Ateneo - UPO

The course aims at providing students with basic mathematical knowledge applied to biological problems.

Villani, Gentili: Matematica. Comprendere e interpretare fenomeni delle scienze della vita, Mc Graw Hill, 2012. Benedetto, Degli Esposti, Maffei: Matematica per le scienze della vita, C.Ed. Ambrosiana. Teaching material is available on the University Platform.

Getting students to learn some elementary concepts and methods of mathematics useful to deal with the typical topics of the applications of mathematics to empirical science. Developing competences in order to solve simple math problems and to be able to effectively communicate the obtained results.

Basic competencies in Mathematics achieved during the High School.

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

Learning monitoring: workshops and tutoring 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.
Through the lectures, the discussions of specific exercises and the individual learning, we espect the student to be familiar with the basic mathematical tools described in the program, to be able to use and explain the main techniques and notions presented in the lectures, to be able to apply such techniques in simple contexts.

The final exam is a written exam (90 mins) possibly followed by a discussion of the test. It consists in 5 to 7 problems or questions. The weight of each problem in the determination of the final grade is declared in the text. Each problem aims at verifying the student's knowledge and his/her ability in applying the knowledge to problems related to the contents of the course. Some problems require a proper explanation in order to verify the competence of the student in communicating and argumentation in Mathematics. During the exam the students can use textbooks and personal notes.

1. Number systems. Approximations. Percentages. Mathematical modelling: problems with linear equations. Equations and inequalities.
2. Analytic geometry: Cartesian coordiante system, straight lines and parabolae. Linear systems.
3. Real functions, graphs, links between graphs and formulas. Trigonometric functions and examples of periodic phenomena. Examples of exponential and logarithmic growth. Function composition. Curves intersections. Limits and continuity.
4. Derivatives. Continuity and differentiability. Derivatives of elementary functions and their graphical representation. Increasing and decreasing functions, maxima and minima of a function. Applications of differential calculus. Worked examples on special functions with major applications in Biology.
5. Primitives. Integrals. Fundamental theorem of calculus. Applications of integration.
6. Examples of differential equations. Differential models of biologic phenomena.

-Knowledge and understanding: knowledge of some basic concepts and methods of mathematics, in particular: real numbers and their representations, main elementary functions, derivative and its geometric interpretation, simple integrals and calculation of areas.

- Applying knowledge and understanding: ability at applying these concepts and methods in the medialization of simple problems (e.g., percentage variations) and 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.