# 00679 - Mathematics

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda. ## Learning outcomes

The course aims at giving the student the basic knowledge of Linear Algebra and of Differential and Integral Calculus in one variable, and several variables. In particular, the ability to compute determinants, to solve linear systems, to compute eigenvalues and of applying the methods of differential and integral calculus to plotting the graph of functions, to computing the area of plane domains and to solve free and constrained maximization problems.

## Course contents

Linear Algebra:

• Linear systems.
• The Gauss-Jordan reduction method.
• Matrices.
• Determinants.
• Rank.
• Vector spaces, bases, dimension.
• Linear dependence.
• Eigenvalues and eigenvectors.
Differential and integral calculus:
• The system of real numbers, the induction principle.
• The topology of the real line.
• Functions
• Sup and inf. Limits and continuity.
• Differentiability and rules of calculus of derivatives. Applications to the monotonicity and convexity.
• The Taylor polynomial.
• Riemann integral, the fundamental theorem of the integral calculus. Primitives. Integration methods.
• Introduction to series.
• Functions of several variables: maxima minima and saddle points
• Constrained maximization; Lagrange multipliers.

Carl P. Simon, Lawrence E. Blume, Mathematics for Economists. Vol 1 W. W, Norton \$ Co Inc.

Cacciafesta, Matematica Generale, Giappichelli

As regards the Linear Algebra part, it might be also useful to look at:
Silvana Abeasis, ELEMENTI DI ALGEBRA LINEARE E GEOMETRIA, Zanichelli

## Teaching methods

Chalk and blackboard have proved powerfully enduring and pervasive technologies in the teaching of Mathematics. However, since we are well aware that we are already in the thrird millennium, sometimes also transparencies and a computer-connected video projector will be used

## Assessment methods

For students enrolled in the present Academic Year partial written exams, according to the academic terms. For all students cumulative written exam. Oral exam only in case of 30 with honors.

The use of electronic devices is not allowed.

## Office hours

See the website of Franco Nardini

See the website of Fabrizio Lillo