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

Basic knowledge of algebra, analytic geometry and trigonometry.

The course relies on frontal lectures supplemented with smaller discussion sections and tutorials.

**Knowledge**. The course enables students to acquire the fundamental knowledge about differential and integral calculus and the ability to solve scientific problems using simple mathematical modeling.

**Applying knowledge and understanding**. The main aim of this course is to provide a fully development ability of the students in using differential and integral calculus to study graphs of functions and to solve simple scientiﬁc problems which derive from a variety of application areas, such as biology, economics and physics.

**Cross-expertise**. (i) ability to identify mathematical tools suitable to solve the problems arising from agricultural research. (ii) ability to learn and interpret the mathematical models used in the scientific studies in agronomy.

Course contents: The theory of real functions of a real variable. 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. The de L’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. Random Variables, Distribution Functions, and Expectation of a random variable. Normal Distribution.

**Learning evaluation methods**. The learning evaluation of the students is carried out by a written test.

**Learning evaluation criteria**. To pass successfully the examination, the student must demonstrate that he/she has fully understood the mathematical concepts presented in the course, is able to use them in solving simple scientific problems, and has ability of synthesis and clarity in written communication.

**Learning measurement criteria**. Attribution of the final mark up to thirty.

**Final mark allocation criteria**. The oral examination consists of five questions concerning the subjects listed in the teaching program, each of ones will be quantified in the range 0 - 6. The degree of 30 “cum laude” is attributed when the student demonstrates complete ability of synthesis and clarity in written communication.

Lecture notes on elementary probability theory

Heinbockel J.H., 2012. “**Introduction of calculus vol.1**”. free ebook.

Villani V., Gentili G., 2012. “**Matematica. Comprendere e interpretare fenomeni delle scienze della vita**”. McGraw-Hill Education.

**Tutorial session**

Only upon appointment by email.

- C.L.T. - Scienze e Tecnologie Agrarie Curriculum TECNOLOGIE AGRARIE (STA - TA)
- C.L.T. - Scienze e Tecnologie Agrarie Curriculum VITICOLTURA ED ENOLOGIA (STA - VE)

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

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

P.I. 00382520427