OVERVIEW

The main aim is to provide students with the fundamental elements of differential and integral calculus for functions of one variable,  also by using graphing software.

AIMS AND CONTENT

LEARNING OUTCOMES

This course aims to provide students with basic knowledge on various topics, such as:
- numerical sets, functions and elementary functions;
- the approximation of real functions through polynomials;
- single-variable differential calculus;
- the problem of measurement: integral calculus;
- using spreadsheets for the analytical study of a function and its graphic representation.
 

AIMS AND LEARNING OUTCOMES

The main expected learning outcomes for this course are:
- mastering mathematical notation;
- knowing the properties and graphs of the main elementary functions;
- being able to follow logical chains of reasoning;
- mastering simple demonstration techniques;
- being able to solve exercises and discuss the reasonableness of the results.

TEACHING METHODS

Lectures with the use of the blackboard.  60 hours of teaching (2/3 theory 1/3 exercises).

SYLLABUS/CONTENT

• Real numbers: Real numbers. Maxima, minima, upper extreme, lower extreme.
• Functions: Elementary functions, compound function, inverse function.
• Limits and continuity: Limits of functions. Continuity. Global properties of continuous functions. Theorems of zeros and intermediate values. Weiestrass Theorem.
• Derivatives: Derivative. Tangent line. Derivative of compound functions and the inverse function. Lagrange's theorem. De l'Hôpital's rule. 
• Integrals: Indefinite integral. Area of a plane region. Integral function. Fundamental theorem of integral calculus. Some integration techniques.

Teaching contributes to achieving the following Sustainable Development Goals of the UN 2030 Agenda

• Goal 4: provide quality, equitable and inclusive education and learning opportunities for all
• Goal 5: Achieve gender equality and empower all women and girls

RECOMMENDED READING/BIBLIOGRAPHY

• G. Crasta, A. Malusa, Elementi di Analisi Matematica e Geometria con prerequisiti ed esercizi svolti, La Dotta,  2015

Lecturer's notes (in italian) are available.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://corsi.unige.it/9274/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written test with open questions

To take part in the written test, you must register by the deadline at
https://servizionline.unige.it/studenti/esami/prenotazione

ASSESSMENT METHODS

The exam is aimed at verifying the student's mastery of calculation techniques and knowledge of the main tools of differential and integral calculus, introduced in the course of the course, and consists of three exercises consisting of several questions of varying difficulty.   The student must be able to correctly solve the exercises and be able to justify the steps required to obtain the final result and use the correct formalism. 
The duration of the test is 2.30 hours. Notes and textbooks may be consulted and the calculator may be used. The use of computers or mobile phones is not permitted. 

Students with a certified DSA, disability or other special educational needs are advised to contact the lecturer at the beginning of the course to agree on teaching and examination methods that, while respecting the teaching objectives, take into account individual learning methods and provide suitable compensatory tools.