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.
• Apply the above knowledge in the solutions of chemical and physical problems.

PREREQUISITES

There are no specific requirements

TEACHING METHODS

The course is delivered through in-class lectures, both theoretical and dedicated to the resolution of exercises, based on teaching methodologies aimed at encouraging students to take an active role in their own learning process.

The course also includes in-class tutorial activities which, through a laboratory-based approach, provide flexible learning pathways that are attentive to students’ needs. These activities contribute to the achievement of the learning outcomes through group activities focused on problem solving, in which students can develop the ability to use mathematical language appropriately and to formulate, compare, and analyse different solution strategies. Attendance at tutorials is optional but strongly recommended.

Course materials are made available on the Aulaweb page of the course and include:

• lecture notes;
• exercise sheets;
• texts and solutions of guided exercises;
• texts and solutions of partial tests and exams from past exam sessions.

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.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The course Istituzioni di Matematiche (“Principles of Mathematics”) is divided into two modules: Elementi di Matematica (“Elements of Mathematics”, first semester) and Elementi di Matematica 2 (“Elements of Mathematics 2”, second semester).

The individual modules do not have separate final examinations; instead, each module includes only a partial test, which may contribute to the final assessment of the course.

The final examination for Istituzioni di Matematiche consists of a written examination and an oral examination, both covering the material taught in the two modules of the course.

The written examination may be replaced by passing two partial tests. The partial test corresponding to the module Elementi di Matematica, taught during the first semester, may only be taken during the first exam session of the winter examination period, scheduled in January. The partial test corresponding to the module Elementi di Matematica 2, taught during the second semester, may only be taken during the first exam session of the summer examination period, scheduled in June.

Students may access the oral examination if they obtain a grade of at least 18/30 in the written examination, or at least 18/30 in both partial tests. The oral examination may be made compulsory if the outcome of the written examination reveals significant gaps in substantial parts of the syllabus, or whenever the instructors deem an additional assessment of the student’s preparation necessary. All other students admitted to the oral examination may choose not to take it.

If the oral examination is not taken, the final recorded grade cannot exceed 24/30 and will coincide with the grade obtained in the written examination, or with the average grade of the two partial tests if this value is below 24/30.

The oral examination, when required or chosen by the student, must be taken within the same exam session as the written examination or, in the case of the partial tests, together with the second partial test.

Students with disabilities or specific learning disorders (DSA/SLD) are referred to the section Further Information.

ASSESSMENT METHODS

The examination is aimed at assessing:

• the acquisition of the concepts and technical content covered in the course;
• the ability to apply such concepts to problem solving;
• the student’s reasoning skills, with particular emphasis on the development and analysis of solution strategies;
• the command of appropriate mathematical language.

The written examination consists of several questions of progressively increasing difficulty, in order to allow an accurate assessment of the extent to which the learning objectives have been achieved. The examination board establishes assessment criteria providing for the assignment of partial scores to the different answers, also taking into account the complexity of the proposed topics. The overall score therefore makes it possible to evaluate the degree of achievement of the intended learning outcomes.

The oral examination is conducted by two instructors with expertise in the subject and is intended to further assess the achievement of the course learning objectives. If such objectives are deemed to have been achieved, the final grade is determined taking into account both the evaluation of the written examination (or the partial tests) and the outcome of the oral examination..

The examination is not passed if the learning objectives are not considered to have been achieved. In such cases, the student is encouraged to strengthen their preparation and to seek further clarification from the instructor, both with regard to the course content and to the study methods to be adopted.

FURTHER INFORMATION

For CTC, the course of Principles of Mathematics is a prerequisite to all the 3rd-year courses.

Compensatory and dispensatory measures Disability/Invalidity/Specific Learning Disorder

Dispensatory measures and compensatory tools are intended to enable students to achieve the same learning objectives as their fellow students, not to facilitate the examination.

The use of compensatory tools and the application of dispensatory measures must be authorised in advance by the teacher in agreement with the Referee.

To take advantage of the adaptations during the examination, fill in the Adaptation request form; the request will be automatically sent by the system to the teacher in charge of the teaching, to the Contact Person of your School/Area/Department and in copy to the Sector; you will also receive a copy of the request sent by e-mail.

The adjustments available to students are as follows:

· Additional time (+30% DSA)

· Additional time (+50% disability/invalidity)

· Additional time during oral exams to organise the answer

· Calculator (programmable and graphing calculators are not allowed)

· Conceptual Maps

· Tables and/or Forms

· Take the exam in written form

· Take the exam in oral form

· Tutor reader (for written tests only)

· Tutor-writer (for written tests only)

Your request for adaptations must be submitted at least 7 working days before the scheduled exam date.

All information for students with disabilities and DSA is available on the webpage: Services for students with disabilities or DSA | UniGe | University of Genoa

Reference for inclusion: Sergio Di Domizio - sergio.didomizio@unige.it