# MATHEMATICS, SECOND PART

- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Delivery method
- Teaching methods

None.

However it is advisable to have passed the Mathematics I exam, or to possess the calculation skills presented in it.

Written exam. The use of the calculator is allowed.

The exam is divided into two parts, designed to evaluate the computational skills, the knowledge of the terminology, the definitions and the main statements presented during the course, the developed analytical skills of the student.

Students can take the exam alternatively as:

General exam.

At the end of the course, during the exam sessions, 90 minute exam tests will be held on the entire course program.

The first part of the test, evaluated 16 points, focuses on statements, definitions and demonstrations presented during the course. The student must present the contents required by the individual questions.

The second part of the test, evaluated 16 points, is composed of more complex exercises, in which the student is required to use the calculation skills and the theoretical results presented in the course in order to provide the solution to the proposed questions.

The exam is passed if the sum of the scores obtained in the two parts is not less than 18 (eighteen). Scores higher than 30 give the right to praise.

Partial tests.

At the end of the first cycle of lessons, in the week of didactic interruption, and at the end of the course in December, two partial tests will be organized, mainly concerning the topics of the part of the course just ended. Each test lasts 50 minutes and is divided into two parts.

The first part of the test, evaluated 8 points, focuses on statements, definitions and demonstrations presented during the course. The student must present the contents required by the individual questions.

The second part of the test, assessed 8 points, is composed of more complex exercises, in which the student is required to use the calculation skills and the theoretical results presented in the course in order to provide the solution to the proposed questions.

Each partial test is passed with at least 6 points.

The exam is passed if, once both partial tests have been passed, the sum of the points obtained is not less than 18 (eighteen). The praise is attributed to a sum greater than 30.

Students with LD are required to contact the disabled service (servizio.disabili@uninsubria.it) to define the individualized training project to be sent to the course owner within 10 days of each exam session being considered to sustain.

The purpose of this course is to teach the student the basic notions of calculus together with the basic techniques and applications that accompany them.

Knowledge and understanding

At the end of the course student will be able to do:

know the fundamentals of mathematical logics, of differential and integral calculus.

The main topics covered in the course will be:

1) Limits of functions and continuity (about 10 hours);

2) Differential calculation with a variable (about 10 hours);

3) Numerical Series (about 8 hours);

4) Integrals (about 12 hours).

1) Limits and continuity for functions:

* limits of functions of a real variable (definition of limit, of right limit, left limit);

* limits of elementary functions with proofs; vertical, horizontal and oblique asymptotes;

* computing limits: the symbols ~ and o;

* continuity for functions of a real variable; points of discontinuity and their characterization; continuity of elementary functions;

* properties of continuous functions: Weierstrass theorem, theorem of intermediate values (a.k.a.

Darboux Theorem), Zeros Theorem.

2) Differential calculation in one variable:

* difference quotient, derivative at a point; geometric interpretation; the equation of the tangent line;

* left and right derivatives, critical points;

* derivative function, derivatives of elementary functions with proofs;

* review of calculus;

* first order differential, relationships between derivability, differentiability and continuity;

* stationary points, a necessary condition for local maximum / minimum points, Fermat's theorem;

* Lagrange mean value theorem;

* Monotonicity test, First order sufficient condition for optimality;

* Taylor's Theorem with Peano's Form of Remainder; Maclaurin's formula;

* Convexity test, Second order sufficient condition for optimality;

* Study of the graph of a function; function study.

3) Series:

* definition; properties and sum;

* necessary condition for convergence;

* series with positive terms, convergence criteria, series with alternate sign terms, absolute convergence.

4) Integrals:

* definite and indefinite integrals, integrals calculation.

Angelo Guerraggio, Matematica – Seconda edizione, Pearson, Milano, 2009.

Elisa Mastrogiacomo, Esercizi di Matematica per l'Economia. Serie, Integrali, Algebra Lineare, Programmazione Lineare Ledizioni 2018 ISBN: 9788867058471

Lectures will discuss both theoretical arguments and solution techniques for most common exercises related to the subject. Additional exercise will be assigned during classes both for individual study and to be solved in the next lecture. Active attendance is strongly recommended.

TA's sessions will be organized.