## Learning objectives

Give the bases of calculus for functions of one real variable, in such a way that the students are able to solve simple problems in the field. Students should be able to draw and read graphs of functions of one variable, to study functions of one real variable and to compute elementary integrals and to solve some differential equations.

## Prerequisites

Mathematics taught in high schools

## Course unit content

Real numbers, elementary algebra, equations and inequalities. Functions and their graphs, elementary functions. The principle of induction. Maximum, minimum, supremum and infimum of sets of real numbers. Limits of sequences and of functions of a real variable. Continuity, derivatives, primitives and their properties. Integrals of continuous functions over intervals. Study of the graphs of functions of one real variable.

## Full programme

1.1. Real numbers.

1.2. Functions and their graphs.

1.3. Operations between functions.1.4. Polynomials, rational and trogonometric functions.

2.1. Limits.

2.2. Continuos functions.

2.3. Theorems on continuos functions.

3.1. derivatives and tangent lines.

3.2. Rules of differentiation.

3.3. Derivatives of elementary functions

3.4. Exponential and logarithm functions.

3.5. Graph of functions.

4.1. Riemann integrals.

4.2. Fundamental Theorem od calculus. Definite integrals.

4.3. Indefinite integrals and methods of integrations.

5.1. Ordinary differential equations: generalities.

5.2. Linear first order differential equations.

5.3. Linear differential equations with constant coefficients.

## Bibliography

Robert Adams

Calcolo differenziale 1

Quinta edizione italiana,

Ed. Zanichelli

P. Marcellini, C. Sbordone: Calcolo, Liguori Editore

A. Nannicini, L. Verdi, S. Vessella: Note ed esercizi svolti di Calcolo 1, Pitagora Editrice.

M. Bramanti, C.D. Pagani, S. Salsa, Matematica Calcolo infinitesimale ed

algebra lineare, seconda edizione, Ed. Zanichelli, ISBN: 8808075478.

S. Salsa, A. Squellati, Esercizi di Matematica, calcolo infinitesimale e algebra

lineare, Vol. I, Ed. Zanichelli, ISBN: 9788808224880.

## Teaching methods

Lectures and exercises

The lessons will be organized as follows:

in person with the possibility of using the lessons also remotely in synchronous mode (via Teams). To promote active participation in the course, various individual and small group activities may possibly be proposed,

through the use of the resources present in Elly. During the lectures, in traditional mode, the

topics will be presented in a formal and rigorous way. There will be exercises using the elly platform. The course will give particular emphasis to the application and calculation aspects, while not neglecting

the theoretical aspect. For this purpose, the exercises carried out in a manner in which the student learns to apply the

theory seen in class when solving concrete problems.

## Assessment methods and criteria

The final exam consists of a written test and, upon request, an oral test.

The written test is structured as follows:

• text containing 30 multiple choice questions, with a penalty assigned in the event of a wrong answer, having as its subject the fundamental topics of the course.

The evaluation of the second part of the written test takes place out of thirty. The written test of '' Mathematical Methods '', yes

intends passed, when at least 18. The final mark is given by the mark obtained in the written test. Any oral test, to be held after the written test and in the same session as the latter, is carried out at the request of the student and consists in the demonstration of significant theorems and / or in the exposition of topics, definitions, dealt with in the lessons . In the latter case, the final grade is the average between the written test and the oral test.

In place of the written test, students can take three intermediate tests. The evaluation of the intermediate tests is out of thirty.

To register for the intermediate tests: connect to http://elly.scvsa.unipr.it/

enter the BIOTECHNOLOGY section, course of "Mathematical Methods" and perform

registration for the intermediate test.

The intermediate written test is structured as follows:

• text containing 30 multiple choice questions, dealing with the fundamental topics of the course, treated up to one week before the mid-term exam.

The evaluation of each intermediate written test is structured as follows:

• The marks of each intermediate test are awarded out of thirty.

• Students who, at the end of the 3 intermediate tests, achieve a higher average

or equal to 18/30 and who have scored a mark greater than or equal to 18/30 in

at least two intermediate tests, pass the '' Mathematical Methods '' exam, with the final grade equal to the average of the 3 intermediate tests as above.

Any oral exam, to be held after the completion of the 3 intermediate tests, by 30 September 2021, is carried out at the request of the student and consists in the demonstration of significant theorems and / or in the exposition of arguments, definitions, dealt with in the lessons. In the latter case, the final grade is the average between the average of the 3 written intermediate tests and the oral exam.

If due to the persistence of the health emergency it was

It is necessary to integrate the carrying out of the exams with the remote modality, the following will be done: remote written tests.

## Other information

The course consists of lectures, exercises, interviews with students, articulated

according to the official calendar and timetable; in particular, interviews with students are

fixed by appointment at the Department of Mathematical, Physical and

Informatiche, Plexus of Mathematics, University Campus, Park Area of Sciences

53 / A.

During the lectures, in traditional mode, i

topics will be presented in a formal and rigorous manner. The course will give particular emphasis to the application and calculation aspects, while not neglecting

the theoretical aspect. For this purpose the exercises carried out in the classroom in which the student learns to apply the application are particularly important

theory seen in class to solve concrete problems. The course notes in PDF format and all the material used during the lessons and exercises are made available to the students on the Elly educational platform.