# MATHEMATICS

## Learning outcomes of the course unit

The Mathematics class for STA aims to enable the student to be autonomous in the quantitative and graphic processing and interpretation of experimental data and / or simple mathematical models of applied sciences.

Therefore she/he has to know how to manipulate algebraic formulas, know elementary functions such as logarithms and exponentials, read Cartesian graphs and know and understand the basic techniques of differential calculus.

The expected learning outcomes are:

1) Knowledge and understanding:

Knowledge of the basic techniques of differential calculus

2) Application capabilities:

Apply the principles of differential calculus to the analysis of simple biological, physical and economic models.

Use and manipulate formulas and equations by easily managing their units of measurement

3) Autonomy of judgment:

Evaluation and interpretation of mathematical models

Evaluation and interpretation of experimental data

Evaluation of teaching

4) Communication skills:

Written and oral communication through the scientifically correct vocabulary of the subject

5) Ability to learn:

Develop a scientific approach in the execution of experiments and in the mathematical formalization of their results.

Ability to successfully carry out the Master's Degree courses of the LM70 class and in particular the Master's Degree course in Food Science and Technology

## Prerequisites

Relative numbers

Basic symbolic algebra manipulation

Polynomials

Remarkable products

Factorization of polynomials

Algebraic fractions and their simplification

1st degree equations

Second degree equations

1st degree inequalities (whole and fractional)

2nd degree inequalities (whole and fractional)

Solution of simple linear systems in several variables

## Course contents summary

Basic concepts and methods of differential and integral calculus for functions of one real variable: number sets, sequences, limits, graphs of functions, derivatives and integrals. Although the presentation of the arguments privileges understanding of the concepts and techniques of calculation with respect to formal rigor, some selected theorems with proof are presented.

## Course contents

1) Numbers and real functions. Basics of sets. Natural, integer, rational, real numbers. Functions and Cartesian representation.

Parabolas and circumferences. Injective and surjective functions, monotonic functions. Inverse function. Composition. Linear functions. Power functions, exponential, logarithm. Trigonometric functions.

2) Limits and continuous functions. Limits of functions. Definition examples and properties of continuous functions. The existence of intermediate values theorem.

Fundamental limits.

The Euler number "e".

3) Derivatives. Definition of derivative. Geometric meaning of the derivative. Rules of derivation. Derivatives of some elementary functions. Higher derivatives.

4) Basic applications of differential calculus. Lagrange's theorem (mean value theorem). Consequences and applications. Points of increase, decrease, maximum and minimum of a function. Convex functions.

5) Elementary theory of integration. Summations. Integral as an area. Integral of a continuous function. Mean value of a function and mean value theorem. The fundamental theorem of integral calculus. Fundamental formula of integral calculus. Indefinite integrals. Integration by summation decomposition. Integration by parts. Integration by substitution.

## Recommended readings

A. Guerraggio: Matematica-Mylab,

Pearson Editore.

Online platform MyMathLab, Ed. Pearson, linked to the book.

Slides of lectures in pdf format.

Additional teaching material uploaded to the Elly platform.

## Teaching methods

Lectures will be organized face to face but will be also remotely available in synchronous mode (via Teams) and asynchronous mode (uploaded on the Elly page of the course).

To promote active participation in the course, various individual activities (exercises) will be proposed through the resources available in the Elly platform.

Lectures are divided into a first part in which concepts and examples are illustrated; a second part, in which an active participation of students is expected, on the resolution of exercises.

The slides produced by tablet during the lessons will be uploaded on a weekly basis on the Elly platform https://elly.saf.unipr.it/2020/.

The slides are considered an integral part of the teaching material.

## Assessment methods and criteria

The final exam consists of a written test and an oral test which can be taken only after having received a sufficient mark in the written test (greater than or equal to 18/30).

For students who have obtained a score of at least 25/30, the oral exam is optional. These students will still have to register for an oral exam to verbalize the grade reported in the paper.

The written test is aimed at ascertaining the calculation and application skills of the methods.

In detail: the written test consists of five questions which include four exercises and a theory question.

The oral exam is aimed at ascertaining the theoretical competences and the exposition skills of the student. On the website of the ELLY course the precise examination topics are reported with examples of possible questions.

In case of impossibility to carry out the examination face-to-face due to sanitary restrictions imposed by the University,

both tests (written and oral) will take place through Teams. The written test will consist of 3 exercises and the oral test will be compulsory for everyone.

## Other informations

In the event of a serious health emergency, the methods of teaching and examination may be subject to changes which will be promptly communicated on Elly and/or on the course website