# Università degli Studi di Napoli "Parthenope"  ## Teaching schedule

2021/2022
Belonging course:
Course of Master's Degree Programme on QUANTITATIVE METHODS FOR ECONOMIC AND FINANCIAL EVALUATIONS
Disciplinary sector:
MATHEMATICAL ANALYSIS (MAT/05)
Language:
Italian
Credits:
6
Year of study:
2
Hours of front activity:
48

Italian

### Course description

The aim of the course is to provide the main mathematical methods
• for studying of optimization problems,
• for modeling and solving economic, financial and corporate problems.

Expected learning outcomes
Knowledge and understanding: The student should be able to prove knowledge of mathematical tools and ability to identify those suitable for modeling and solving economic, financial and corporate issues.
Applying knowledge and understanding: the student should be able to apply the acquired knowledge in order to resolve the assigned problems.
Making judgements: the student should be able to use the acquired knowledge also in an autonomous way, by also applying them to specific issues related to optimization problems.
Communication: the student should be able to answer in a clear and thorough way to the questions of the written examination and to those of the possible oral examination.
Lifelong learning skills: the student should be able to show a good learning ability, by widening, for example, his/her knowledge with use of relevant bibliographic references.

### Prerequisites

Contents of the course of Calculus I

### Syllabus

Functions of several variables: Limits and Continuity. Partial Derivatives. Higher Order Derivatives: Schwarz Theorem. Gradient vector and Differentiability. Directional Derivatives. Quadratic Forms. Convex Functions. Local and Global Maxima and Minima. Constrained Maximization problems. (24 hours)

Curves: introduction. Tangent vector to a curve. Orientation of a curve. Rectifiable curve: length of a curve. (2 hours)

Ordinary Differential Equations: Existence and Uniqueness: the Cauchy problem, Linear First Order Equations, Linear Second Order Equations, Separable Equations, Bernoulli Equations. Systems of Differential Equations. (18 hours)

Mathematical models: examples. (4 hours)

Functions of several variables. Local and Global Maxima and Minima. Constrained Maximization problems. (24 hours)
Curves. (2 hours)
Ordinary Differential Equations. (18 hours)

Mathematical models: examples. (4 hours)

### Teaching Methods

The course includes frontal lessons, during which the themes of the program are discussed, and exercises in attendance.

### Textbooks

• N.Fusco, P.Marcellini, C.Sbordone: Elementi di Analisi Matematica due, Zanichelli Editore, 2020.
• P. Marcellini, C. Sbordone: Esercitazioni di Analisi Matematica due - prima parte e seconda parte – Zanichelli Editore, 2017
• C.P. Simon - L.E. Blume, Mathematics for Economists

### Learning assessment

The assessment is based on written examination (the use of notes, books and informatics devices -smartphone, tablet, pc, ecc.- is not allowed) and an oral interview. The written test is composed of exercises in order to assess the achievement by the student of the learning objectives. The oral exam focuses on the theoretical topics dealt with during the course and it is designed to evaluate the student's ability to express and formalize mathematical concepts. The vote of the examination is expressed in scale from 0 to 30, and it is results of written and oral examination. The laude can be assigned if the student shows, in his/her answers, a particular ability to deepen the topics mentioned in the examination’s questions.