OVERVIEW

Elements of Mathematics  is the first module of the course "Istituzioni di Matematiche";  the subject of "Elements of Mathematics" is the study of real functions of one variable, the differential calculus, the integral calculus and complex numbers.

AIMS AND CONTENT

LEARNING OUTCOMES

The course will provide tools and content to be used in subsequent chemical and physical courses: study of functions of one variable, differential and integral calculus, complex numbers.

AIMS AND LEARNING OUTCOMES

Acquisition of a correct methodological approach to learning of scientific disciplines, based on the use of language and mathematical reasoning as useful  tools for the interpretation of the real world and not as mere abstract notions.

Acquisition of group work skills, metacognitive reflection on one's own work and that of others, error detection and analysis and input for reflection.

Acquisition of specific technical contents:

• the study of real functions of one variable
• the differential calculus, and the integral calculus
• the complex numbers.

Acquisition of the ability to apply the above knowledge in the solutions of chemical and physical problems.

PREREQUISITES

• Algebraic calculus, polynomial and fractional equations and inequations
• Analytical geometry elements (Cartesian coordinate system in the plane, equations of lines and of particular parables)
•  Absolute value, definition and basic properties, simple equations and inequations
•  Roots, definition and basic properties, simple equations and inequations
• Powers, exponentials, logarithms, definition and basic properties
• Basics on exponential and logarithmic functions
• Basic elements of trigonometry

TEACHING METHODS

The course is organized in theoretical and exercises lectures, which are based on teaching methods that aim to encourage students to take an active role in the development of the learning process.

The course also provides instructional tutorials which are based on a workshop approach and make it possible to implement flexible learning pathways adapted to the needs of individual students.

The course material  is made available on the Aulaweb site of the course: handouts of lectures, exercises sheets, texts and solutions of guided exercises, texts and solutions of written exams from previous years.

SYLLABUS/CONTENT

• Real numbers.
• Functions of one real variable: elementary functions, limits and continuity, differential calculus. Theorems on continuous and derivable functions.
• Application of derivatives: the Taylor formula.
• Integral calculus: primitives and integration rules. Calculation of areas. Improper integrals.
• Complex numbers.

RECOMMENDED READING/BIBLIOGRAPHY

Istituzioni di Matematica , M.Bertsch, Ed. Bollati Boringhieri
Analisi Matematica 1 e 2, M.Bramanti, C.D. Pagani, S.Salsa Ed. Zanichelli

TEACHERS AND EXAM BOARD

Exam Board

SARA NEGRI (President)

FRANCESCO VENEZIANO

LESSONS

LESSONS START

The class will start according to the academic calendar:

https://corsi.unige.it/corsi/11634/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists in a written test and in an oral test on the topics treated in the course. The written and the oral tests must be taken in the same exam session (January-February, June-July, or September).

Students with DSA certification (specific learning disabilities), disability or other special educational needs are advised to contact the teachers at the beginning of the course to establish teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

ASSESSMENT METHODS

The assessment concerns the acquisition of the concepts contained in the course, the ability to apply these concepts to the resolution of exercises and the reasoning skills of the student.

The written exam is organized on several questions with graded difficulty, which make it possible to obtain a precise assessment of the degree of achievement of the educational goals. To this aim, the board of examiners establishes the criteria for the award of partial scores to the various responses taking into account the difficulty of the proposed topics. Based on these criteria it is possible to accurately associate the total score gained to the achievement of the expected learning outcomes.

The oral exam is always conducted by two professors with years of experience of examinations in the discipline. The exam commission verifies with high accuracy the achievement of the educational objectives. If these objectives are considered met, a weighted average of the written (complete or intermediate) and oral exam evaluation is done. Each academical year the exam commssion sets the relative weight to be given to each test.

The exam is not passed when the educational objectives are not met; in this case the student is invited to deepen the study and to require further explanation by the lecturer about some parts of the contents and about the study method to be adopted.

Exam schedule