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MATHEMATICAL ANALYSIS 1

CODE 98340
ACADEMIC YEAR 2021/2022
CREDITS
  • 15 cfu during the 1st year of 8721 INGEGNERIA NAUTICA (L-9) - LA SPEZIA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/05
    LANGUAGE Italian
    TEACHING LOCATION
  • LA SPEZIA
  • SEMESTER Annual
    MODULES This unit is a module of:
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The course is directed to first year students which are familiar with basic notions in elementary Mathematics

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The course aims to provide the basic knowledge preparatory to other courses that require mathematical methods and tools.

    AIMS AND LEARNING OUTCOMES

    The course provides basic notions about Functions of one variable, integration of continuous functions and first order ODE’s in view of applications in Physics and Nautic Engineering.

    PREREQUISITES

    Basic notions in elementary mathematics.

     

    TEACHING METHODS

    90 hours  of lectures . Distance lectures until the end of sanitary emergency an subsequently frontal lectures.

    SYLLABUS/CONTENT

    1) Real numbers and the real line. Cartesian coordinates in the plane. Functions and their graphs. Limits and continuity. Theorems about continuous functions. The derivative. Differentiation rules: product, reciprocal, quotient and chain rule. Monotone functions: the inverse function theorem. Derivatives of some elementary functions. Theorems about differentiable functions: Rolle, Lagrange, Cauchy. Higher order derivatives. Extreme values, convexity and inflection. Sketching the graph of a function.

    2) Integration. Sums and sigma notation. Areas as limits of sums. The definite integral. Properties of the definite integral. The fundamental Theorem of Calculus. Changes of variable: the method of substitution. Areas of plane regions. Integration by parts. Integrals of rational functions.

    3) L’Hopital’s rule.  Taylor’ formula and its applications.

    3) Ordinary differential equations. First order equations: separable equations, linear equations. Cauchy problems: existence and uniqueness theorem. Linear ODE’s with constant coefficients.

    RECOMMENDED READING/BIBLIOGRAPHY

     R.A. Adams, Calcolo Differenziale 1 Casa

    Editrice Ambrosiana.

    Notes & Exercises in  aulaweb ( a.a. 10/11 and the following)

    TEACHERS AND EXAM BOARD

    Exam Board

    DANILO PERCIVALE (President)

    VALENTINA BERTELLA

    SERGIO DE MICHELI

    MARIA VIRGINIA CATALISANO (President Substitute)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    A written test is required which could be followed by another confirmation test

    ASSESSMENT METHODS

    Outcome of  written test and its  confirmation.

    Exam schedule

    Date Time Location Type Notes
    10/01/2022 09:00 LA SPEZIA Scritto LA PROVA DI ANALISI MATEMATICA 1 DEL 8/6 E' POSTICIPATA AL 9/6 ORE 9
    24/01/2022 09:15 GENOVA Scritto
    07/02/2022 14:30 LA SPEZIA Scritto
    08/06/2022 09:00 LA SPEZIA Scritto LA PROVA DI ANALISI MATEMATICA 1 DEL 8/6 E' POSTICIPATA AL 9/6 ORE 9
    08/07/2022 09:00 LA SPEZIA Scritto LA PROVA DI ANALISI MATEMATICA 1 DEL 8/6 E' POSTICIPATA AL 9/6 ORE 9
    07/09/2022 09:00 LA SPEZIA Scritto

    FURTHER INFORMATION

    Professor will receive students by appointment.