OVERVIEW

The course Institutions of Mathematics constits of the modules Elements of Mathematics (cod. 72565, 1srt semester) and Elements of Mathematics 2 (cod. 72566, 2nd semester). The subject of the course is the study of real functions of one and two real variables, the differential calculus, and the integral calculus.

This section provides information that is common to the two modules; the specific information can be found in the modules sheets.

AIMS AND CONTENT

LEARNING OUTCOMES

Topic of the course is the study of real functions with one or two real variables, with the differential and integral calculus. We want to give students the tools to use these essential notions in the following courses of physical and chemical character.

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.

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 classroom and online 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 material course 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

The detailed programs of the two modules are described in the modules sheets.

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

VICTOR LOZOVANU (Substitute)

LESSONS

LESSONS START

Since 25/9/2017, according to the schedule indicated on the sites  www.ctc.unige.it and http://www.fisica.unige.it/scienzadeimateriali/

Class schedule

MATHEMATICAL INSTITUTIONS

EXAMS

EXAM DESCRIPTION

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

The written exam can be replaced by the successful completion of two intermediate tests carried out during the course. It is possible to try again one of the two intermediate tests during the written test session of any of the exams. In any case, the scores of the intermediate tests are valid only till February of the following year.

The oral exam, at the student's choice, can take place in traditional modality, or in an experimental laboratory modality, through two ad hoc tests each relating to each semester.

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 tests (intermediate and complete) are 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 examination, both in the traditional and in the experimental modality, 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

FURTHER INFORMATION

For CTC the course of Institutions of Mathematics is a prerequisite to the 2nd-year course of Physical Chemistry 2, and to all the 3rd-year courses.