OVERVIEW

This introductory calculus course presents the basics topics related to differentiation and integration of functions of one variable.

AIMS AND CONTENT

LEARNING OUTCOMES

The teaching unit aims to provide students with the basic notions of differential and integral calculus for functions of one variable. The Calculus I course is the natural continuation of the mathematics topics studied in secondary school.

AIMS AND LEARNING OUTCOMES

At the end of this course the students are expected:

• to master the mathematical notation;
• to know the properties of the elementary functions and their graph;
• to be able to follow the mathematical arguments;
• and to solve simple exercises, and discuss the results obtained.

PREREQUISITES

Sets, equalities and inequalities, analytic geometry, trigonometry.

TEACHING METHODS

Frontal lectures, covering theory and exercises.

SYLLABUS/CONTENT

Real numbers and functions - Real numbers, functions, elementary functions, composition of functions, inverse function.

Limits and continuity - Limits of functions. Continuity. Global properties of continuous functions. The intermediate value theorem and the extreme value theorem.

Differentiation - Derivative of a function. Tangent line. Derivative of the composite function and of the inverse function. The theorems of Rolle and Lagrange. De l’Hôpital's rule. 

Integration - Riemann sums. Indefinite integral. Area of a planar region. Mean value theorem. Integral functions. The fundamental theorem of calculus. Calculating primitives.

RECOMMENDED READING/BIBLIOGRAPHY

Some notes and exercises are available.

Recommended books

• C. Canuto, A. Tabacco, Mathematical Analysis 1, ISBN: 9788891931115 
• M. Oberguggenberger, A. Ostermann, Analysis for Computer Scientists: Foundations, Methods, and Algorithms, Springer-Verlag, 
  ISBN 978-0-85729-445-6
• M. Baronti, M., F. De Mari,  R. van der Putten, I. Venturi,  Calculus Problems, Springer-Verlag, ISBN: 978-3-319-15427-5

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

According to the calendar approved by the Degree Program Board:  https://corsi.unige.it/en/corsi/11896/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Only students who have registered (through the university's online services) will be able to take the exam. The exam is composed of two parts:

• a test made of multiple-choice questions, about the theory seen during the course and with simple exercises;
• a written test with more complex problems.

In order to sit the written part, the student has to pass the multiple-choice test. Students can take the written exam in the same session as the test, or in one of the subsequent sessions, but only once (then, the test has to be retaken). The final mark is given by

                 (first part)*1/3 + (second part)*2/3

If a student fails the exam, they will have to retake both parts, regardless of the test result.

ASSESSMENT METHODS

• The first part of the exam allows us to verify the knowledge of the students on the topics of the course, and the ability of the students to handle the mathematical notation and to make simple deductive reasonings.
• The second part allows us to verify the ability to solve exercises and the knowledge of the main tools related to differentiation and integration.

FURTHER INFORMATION

Compensatory and dispensatory measures Disability/Invalidity/Specific Learning Disorder

Dispensatory measures and compensatory tools are intended to enable students to achieve the same learning objectives as their fellow students, not to facilitate the examination.

The use of compensatory tools and the application of dispensatory measures must be authorised in advance by the teacher in agreement with the Referee.

To take advantage of the adaptations during the examination, fill in the Adaptation request form; the request will be automatically sent by the system to the teacher in charge of the teaching, to the Contact Person of your School/Area/Department and in copy to the Sector; you will also receive a copy of the request sent by e-mail.

The adjustments available to students are as follows:

• Additional time (+30% DSA)
• Additional time (+50% disability/invalidity)
• Additional time during oral exams to organise the answer
• Calculator (programmable and graphing calculators are not allowed)
• Conceptual Maps
• Tables and/or Forms
• Take the exam in written form
• Take the exam in oral form
• Tutor reader (for written tests only)
• Tutor-writer (for written tests only)

Your request for adaptations must be submitted at least 7 working days before the scheduled exam date.

All information for students with disabilities and DSA is available on the webpage: Services for students with disabilities or DSA | UniGe | University of Genoa

Reference for inclusion: Sergio Di Domizio - sergio.didomizio@unige.it