Mathematics

Degree course: 
Corso di First cycle degree in ENVIRONMENTAL AND NATURAL SCIENCES
Academyc year when starting the degree: 
2019/2020
Year: 
1
Academyc year when helding the course: 
2019/2020
Course type: 
Basic compulsory subjects
Credits: 
9
Period: 
First Semester
Standard lectures hours: 
72
Detail of lecture’s hours: 
Lesson (72 hours)
Requirements: 

The course does not require special prerequisites.

Final Examination: 
Orale

The objective of the final exam is to verify the level of achievement of the educational objectives, evaluating in the first place the possession of the basic cognitive elements and therefore the student's ability to use them autonomously for the resolution of real problems. The exam topics will be consistent with the types of topics and the methods of study and analysis related to the topics covered. The exam includes a written test that serves only as a general orientation test and does not include a grade, and an oral test in which the student must in particular be able to explain what he has done to the writing.
To pass the exam it is necessary to be able to explain the theorems and the fundamental concepts, also with the aid of mnemonic means, and to be able to perform simple but meaningful exercises in relation to the theory.
The final evaluation, expressed in thirtieths, will take into account the completed learning (60%), the ability to apply the theoretical concepts (20%), the autonomy of judgment (10%) and the communication skills

Assessment: 
Voto Finale

The course aims to provide the student with the knowledge and skills necessary to face the study of Mathematics, allowing him to acquire a rigorous scientific method of reasoning and to apply this method to the study of the subjects he will address in the course of future studies, using the knowledge and skills acquired. In particular, he is required to acquire knowledge related to:
- Acquisition of theoretical and operational skills in the field of differential and integral calculus
- Acquisition of the rudiments of the Probability and Statistics calculation
- Acquisition of basic concepts of Algebra
The student will develop specific competences related to the development of communication skills, a deeper knowledge of the scientific language and the skills of learning and individual judgment.

Real numbers
Functions and Limits
Basic functions.
Differential calculus
Integral calculus
Differential equations
Linear Algebra
Complex Numbers
Statistics

The topics covered will allow the student to acquire the basic and advanced knowledge for dealing with the specific topics of the subject, thanks to the skills and competences developed, and will also allow him to develop further abilities to apply the knowledge acquired to the problems of the environmental context, for which the knowledge and understanding of mathematics are of fundamental importance.

Real numbers - elementary properties of real numbers. Absolute value. Power and logarithm. Lower and upper extremity

Functions and Limits - monotone functions. Limits and their properties. Continuity and fundamental properties of continuous functions.

Basic functions - Trigonometric, exponential, hyperbolic and inverse functions.

Differential calculus - Derivatives of real functions and their properties. Theorems of Rolle, Lagrange and Cauchy. De L’Hopital theorem on limits. Taylor polynomials.

Integral calculus - Integration of continuous functions. Integral functions. First and second fundamental Theorem of Calculus.
Integration by parts and by substitution.

Differential equations - Overview of the first order differential equations. Solution of the Cauchy problem for linear equations and separable variables.

Linear Algebra - Real vector spaces. Matrices and linear applications. Determinants. Solutions of linear systems of equations.

Complex Numbers - The complex field as an extension of the real one. The Complex plane. Vector, polar, exponential form. Geometry of the sum and product operations in the complex plane. N-th roots of a complex number.

Statistics - Average, mode, median. Standard deviation and variance. Least squares - Statistical significance.
Graphic representations and how to interpret them.

It is suggested the use of a good high school text that includes also a chapter on Statistics and Probability.

Alternatively,
Vinicio Villani, Graziano Gentili, Mathematics. Understanding and interpreting life science phenomena. McGraw-Hill Education

The educational objectives of the course will be achieved through classroom lectures supported by videoconferencing. At the beginning of the lessons, at the request of the students, the teacher will provide clarifications and insights on the topics covered in the previous lessons. It will also be possible to ask for clarifications at any time during the lessons.

Students are received by previous telephone appointment..

Professors