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.

D. Benedetto, M. Degli Esposti, C. Maffei "Matematica per le scienze della vita",  Casa Editrice Ambrosiana.

TEACHERS AND EXAM BOARD

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written exam and optional oral exam.

ASSESSMENT METHODS

The written exam may include exercises on any of the topics covered in the course.

The oral exam may consist of solving an exercise on the blackboard or answering questions to assess the understanding of definitions and theorems discussed during the course.

To take part in the written exam, students must register at least two days before the exam date on the website:

https://servizionline.unige.it/studenti/esami/prenotazione

The written exam is passed if the score is equal to or higher than 18/30.

Candidates who pass the written exam may freely decide whether or not to take the oral exam, which must be held during the same exam session as the written exam:

• for those who choose not to take the oral exam, the final grade is calculated as follows:

equal to the written exam grade if this is less than or equal to 24/30;
equal to 25 if the written exam grade is 25 or 26;
equal to 26 if the written exam grade is 27 or 28;
equal to 27 if the written exam grade is 29 or 30;

• for those who choose to take the oral exam, the final grade is the average of the grades obtained in the written and oral exams.