# Matematica | PARTIAL DIFFERENTIAL EQUATIONS

## Matematica PARTIAL DIFFERENTIAL EQUATIONS

 0522200007 DIPARTIMENTO DI MATEMATICA EQF7 MATHEMATICS 2022/2023

 YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2018 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/05 6 48 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS
 LOREDANA CASO T
ExamDate
EQUAZIONI DIFFERENZIALI ALLE DERIVATE PA12/06/2023 - 09:00
EQUAZIONI DIFFERENZIALI ALLE DERIVATE PA03/07/2023 - 09:00
Objectives
THE COURSE AIMS TO PROVIDE AN OVERVIEW OF THE CLASSICAL THEORY OF PARTIAL DIFFERENTIAL EQUATION.
KNOWLEDGE AND UNDERSTANDING: THE COURSE IS DEDICATED TO THE DEVELOPMENT OF THE THEORY OF CHARACTERISTICS, OF FUNDAMENTAL SOLUTIONS AND GREEN'S FUNCTIONS IN THE RESOLUTION OF SOME PDE.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING: ONE OF THE OBJECTIVES OF THE COURSE IS TO MAKE THE STUDENT ABLE TO RECOGNIZE AND RANK A PDE. IN PARTICULAR INSTRUMENT WILL BE PROVIDED FOR THE RESOLUTION OF CERTAIN TYPES OF PDE. ANOTHER AIMS IS TO MAKE THE STUDENT ABLE TO ANALYZE AND OPERATE THE CLASSICAL THEORY OF PDE.
Prerequisites
BASIC TOPICS OF THE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS, AND THE THEORY OF MEASURE AND INTEGRATION FOR FUNCTIONS OF SEVERAL VARIABLES.
Contents
PARTIAL DIFFERENTIAL EQUATIONS AND THEIR CLASSIFICATION. SOME PDE ELEMENTARY SOLVABLE. INTRODUCTION TO THE METHOD OF CHARACTERISTICS AND APPLICATIONS TO QUASILINEAR PDE. LAPLACE'S EQUATION. HEAT EQUATION. WAVE EQUATION.
Teaching Methods
LECTURES
Verification of learning
LA VERIFICA DELL’APPRENDIMENTO AVVIENE ATTRAVERSO UNA PROVA ORALE E PREVEDE UNA EVENTUALE PROVA SCRITTA, AD INTEGRAZIONE DELLA PROVA ORALE. IN PARTICOLARE, SULLA BASE DELLE METODOLOGIE, DEGLI STRUMENTI E DEI CONTENUTI IMPARTITI DURANTE LE LEZIONI, LO STUDENTE DEVE DIMOSTRARE DI ESSERE IN GRADO DI: COMPRENDERE IL PROBLEMA, TROVARNE LA CORRETTA INTERPRETAZIONE MATEMATICO-QUANTITATIVA, RICONOSCERE LE METODOLOGIE APPLICABILI, SVILUPPARE IL CONTESTO DI CALCOLO APPROPRIATO, COMPRENDERE LE RISPOSTE DEDOTTE DAL METODO E LE SUE INFERENZE.
Texts
1. LAWRENCE C. EVANS, PARTIAL DIFFERENTIAL EQUATIONS, AMERICAN MATHEMATICAL SOCIETY, 2002.
2. FRITZ JOHN, PARTIAL DIFFERENTIAL EQUATIONS, SPRINGER VERLAG, 1991.