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 (36 hours) and exercises lectures (30 hours), which, together with are based on teaching methods that, together with tutoring activities, 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

Matematica per le scienze, M. Bramanti, F. Confortola, S. Salsa Ed. Zanichelli

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

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written and an oral test, to be taken within the same session
(June-July, September, January-February). For Chemistry students the written test can be replaced by two partial tests, one for each semester, while for Materials Science students the written test is a single one.

Students with certified DSA, disabilities or other special educational needs are advised to contact the teachers at the beginning of the course to identify teaching and exam methods which, in compliance with the teaching objectives, take into account the learning methods individual and provide suitable compensatory tools.

ASSESSMENT METHODS

The final assessment will evaluate the acquisition of the concepts and technical contents addressed in the course, the ability to apply these concepts to problem solving, the student's reasoning ability, in particular the ability to propose and analyze solution strategies, the mastery of mathematical language. .

The written test is organized on several questions with graduated difficulties which allow for a precise assessment of the degree of achievement of the training objectives. The examination commission establishes criteria for assigning partial scores to the various answers, which also take into account the difficulty of the proposed topics. Based on these criteria it is possible to  associate with precision a total score acquired to the achievement of the learning outcomes.

The oral exam is always conducted by two tenured teachers with many years of experience in exams in the discipline. The commission verifies with high accuracy the achievement of the educational objectives. If the objectives are considered as achieved, a weighted average is made of the evaluations of the written test (or intermediate tests) and the oral one. The commission decides, for each academic year, what relative weight to give to each test.

The exam is not passed when the training objectives have not been achieved; in this case the student is invited to study further and make use of further explanations from the lecturer, both on some contents and on the study method to be adopted.

Exam schedule

FURTHER INFORMATION

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 Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.