Electronics Engineering | Course catalogue

MATHEMATICAL METHODS FOR INFORMATION ENGINEERING

Course objectives

Learning of advanced knowledge of Mathematical Analysis towards applications. Differential Calculus in several variables, minima and maxima with constraints. Analysis of mathematical models. A) Knowledge and understanding: to know basic concepts and their use in exercises of mathematical analysis with the support of texts and lecture notes in Mathematical Methods for Information Engineering. B) Applying knowledge and understanding: to be able to use the acquired knowledge and understanding in solving problems and to communicate the arguments. C) Making judgements: to be able to collect and understand exercises results to solve similar problems in in an autonomous context. To single out common features in different problems D) Communication skills: to relate about assumptions, problems and solutions to wide audiences. E) Learning skills: to acquire the competence that is necessary for advanced study.

Channel 1

PAOLA LORETI Lecturers' profile

Program - Frequency - Exams

Course program

R^n space. Directional Derivatives.Differentiability. Convex sets and convex functions. Characterizing properties. Convexity and optimization. Local and global minima (maxima). Constrained optimization.Lagrange multiplier method. Fritz John conditions. Constrained qualification. Karush-Kuhn-Tucker Conditions. Duality: primal and dual problem. Examples of optimal control problems. The value function. The dynamic programming principle and the Hamilton-Jacobi-Bellman equation Theoretical concepts (40 ore) Example and exercises (20 ore)

Prerequisites

Basic knowledge of mathematical analysis are important requirements: Differential calculus for functions of several variables. Local maxima and minima.

Books

Nicola Fusco Paolo Marcellini Carlo Sbordone Lezioni di analisi matematica due 2020 Zanichelli Editore Sandro Salsa - Carlo D. Pagani Analisi matematica. 2. Zanichelli Mathematical Analysis: Functions of Several Real Variables and Applications di Nicola Fusco , Paolo Marcellini, Carlo Sbordone Springer International Publishing AG,

Teaching mode

Traditional course: theory and exercises. The expected learning outcomes have as main features to acquire knowledges about the topics of the course. For this reason the principal method consist in taking the course by means of frontal lessons about theory, examples and exercises.

Frequency

Mandatory attendance is not required

Exam mode

Discussion on the program topics. Written exam with exercises. Oral exam on the program topics. To pass the examination the student has to get a mark not less than 18/30. The student has to show a sufficient knowledge of the topics of the syllabus of Mathematical Analysis II, and to be able to solve exercises on the topics of the syllabus. To get the mark 30/30 e lode, the student has to show an excellent knowledge of all the topics of the syllabus.

Bibliography

Stephen Boyd , Lieven Vandenberghe Convex Optimization Stanford University Press Lecture notes with exercises on the web page of Prof. Paola Loreti (Dipartimento di Scienze di Base e Applicate per l'Ingegneria)

Lesson mode