Teaching code

4S00030

Academic staff

Sisto Baldo, Giacomo Canevari

Coordinator

Sisto Baldo

Credits

12

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

Period

Semester 1  dal Oct 1, 2024 al Jan 31, 2025.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The course introduces to the basic concepts and techniques of differential and integral calculus emphasizing methodology and applications over the more formal aspects. The aim is to provide the students with basic tools for addressing scientific issues which can be formalized in the language and methods of calculus. At the end of the course the student must be able to demonstrate an adequate synthesis and abstraction ability, be able to recognize and produce rigorous demonstrations and be able to formalize and solve problems of moderate difficulty, limited to the syllabus of the teaching. Main topics: real numbers, sequences and series, limits, continuous functions, differential and integral calculus for functions of one real variable, introduction to ODEs, topology of the real line.

Prerequisites and basic notions

An adequate knowledge and the mathematical and scientific skills typical of high school are required:
- Sets and functions, numerical and literal calculus, methods for solving equations and inequalities (and systems of equations and inequalities) of the first and second degree.
- Geometric properties of the main plane and solid figures and their elementary properties.
- Representation in the Cartesian plane of geometric elements.
- Basics of trigonometry.
- Functions, graphs, relations.
- Powers, roots, absolute value.
- Exponential and logarithm and their graphs.
- Trigonometric functions and their graphs.
- Solving simple equations and inequalities constructed with these functions.
- Representation of data, relations and functions with formulas, tables, bar charts and other graphing modes.
- Logical deductions of moderate complexity and logical implications between elementary sentences.

Program

Properties of real numbers. Sequences and series. Limits. Continuous functions. Differential and integral calculus for functions of one real variable. Elementary ordinary differential equations.
Topology of the real line.

Bibliography

Didactic methods

Lectures and exercise sessions in class. Tutoring in class and for groups of students. Home assignments.
Notes, exercises and additional material will be available on Moodle.
The rights of students will be preserved in situations of travel limitation or confinement due to national provisions to combat COVID or in particular situations of fragile health. In these cases, you are invited to contact the teacher directly to organize the most appropriate remedial strategies.

Learning assessment procedures

The final exam consists of a written test followed, in case of a positive result, by an oral test. The written test consists of some exercises on the program: students are exonerated from the first part of the test if they pass a mid-term test at the beginning of december.

Evaluation criteria

The written test evaluates the ability of students at solving problems pertaining to the syllabus of the course, and also their skills in the analysis, synthesis and abstraction of questions stated either in the natural language or in the specific language of mathematics. The written test is graded on a scale from 0 to 30 points (best), with a pass mark of 18/30.
The oral exam aims at verifying the ability of students at constructing correct and rigorous proofs and their skills in analysis, synthesis and abstraction.

Criteria for the composition of the final grade

The written exam is graded on a scale from 0 to 30. If replaced with the two mid-term tests, the corresponding results are averaged to obtain the final marks.
The oral exam is graded on a scale from -5 to +5 point, which are added to the marks earned in the written test.

Exam language

Italiano