OVERVIEW

The teaching aims to provide the mathematical skills indispensable for the language of science, presenting basic concepts and methodologies of algebra and mathematical analysis.

AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

With this teaching the student will acquire the following competences:

• numerical sets and their operations,
• factoring of polynomials,
• solving linear systems,
• calculation of limits of successions and functions,
• elementary properties of continuous functions of a real variable,
• elementary properties of differentiable functions of a real variable,
• calculation of integrals for functions of a real variable.

TEACHING METHODS

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.

SYLLABUS/CONTENT

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.

RECOMMENDED READING/BIBLIOGRAPHY

 A.M. Bigatti, L. Robbiano, "Matematica di base", Casa Editrice Ambrosiana.

TEACHERS AND EXAM BOARD

Exam Board

MARCO BENINI (President)

CLAUDIO BARTOCCI

SIMONE MURRO (President Substitute)

LESSONS

Class schedule

INSTITUTIONS OF MATHEMATICS

EXAMS

EXAM DESCRIPTION

Written exam and oral exam.

ASSESSMENT METHODS

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.

Exam schedule