, critical points, monotony, relative maxima and minima.
Defined integrals: Definition, geometric interpretation, primitives, fundamental theorem of integral calculus, use of primitives for calculating integrals, integration by substitution and by parts.
A.M. Bigatti, L. Robbiano, "Matematica di base", Casa Editrice Ambrosiana.
Ricevimento: By appointment.
MARCO BENINI (President)
CLAUDIO BARTOCCI
SIMONE MURRO (President Substitute)
INSTITUTIONS OF MATHEMATICS
Written exam and oral exam.
The written exam may include exercises on factoring polynomials, solving linear systems, geometry of lines in the plane, calculating limits, studying continuous and derivable functions and calculating integrals.
The oral exam may involve carrying out an exercise on the blackboard or verifying the learning of the definitions and theorems covered in the course.
