Ateneo - UPO

Real and complex numbers; Real functions of one variable; Integrals.

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

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 real problems, especially of chemical type. 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.

Lectures, training sessions, activities by means of the University Platform.

Learning monitoring and assessment: workshops and activities also supported by the use of
the Moodle platform of the University. Some of these activities have as educational goal the self-evaluation. The formative activities are discussed and corrected with the students.

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.

Real numbers: recalls on field structure, completeness and its consequences. Complex numbers: definitions and basic properties, polar form, algebraic operations and nth roots. Real functions of one variable: domain, co-domain, properties. Limits and continuity: proprieties and theorems. 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.

-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.