Mathematics
A.Y. 2024/2025
Learning objectives
The course aims to introduce some mathematical concepts and methods, with particular attention to the development of the most useful aspects of the discipline for a real understanding of the topics covered in the courses characterizing the agricultural and environmental degree courses.
The aim is to provide students with an adequate theoretical understanding of the topics covered, together with an adequate ability to perform the calculation procedures involved and provide the theoretical and technical tools to formulate and solve in a rigorous way simple applicative problems.
The course has as a transversal objective to help students develop an effective method of study, useful not only to face other exams during the academic career but also for the self-training required in many working situations.
The aim is to provide students with an adequate theoretical understanding of the topics covered, together with an adequate ability to perform the calculation procedures involved and provide the theoretical and technical tools to formulate and solve in a rigorous way simple applicative problems.
The course has as a transversal objective to help students develop an effective method of study, useful not only to face other exams during the academic career but also for the self-training required in many working situations.
Expected learning outcomes
At the end of the course, the student will be able to:
· manipulate formulas containing algebraic expressions, percentages and proportions, radicals, logarithms and exponentials, solve equations and inequalities, use the main tools and techniques of analytical geometry, plane and solid geometry and trigonometry;
· plot and interpret graphs of functions of one variable in different contexts, calculate limits, derivatives and integrals, and use these concepts to describe and solve real problems;
· understand and independently perform some simple mathematical steps commonly used in the scientific literature of agricultural and environmental sciences;
· critically use some simple software to describe and address applicative problems;
· acquire some additional new mathematical knowledge independently.
· manipulate formulas containing algebraic expressions, percentages and proportions, radicals, logarithms and exponentials, solve equations and inequalities, use the main tools and techniques of analytical geometry, plane and solid geometry and trigonometry;
· plot and interpret graphs of functions of one variable in different contexts, calculate limits, derivatives and integrals, and use these concepts to describe and solve real problems;
· understand and independently perform some simple mathematical steps commonly used in the scientific literature of agricultural and environmental sciences;
· critically use some simple software to describe and address applicative problems;
· acquire some additional new mathematical knowledge independently.
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, vertical and oblique 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; change rates; application 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. (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, vertical and oblique 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; change rates; application 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. (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 e-learning platform associated with the textbook, use of educational software, group work, 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 e-learning platforms (Ariel and Moodle) 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)
Exercises and interactive activities on Ariel
(ISBN 9788891910615, Euro 29,00)
Exercises and interactive activities on Ariel
Assessment methods and Criteria
To take the exam, students must be duly enrolled through SIFA and must report to the front of the classroom 15 minutes before the start of the written test, equipped with photo ID and protocol sheets.
The written test is 120 minutes in length and consists of seven open-ended exercises related to basic mathematics topics and those 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 out of 30.
No books or notes may be consulted during the writing, but it is allowed to bring a form organized in one double-sided A4 sheet (2 double-sided A4 sheets for students with DSA). The formulary may include formulas and a direct example of application but not the performance of exercises. Also, during the written test you cannot communicate with other students, under penalty of immediate expulsion from the classroom. During the first written test, you may not leave the classroom; you may hand in or withdraw after one hour from the start of the test.
The oral test may be taken only if the written test is passed with a grade greater than or equal to 18 out of 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 appear 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 written test is 120 minutes in length and consists of seven open-ended exercises related to basic mathematics topics and those 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 out of 30.
No books or notes may be consulted during the writing, but it is allowed to bring a form organized in one double-sided A4 sheet (2 double-sided A4 sheets for students with DSA). The formulary may include formulas and a direct example of application but not the performance of exercises. Also, during the written test you cannot communicate with other students, under penalty of immediate expulsion from the classroom. During the first written test, you may not leave the classroom; you may hand in or withdraw after one hour from the start of the test.
The oral test may be taken only if the written test is passed with a grade greater than or equal to 18 out of 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 appear 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/07 - MATHEMATICAL PHYSICS - University credits: 6
Practicals: 48 hours
Lessons: 24 hours
Lessons: 24 hours
Professors:
Morando Paola, Spreafico Maria Luisa Sonia
Shifts:
Educational website(s)
Professor(s)