Unit MATHEMATICS
- Course
- Economics and culture of human nutrition
- Study-unit Code
- GP000458
- Curriculum
- In all curricula
- Teacher
- Luca Zampogni
- Teachers
-
- Luca Zampogni
- Hours
- 54 ore - Luca Zampogni
- CFU
- 6
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- Learning activities
- Base
- Area
- Matematiche, fisiche, informatiche e statistiche
- Academic discipline
- 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.