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MATHEMATICAL ANALYSIS 4

CODE 86902
ACADEMIC YEAR 2021/2022
CREDITS
  • 6 cfu during the 1st year of 8738 INGEGNERIA NAVALE (LM-34) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/05
    LANGUAGE Italian
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The course focuses on Fourier analysis methods as applied to the solutions of boundary value problems for classical partial differential equations. Thus, a mathematical presentation of Fourier series and transforms is presented, combining a reasonable amount of formal precision with applications to explicit problems, to be solved with workable formulae. The basic facts about analytic functions of one complex variable are also introduced because of their pervasive use in applications, with particular emphasis on the elementary and fundamentally geometric aspects of analyticity.

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The main objective is to achieve a solid basic operative knowledge of Fourier analysis techniques (Fourier series and Fourier transform) for functions of one real variable as applied to boundary value problems for the classical partial differential equations (heat, Poisson, waves), and to understand the main properties of analytic functions of one complex variable.

    AIMS AND LEARNING OUTCOMES

    Students are expected to master the  basic Fourier analysis techniques (series and transforms) that are needed in order to solve standard boundary value problems for classical partial differential equations (heat, Laplace-Poisson, waves), both using series expansions and integral formulae. Basic operative knowledge concerning analytic functions of one complex variable is also expected.

    PREREQUISITES

    Calculus of functions of one and several real variables, linear algebra

    TEACHING METHODS

    Blackboard and computer illustrations

    SYLLABUS/CONTENT

    Fourier series for periodic functions and Fourier transform on R; main properties and applications to finding solutions of boundary value problems for the classical PDE, essentially through separation of variables techniques or via Fourier transform methods. The notion of holomorphic map is introduced and the main properties of analytic functions are investigated.

    RECOMMENDED READING/BIBLIOGRAPHY

    S. Salsa - Partial differential equations in action: from modelling to theory - Springer 2016

    TEACHERS AND EXAM BOARD

    Exam Board

    MATTEO SANTACESARIA (President)

    FILIPPO DE MARI CASARETO DAL VERME (President Substitute)

    ERNESTO DE VITO (President Substitute)

    LESSONS

    LESSONS START

    The class will start according to the academic calendar.

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    Written and oral examination

    ASSESSMENT METHODS

    Students are required to work on standard problems in series expansions, Fourier transforms, applications to boundary value problems for classical PDE and basic properties of analytic functions.

    Exam schedule

    Date Time Location Type Notes
    28/01/2022 09:30 GENOVA Scritto
    11/02/2022 09:30 GENOVA Scritto
    17/06/2022 09:30 GENOVA Scritto
    08/07/2022 09:30 GENOVA Scritto
    09/09/2022 09:30 GENOVA Scritto