OVERVIEW

The modules Elements of Mathematics (1st semester) and Elements of Mathematics 2 (2nd semester) constitute the course Principles 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

Provide tools and contents to be used in subsequent chemical and physical courses: differential equations with separable variables, linear 1st order, linear 2nd order with constant coefficients. Numerical series. Functions in two variables. Double integrals.

AIMS AND LEARNING OUTCOMES

The course aims at providing students with tools to reach the following learning outcomes:

• Acquire a correct methodological approach to learning of scientific disciplines, based on the use of mathematical language and reasoning as a tool for the interpretation of the real world and not as mere abstract notions.
• Know and understand the meaning of specific technical contents:
  • the notion of differential equation and solutions of the most common types of differential equations,
  • the notion of series and some criteria for convergence,
  • the main properties of functions in two variables,
  • the computation of double integrals.
• Use of the mathematical language to describing and solving problems of theorical or applied nature.
• Acquire work group skills, metacognitive reflection on one's own work and that of others.
• Propose and analyse solving strategies, detect errors and give input for reflection.
• Apply the above knowledge in the solutions of chemical and physical problems.

PREREQUISITES

There are no specific requirements

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 instructional tutorials, which are supplied in a workshop form 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

• Series and convergence criteria.
• Differential equations (separable differential equations, first-order linear differential equations, second-order linear differential equations with constant coefficients).
• 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 maxima and minima, absolute maximum and minimum on closed and bounded regions.
• 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

LESSONS

LESSONS START

The class will start according to the academic calendar.

EXAMS

EXAM DESCRIPTION

The module Elements of Mathematics 2 is the second of the two modules composing the course Principles of Mathematics. The single module has no exam but a partial test that can contribute to the final mark for the whole course "Istituzioni di Matematica". 

The exam for the course Principles of Mathematics consists of a written test and an oral test about the arguments treated out in the two modules. 

The written test can be replaced by the successful completion of two partial tests: the first one on the contents of the module Elements of Mathematics takes place at the end of the first semester during the winter exam session, and a second one on the contents of the module Elements of Mathematics 2 that takes place at the end of the second semester during the summer exam session.

Students must achieve the minimum mark of 18/30 in the written test (or in each of the two partial tests) to be admitted to the oral examination. Among the students admitted to the oral examination, those the teachers think need a complemetary examination must do the oral test. All the other admitted students can avoid the oral examination. In this last case, the registered final mark of the exam will be the minimum between 24 and the mark achieved in the written test (or the average of the two marks achieved in the partial tests). Written and oral tests must be done in the same exam session. 

Students with SLD (specific learning disability) certification, 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 into account of individual learning arrangements and provide appropriate compensatory tools.

ASSESSMENT METHODS

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

Both the partial and the complete written tests 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, the average of the written (complete or partials) and oral exam evaluation is done. 

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 Principles of Mathematics is a prerequisite to all the 3rd-year courses.

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.