# Unit MATHEMATICS

Course
Agricultural and environmental sciences
Study-unit 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
MAT/05
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents
General properties of real-valued 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, half-lines, 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.

First-degree 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 half-lines. 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.
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