Unit MATHEMATICS
- Course
- Food science and technology
- Study-unit Code
- GP000934
- Curriculum
- Tecnologie agro-alimentari
- Teacher
- Rita Ceppitelli
- Teachers
-
- Rita Ceppitelli
- Rita Ceppitelli
- Hours
- 22 ore - Rita Ceppitelli
- 32 ore - Rita Ceppitelli
- 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
- To provide students with basic knowledge about formulating, solving and discussing simple mathematical models in biology, economy, engineering. Elementary functions. Equations and inequalities. Sequences, iterative process. Limit, continuity, derivative. Riemann integral and the area of regions between two graphs.
- Reference texts
- James STEWART “CALCOLO Funzioni di una variabile”, Maggioli Editore 2013. (Original english language edition: Calculus-Concepts and Contexts, 2nd edition.)
Lecture notes available online. - Educational objectives
- Knowledge:
1. Elementary functions, exponential and logarithmic maps.
2. Sequences
3. Limits.
4. Continuity of functions.
5. Derivatives and applications. Some elements of differential calculus.
6. Critical and extremal points.
7. Integrals and applications.
Ability:
1. To define and analyze simple mathematical models.
2. To solve equalities and inequalities of various kind.
3. To draw, interpret and study the graphs of functions.
4. To compute limits, derivatives and integrals. - 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.
- Teaching methods
- The course is organized as follows: lectures on all subjects of the course, classroom exercises to prepare the students for the written exams. It is planned a tutor teaching activity.
- Other information
- Attendance: optional but strongly recommended
- Learning verification modality
- The exam is made of both a written and oral test.The written test consists of the solution of four problems and has a duration of at most three hours. Its 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
- A - B. Functions, Equations and inequalities. Definition of a single-valued function. Monotonic and inverse functions. Operation with functions, composite functions. Algebraic functions: linear, quadratic, cubic, rational, nth root, absolute-value, greatest-integer functions. Trigonometric functions. Geometric transformations : translations and reflections. Using Excel or Computer Algebra Systems to explore the main properties in their graphs.
Linear, quadratic, rational, irrational, modulus (absolute value) equations and inequalities. Linear systems, Cramer's rule.
C. Iterative processes - Exponential functions. Sequences, recursive formula. Arithmetic and geometric progressions.
Logarithmic and exponential functions and their graphs. Logarithmic and exponential equations and inequalities.
Applications: mitosis, Fibonacci sequence, simple and compound interest in Economy, radioactive decay. Semilogarithmic coordinate systems.
D. Limits. Introduction to limits. Theorem on uniqueness of limits. Infinite limits and limits at infinity. Continuity of a function : definition and basic theorems. The types of discontinuity. The calculation of limits. Some special limits. The squeezing Theorem.
E . Derivatives. Tangent lines and derivatives: geometric interpretation. The derivative as the rate of change. Some differentiation formulas. The derivative of composite and inverse functions. The L'Hôpital's Theorem. Estrema of the functions. The Férmat's Theorem. Concavity, convexity, derivative test for convexity.
F. Integral. Riemann integral. The method of exhaustion. The area of regions between two graphs. Mean value theorems for integrals. Indefinite integrals. Fundamental theorem of integral calculus. Integration by substitution (elementary integrals).