Unit MATHEMATICS
 Course
 Agricultural and environmental sciences
 Studyunit Code
 80010406
 Curriculum
 In all curricula
 Teacher
 Luca Zampogni
 Teachers

 Luca Zampogni
 Hours
 54 ore  Luca Zampogni
 CFU
 6
 Course Regulation
 Coorte 2021
 Offered
 2021/22
 Learning activities
 Base
 Area
 Matematiche, fisiche, informatiche e statistiche
 Academic discipline
 MAT/05
 Type of studyunit
 Obbligatorio (Required)
 Type of learning activities
 Attività formativa monodisciplinare
 Language of instruction
 Italian
 Contents
 General properties of realvalued functions. Sequences and iterative processes. Limits and continuity of a function. Properties of a continuous function. Elements of differential calculus: the derivative of a function. Rules of differentiation and properties of a differentiable function. Qualitative graph of a function. Riemann integral. Areas and primitives of a function. Rules of integration.
 Reference texts
 James Stewart: "Calcolo. Funzioni di una Variabile", Maggiolini Ed.
Lecture notes written by the professor  Educational objectives
 To understand and elaborate phenomena in a mathematica framework, as to develop and study simple but useful mathematical models.
To learn to use mathematical objects and to understand the results which are furnished by calculus.  Prerequisites
 The following basic knowledge is required for the student to understand and reach the objectives of the course of Mathematics:
Numerical sets: natural numbers, integer numbers, rational numbers and related algebraic structures. Fundamental properties of operations. Oriented line, irrational numbers. The real numbers.
Proportions and percentages.
Basis of Euclidean geometry: points, segments, halflines, angles. Talete’s Theorem. Triangles. Pitagora’s and Euclid’s Theorems.
Powers and scientific representation. Fundamental properties of powers. Powers with random exponent. Roots of numbers. Logarithms and their properties.
Fundamental techniques of polynomial calculus: decomposition, product, L.C.M. and G.D.C., divisions. Reduction of a rational polynomial expression.
Basic concepts of plane analytical geometry: cartesian coordinate system, midpoint and distance between two points, straight line equations.
Firstdegree equations and inequalities.  Teaching methods
 Lectures and exercises with the support of a Tutor
 Other information
 Optional but recommended attendance
 Learning verification modality
 The exam is made of both a written and oral test.
The written test consists of the solution of some problems and has a duration of at most three hours. It’s objectives are the following:
The understanding of the proposed problems;
The handling of mathematical instruments;
The interpretation of the results obtained.
The oral test consists of a talk of about 30 minutes and is aimed at testing the degree of comprehension reached by the student and his skills in handling mathematical objects, with particular attention to his capacity of finding connections between the topics explained.  Extended program
 Topology of the real line. Intervals and halflines. Lines and parabolas. Exponential and logarithmic equations and inequalities. Functions. Symmetries and transformations. Linear and parabolic mathematical models. Sequences and series. Iterations. Exponential growth. Limits. Continuity and properties of continuous functions defined in an interval. Methods to compute the limits. Derivative. Definition and applications. Theorems concerning differentiable functions. Monotonicity, maxima and mimina. Second derivative. Convex functions. Primitive and area. The Riemann integral. Integrable functions and properties. Mean value, Integral function and application. The fundamental theorem of calculus.