D3a - Dipartimento di Scienze Agrarie, Alimentari e Ambientali - Guida degli insegnamenti (Syllabus)

Elementary algebra, equations and inequalities, goniometry and analytic geometry.

The course will be conducted through lectures in both theoretical and practical content.

*Knowledge and understanding*

After completing the course, students will be able to understand the key issues and dimensions of mathematical analysis (continuity, differentiability, integrability).

*Applying knowledge and understanding*

At the end of the course students will also use the following main tools of analysis: limits, derivatives, integrals. Using such knowledge, they will need to be able to solve optimization problems.

*Cross-expertise*

Exercises done in class with the mode of solution concepts of practical applications and discussions will enable students to improve their autonomy and their skills in terms of communication, learning and critical approach.

The set, R, of real numbers and topology in R. Function algebra. Elementary functions (the first- and the second-degree polynomials, the exponential, the logarithm and the goniometric functions). Bounded functions, supremum, infimum, maximum and minimum of a function. Monotone functions. Composite and inverse functions. Limits of real functions of real variable. Calculus of elementary limits. Continuous functions and their fundamental properties. Continuous functions on intervals. Introduction to derivative: growth rate. Geometric meaning of derivative. Derivative formulas. Successive derivatives. Derivative and monotonicity. Relative maximum and minimum of derivable function. Convex functions. Asymptotes of a planar curve. Hopital’s theorems. The study of the graphs of functions. Applications of the theory of real functions to natural and biological sciences. An outline to the Integration Theory. Definite Integral and its properties. Geometric meaning of Definite Integral. Definition of Indefinite Integral and its properties. Indefinite Integral of elementary functions. Fundamental theorem of the Integral Calculus. Indefinite integral and integration methods: sum decomposition, by parts and substitution. Improper Integrals. Principles of probability theory and random variables.

*Learning evaluation methods *

The final examination is written. It consists of short exercises and questions designed to assess the learning of the topics covered and the actual ability to apply their knowledge. During the written exam it is not allowed to consult any material support.

*Learning evaluation criteria *

In the written exam, the student must demonstrate knowledge of the topics and methods for functions of several variables and classical financial mathematics. The ability to apply the acquired knowledge is evaluated by solving the assigned problems.

*Learning measurement criteria*

The final mark is attributed in thirtieths.

*Final mark allocation criteria*

The final grade is set on the basis of written exam, as the sum of the scores obtained on individual exercises. The score of each exercise is awarded on the basis of its difficulty.

E. Ballatori, L. Ferrante, Introduzione alla Biomatematica. Ed. Margiacchi-Galeno

- C.L.T. - Scienze e Tecnologie Alimentari (STAL)

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

P.I. 00382520427