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
FIRST PART - BASICS OF ALGEBRA
1- Equations and inequalities of I and II degree, fractional and irrational, system of inequalities.
2 - Functions: direct and inverse proportion, exponential and logarithmic functions,.
3 - Exponential and logarithmic equations and inequalities.
4 - Goniometric functions, equations and inequalities
5 - Trigonometry: right-angled triangle solution.
SECOND PART - MATHEMATIC ANALYSIS
1 - Real functions of real variable: domain and codomain.
2 - Limits: definition, indeterminate forms and their resolution, significant limits.
3 - Derivatives of elementary functions, derivation rules, derivatives of compound functions. Relationship between continuity and derivability.
4 - Study of the graph of a function: domain and limits, creasing and decreasing functions, first and second derivative, max/min and inflextion points, graph of the function.
5 - 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.
THIRD PART - RUDIMENTS OF FINANCIAL MATHEMATICS (Appendix to the Course)
1 - Capitalization and discount.
2 - Yield, amortization and leasing.
1- Equations and inequalities of I and II degree, fractional and irrational, system of inequalities.
2 - Functions: direct and inverse proportion, exponential and logarithmic functions,.
3 - Exponential and logarithmic equations and inequalities.
4 - Goniometric functions, equations and inequalities
5 - Trigonometry: right-angled triangle solution.
SECOND PART - MATHEMATIC ANALYSIS
1 - Real functions of real variable: domain and codomain.
2 - Limits: definition, indeterminate forms and their resolution, significant limits.
3 - Derivatives of elementary functions, derivation rules, derivatives of compound functions. Relationship between continuity and derivability.
4 - Study of the graph of a function: domain and limits, creasing and decreasing functions, first and second derivative, max/min and inflextion points, graph of the function.
5 - 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.
THIRD PART - RUDIMENTS OF FINANCIAL MATHEMATICS (Appendix to the Course)
1 - Capitalization and discount.
2 - Yield, amortization and leasing.
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 and group work as a motivational lever for the learning of the subject and as a tool of verification and self-evaluation about curricular themes.
The course uses e-learning platform Ariel, where periodically 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.
The course uses e-learning platform Ariel, where periodically 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
Any high school maths book is useful, starting from equations and inequalities, including exponential, logarithmic and trigonometric study, until the Mathematical Analysis (derivatives and integrals, study of the graph of a function.
Assessment methods and Criteria
The examination is constituted by two written tests (related to the first and second part of course) and one oral test. Both written tests can be sustained also in different periods and not sequentially, if needed. To be admitted to oral test, the result of each written test must be at least 16/30. The examination aims to evaluate the student's ability to use an appropriate language and symbolism, to focus the path of solving a problem through algebraic and graphic models and to analyze and interpret the results obtained.
Time for each written test: 2h.
Time for each written test: 2h.
MAT/01 - MATHEMATICAL LOGIC - University credits: 6
Practicals: 24 hours
Lessons: 36 hours
Lessons: 36 hours
Professor:
Carone Fabiani Filippo
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Professor(s)