Mathematics
A.Y. 2024/2025
Learning objectives
The goal of the course is to introduce some mathematical concepts and tools with particular reference to the topics which can be useful for applications to Agricultural and Food Sciences. The course aims at helping students to gain an adequate theoretical understanding of the matter, as well as good computational skills. At the end of the course students should be able to exploit their math knowledge in order to set and solve simple applied problem in a rigorous way.
Expected learning outcomes
Knowledge and understanding concepts of basic mathematics and elementary Mathematical Analysis. In particular, with regard to basic mathematics, the student will be able to manipulate formulas containing algebraic expressions, percentages and proportions, radicals, logarithms and exponentials, to solve equations and inequalities, to use the main tools and techniques of analytical geometry, plane and solid geometry and trigonometry. As far as elementary Mathematical Analysis is concerned, the student will be able to draw and use graphics of real functions of one variable in many different frameworks, to calculate limits, derivatives and integrals and to use these concepts for describing and solving real problems. Moreover, students will be able to understand and execute autonomously simple mathematical steps commonly used in the scientific literature of his own sector.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
1. Numerical sets: the sets N, Z, Q, R. The real line and the symbols of ± ∞. Absolute value, nth roots, logarithms and exponentials: definitions and properties. Percentages, averages and proportions and their use in solving real problems (1/2 CFU).
2. Equations and inequalities: I and II degree and reducible to them, fractional, irrational, exponential and logarithmic, trigonometric, irrational, with absolute values; inequality systems (1/2 CFU).
3. Real functions of a real variable: The concept of function: Domain, codomain, graph, injective and surjective functions, monotone and invertible functions, composition of functions, symmetries (1/2 CFU)
4. The Cartesian plane: coordinates, straight line equations, orthogonality, parallelism, distance between points, distance of a point and a straight line, midpoint and axis of a segment. Linear functions and their applications to real problems. Two-variable inequality systems for the description of suitable regions of the plane. Goniometry and trigonometry: definitions and main properties, sinus theorem and Carnot theorem, applications to real problems (1CFU).
5. Elementary functions and their graphs: linear functions, powers and roots, exponentials, logarithms, goniometric functions, modulus and sign: definitions, properties, graphs. Elementary operations on graphs (translations, symmetries, absolute values) (1CFU)
6. Limits: definition, indeterminate forms and their resolution, significant limits, hierarchy of infinites and infinitesimals, asymptotic approximations for the resolution of indeterminate forms. Horizontal and vertical asymptotes. Continuous functions (1/2 CFU)
7. Derivatives: derivatives of elementary functions, derivation rules, derivatives of composition of functions. Relationship between continuity and derivability. Geometric meaning of the first derivative and its applications; tangent lines; monotony and search for points of maximum and minimum and applications to optimization problems. Second derivative, concavity and inflection points. Qualitative study of the graph of a function (1 CFU)
8. Integrals: Indefinite integrals: notion of primitive function, primitives of elementary functions, search for primitives. Integration methods (immediate integrals, by substitution, by parts, integration of rational functions). Definite integrals: Fundamental Theorem of Integral Calculus and its applications. Calculation of areas of flat regions. Real problems that can be solved by using integrals. (1CFU)
2. Equations and inequalities: I and II degree and reducible to them, fractional, irrational, exponential and logarithmic, trigonometric, irrational, with absolute values; inequality systems (1/2 CFU).
3. Real functions of a real variable: The concept of function: Domain, codomain, graph, injective and surjective functions, monotone and invertible functions, composition of functions, symmetries (1/2 CFU)
4. The Cartesian plane: coordinates, straight line equations, orthogonality, parallelism, distance between points, distance of a point and a straight line, midpoint and axis of a segment. Linear functions and their applications to real problems. Two-variable inequality systems for the description of suitable regions of the plane. Goniometry and trigonometry: definitions and main properties, sinus theorem and Carnot theorem, applications to real problems (1CFU).
5. Elementary functions and their graphs: linear functions, powers and roots, exponentials, logarithms, goniometric functions, modulus and sign: definitions, properties, graphs. Elementary operations on graphs (translations, symmetries, absolute values) (1CFU)
6. Limits: definition, indeterminate forms and their resolution, significant limits, hierarchy of infinites and infinitesimals, asymptotic approximations for the resolution of indeterminate forms. Horizontal and vertical asymptotes. Continuous functions (1/2 CFU)
7. Derivatives: derivatives of elementary functions, derivation rules, derivatives of composition of functions. Relationship between continuity and derivability. Geometric meaning of the first derivative and its applications; tangent lines; monotony and search for points of maximum and minimum and applications to optimization problems. Second derivative, concavity and inflection points. Qualitative study of the graph of a function (1 CFU)
8. Integrals: Indefinite integrals: notion of primitive function, primitives of elementary functions, search for primitives. Integration methods (immediate integrals, by substitution, by parts, integration of rational functions). Definite integrals: Fundamental Theorem of Integral Calculus and its applications. Calculation of areas of flat regions. Real problems that can be solved by using integrals. (1CFU)
Prerequisites for admission
As a first semester course in the first year, there are no specific prerequisites other than those required for entrance to the degree course.
