Natural Sciences

Activity type

Discipline matematiche, informatiche e statistiche

SSD

MATH-03/A

Year

1st year

Semester

2nd semester

CFU

5

Hours distribution

50 classroom hours

Lecturers

STEFANO ROSSI

Activity type

Discipline matematiche, informatiche e statistiche

SSD

MATH-03/A

Year

1st year

Semester

1st semester

CFU

4

Hours distribution

40 classroom hours

Lecturers

LUCA MASSIMO ANDREA MARTINAZZI

Dublin Descriptors

Cultural relevance of mathematical thought

Knowledge and understanding: learning elementary techniques of the theory of integration and differential equations, and how to solve some basic examples; knowledge of basics of linear algebra and plane geometry with application to statistics.

Applying knowledge and understanding: at the end of the course students will be able to compute simple integrals by parts or substitution, to solve simple differential equations and problems about lines and vectors in plane geometry, with some applications to statistics.

Critical and judgmental skills: at the end of the course students will have learned the basic ideas of the theory of integration and of differential equations, and some algebraic and geometrical tools needed to understand and express basic concepts of physics and statistics in the appropriate mathematical language.

Communication skills: ability of exposition with clarity, also in written form, of notions, theorems and methods learned during the course.

Learning skills: the acquired knowledge will allow the students to undertake successfully the subsequent study of more technical notions of mathematical analysis, physics and statistics.

To understand the fundamental principles of algebra, geometry, differential and integral calculus for functions of a real variable. To develop the ability to qualitatively analyze the behavior of a function and interpret its properties, including through graphical representations. To understand the role of mathematics as a language and fundamental tool for the modeling, analysis, and interpretation of phenomena in the natural sciences and, more broadly, in the applied sciences.

Knowledge of the topics covered in the first module of Elemantary Calculus is required. Attendance at the mathematics preparatory courses organized by the Faculty of Mathematical, Physical and Natural Sciences is strongly recommended.

Module: ADVANCED CALCULUS
Continuous functions, Intermediate Value Theorem, and Existence Theorem for zeros.
Differentiation and its geometric interpretation, differentiation rules, derivatives of elementary functions, differentiation of composite functions.
Absolute and relative maxima and minima, higher-order derivatives, concavity and convexity, graph of functions.
Antiderivatives and definite integrals, properties, integration by parts and change of variables, computation of areas.
Differential equations: models and notable examples.
Solution of first-order ordinary differential equations in normal form: linear equations and equations solvable by separation of variables.
Second-order linear differential equations.
Introduction to functions of two variables: graphs as surfaces, partial derivatives, level curves, gradient vector.


Module: ELEMENTARY CALCULUS
N/D

Module: ADVANCED CALCULUS
Matematica per le Scienze, A. Guerraggio, Pearson
Matematica per le Scienze della Vita, D. Benedetto, M. Degli Esposti, C. Maffei, Zanichelli



Module: ELEMENTARY CALCULUS
N/D

Module: ADVANCED CALCULUS
Le matematiche, A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrentev, Bollati Boringhieri


Module: ELEMENTARY CALCULUS
N/D

The course is based on lectures in classroom, aiming to transfer to students the fundamental concepts of the discipline. Lecture (60%), exercise sessions (40%).

Lecture attendance is strongly recommended, as it facilitates a better understanding of the topics covered in the course.

The examination is designed to assess students' learning through a written exam (consisting of problems similar to those solved during the exercise sessions) and, If deemed appropriate by the professor, by a short oral exam based on the discussion of the main topics covered in the course. The written exam lasts approximately two-three hours and may be replaced by two intermediate tests, each lasting about two hours. To pass the examination, students must obtain a grade of at least 18/30. They are expected to demonstrate a satisfactory understanding of the main concepts introduced during the course and the ability to solve at least the more straightforward exercises assigned during the course.

Advanced Calculus: The first intermediate test, held halfway through the course, focuses primarily on differential calculus, optimization problems and analysis of functions. The second test, held at the end of the course, covers integral calculus and differential equations.

Module: ADVANCED CALCULUS

• Continuous functions, Intermediate Value Theorem, and Existence Theorem for zeros.Differentiation and its geometric interpretation, differentiation rules, derivatives of elementary functions, differentiation of composite functions.Absolute and relative maxima and minima, higher-order derivatives, concavity and convexity, graph of functions.Antiderivatives and definite integrals, properties, integration by parts and change of variables, computation of areas.Differential equations: models and notable examples.Solution of first-order ordinary differential equations in normal form: linear equations and equations solvable by separation of variables.Second-order linear differential equations.Introduction to functions of two variables: graphs as surfaces, partial derivatives, level curves, gradient vector.