Ateneo - UPO

The aim of the course is to provide students with a mastery of basic knowledge in mathematics also applied to modelling problems of natural phenomena.

M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica 1 con elementi di geometria e algebra lineare, Zanichelli, Bologna W. Dambrosio, Analisi Matematica. Fare e comprendere, Zanichelli C.B Boyer, Storia della matematica, Mondadori

To provide to the student the knowledge of the mathematical instruments and concepts necessary to face the problems along the degree course in Chemistry. They will be able to use the learned methods in the solution of mathematical problems. Communication skills: the students will be able to use a suitable mathematical language in relation to the course arguments and methods. Making judgements: stimulate the critical sense in the justification of the strategy adopted in the solution of the exercises.

Basic competencies in Mathematics achieved during the High School.

Interactive lectures, practical exercises, use of software to promote classroom participation and provide formative feedback, use of the university's Moodle platform and mathematical software. Workshop activities promoting cooperative learning and the development of problem-solving skills. Innovative teaching activities.

Learning monitoring: workshops and activities also supported by the use of the Moodle platform of the University. These activities have an educational goal: they are discussed and corrected with the students.
During classroom discussions, the origin and evolution of mathematical ideas and theories is analysed, and their foundations, concepts and methods will be explored. The factors that influenced, favoured or hindered its development is also examined, along with the historical interactions of mathematics with other scientific disciplines.
Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/services-students-physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs can refer to the teacher in charge of the course to define the examination modalities.

The exam consists of written tests followed by an oral discussion. It is possible to access the oral discussion only if the written test has been passed
The written test may lasts between 60 and 90 minutes and consists of a minimum of 4 and a maximum of 7 exercises. The score assigned to each exercises is indicated in the exam text. The exercises require to use knowledge and methods in problem solving situations related to the contents declared in the course program. In the exercises require to justify statements and answers to check also the skills related to knowing how to communicate and argue in mathematics.
The written test is considered sufficient if the basic knowledge and skills in the resolution of the exercises are showed. Excellence is achieved by showing knowledge and skills on all the topics covered in the written test and if the student masters well the theoretical aspects and the mathematical language during the oral discussion, showing critical sense in the motivation of the adopted strategy.
During the written tests, students can consult texts and notes on paper.

Natural numbers, integers, rational numbers and real numbers: recalls structures and proprieties. Complex numbers: definitions and basic properties, polar form, algebraic operations and nth roots. Basic of Algebra. Outlines of historical-epistemological aspects related to the development of algebra. Real functions of one variable: domain, co-domain, properties. Limits and continuity: proprieties and theorems. Historical outline of calculus. Derivatives: definition and geometrical meaning. Maxima, minima, inflection points. Root-finding algorithms. Integrals: definite and indefinite integrals; main methods of integration. Fundamental theorem of calculus. Applications of integral calculus to areas computation. Sequences and series: a brief outline.

-Knowledge and understanding: knowledge of some basic concepts and methods of mathematics. In particular: knowledge of the complex numbers. Knowledge of elementary functions. Knowledge of the continuous and derivable functions. Knowledge of the definite and indefinite integral.
- Applying knowledge and understanding: ability to deal with complex numbers. Know how to recognize function properties. Ability to find derivates and integrals. Use these skills in the interpretation of graphs.
-Making judgements: ability at realizing potential and limits of the concepts and methods adopted.
-Communication skills: ability at communicating the description and the motivations of one's own solution procedures in a clear and complete fashion.
- Learning skills: ability to use the educational materials for a critical and reflective study.