Teaching methods
Frontal lessons, exercises, use of educational software, group work, interdisciplinary workshops, use of didactic games as a motivational lever for the learning of the subject and as a tool of verification and self-evaluation on curricular themes. The course uses the e-learning platforms MyAriel where weekly exercises and other teaching materials related to the topics covered in the lesson are uploaded. Attendance at the course, although not compulsory, is strongly recommended.
Teaching Resources
Silvia Annaratone, Matematica sul campo. Metodi ed esempi per le scienze della vita 2/Ed. con MyLab
(ISBN 9788891910615, Euro 29,00)
Esercizi e attività interattive su MyAriel
(ISBN 9788891910615, Euro 29,00)
Esercizi e attività interattive su MyAriel
Assessment methods and Criteria
To take the exam, students must be duly registered through SIFA and must report to the front of the classroom 15 minutes before the start of the written test with photo ID and protocol sheets.
The exam consists of a written test and an oral test, both of which are mandatory.
The written test, lasting 120 minutes, consists of seven open-ended exercises about both basic mathematics topics and topis covered in the course, and is designed to test the student's ability to use mathematical methods and tools in different situations and to identify appropriate strategies for problem solving. The written test is considered passed if the student has achieved a score of at least 18/30.
A form may be brought along during the written test, which consists of one side of A4 paper containing only those formulas that the candidate considers useful. No exercises may be given on the form. The form will besigned by the professor at the beginning of the test and should be handed in with the paper (it is recommended to bring a photocopy and not the original). During the written test it is forbidden to consult books, notes, use calculators of any kind, computers and cell phones. It is also forbidden to communicate with fellow students, under penalty of immediate expulsion from the classroom. During the entire written test it is also forbidden to leave the classroom: in particular during the first hour it will not be possible to leave the classroom for any reason. At the end of the first hour, students who wish to do so may hand in or withdraw.
The oral test may be taken only if the written test is passed with a grade greater than or equal to 18/30, and only in the same session as the written test. The oral test is intended to assess the student's ability to use appropriate language and symbology, to focus on the solution path of a problem through algebraic, analytical and graphical models, and to analyze and interpret the results obtained. Students who, having passed the written test, do not show to take the oral test will be rejected.
The final exam grade will be the arithmetic average of the written and oral grades and will be expressed in thirtieths.
Simulations of written tests will be available on the teaching Moodle site.
Students with SLD or disability certifications are kindly requested to contact the teacher at least 15 days before the date of the exam session to agree on individual exam requirements. In the email please make sure to add in cc the competent offices: [email protected] (for students with SLD) o [email protected] (for students with disability).
The exam consists of a written test and an oral test, both of which are mandatory.
The written test, lasting 120 minutes, consists of seven open-ended exercises about both basic mathematics topics and topis covered in the course, and is designed to test the student's ability to use mathematical methods and tools in different situations and to identify appropriate strategies for problem solving. The written test is considered passed if the student has achieved a score of at least 18/30.
A form may be brought along during the written test, which consists of one side of A4 paper containing only those formulas that the candidate considers useful. No exercises may be given on the form. The form will besigned by the professor at the beginning of the test and should be handed in with the paper (it is recommended to bring a photocopy and not the original). During the written test it is forbidden to consult books, notes, use calculators of any kind, computers and cell phones. It is also forbidden to communicate with fellow students, under penalty of immediate expulsion from the classroom. During the entire written test it is also forbidden to leave the classroom: in particular during the first hour it will not be possible to leave the classroom for any reason. At the end of the first hour, students who wish to do so may hand in or withdraw.
The oral test may be taken only if the written test is passed with a grade greater than or equal to 18/30, and only in the same session as the written test. The oral test is intended to assess the student's ability to use appropriate language and symbology, to focus on the solution path of a problem through algebraic, analytical and graphical models, and to analyze and interpret the results obtained. Students who, having passed the written test, do not show to take the oral test will be rejected.
The final exam grade will be the arithmetic average of the written and oral grades and will be expressed in thirtieths.
Simulations of written tests will be available on the teaching Moodle site.
Students with SLD or disability certifications are kindly requested to contact the teacher at least 15 days before the date of the exam session to agree on individual exam requirements. In the email please make sure to add in cc the competent offices: [email protected] (for students with SLD) o [email protected] (for students with disability).
MAT/02 - ALGEBRA - University credits: 6
Practicals: 48 hours
Lessons: 24 hours
Lessons: 24 hours
Professor:
Morando Paola
Shifts:
Turno
Professor:
Morando PaolaProfessor(s)