# ELEMENTS OF MATHEMATICS 2

7 credits during the 1st year of 8765 Material Science (L-30) GENOVA

OVERVIEW

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

## 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.

Acquisition of the concept of differential equation and of the ability to solve the most common types of differential equations. Acquisition of the concept of number series and of some criteria for the convergence.

Acquisition of the main properties of functions in two variables and of the computation of double integrals.

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

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

- Differential equations.
- Numerical series and convergence criteria.
- Elements of analytic geometry in the plane and in the space.
- Functions of several variables: domains and level curves, limits and continuity, differentiability, critical points, relative minima and maxima, maximum and minimum absolute and bound.
- Double integrals in Cartesian coordinates and polar coordinates.

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

**Ricevimento:** At the end of the lessons or by appointment.

## LESSONS

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.

LESSONS START

Since 19/2/2018, according to the schedule indicated on the site www.ctc.unige.it and on the site http://www.fisica.unige.it/scienzadeimateriali/

## EXAMS

Exam description

The exam consists of a written test and an oral test about the arguments carried out 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 2019.

The evaluation criteria of the online laboratory activities will be described on the Aulaweb course module.

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 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.

## 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.