Salta al contenuto principale della pagina

MATHEMATICAL ANALYSIS 1

CODE 56584
ACADEMIC YEAR 2022/2023
CREDITS
  • 12 cfu during the 1st year of 8784 INGEGNERIA MECCANICA (L-9) - LA SPEZIA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/05
    LANGUAGE Italian
    TEACHING LOCATION
  • LA SPEZIA
  • SEMESTER Annual
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The aim of this course is to provide a practical working tool for students in Engineering or in any other field where rigorous
    Calculus is needed. The basic focus is on functions of one real variable and  basic ordinary differential equations, separation
    of variables, linear first-order, and constant coefficients ODE.

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The aim is to achieve good knowledge of differential and integral calculus for one or two variables functions.

    AIMS AND LEARNING OUTCOMES

    The student will have to acquire a solid ability in Mathematical Analysis, in particular he must know how to study a function of one or more real variables. Moreover  he will have to know how to apply the various theorems for the resolution  of simple differential equations of the first order and higher order (linear with constant coefficients).

    PREREQUISITES

    Elementary algebra: equations and inequalities, trigonometry.

    TEACHING METHODS

    106 hours of  lessons. During the theoretical lessons the definitions and the theorems will be presented with many examples and applications. During the other part of the course  many exercises will be solved.  During the academic year some guided exercises will be carried out.

    SYLLABUS/CONTENT

    Real numbers, infimum and supremum, functions of one real variable, elementary functions, limits, infinitesimals and infinities, continuous functions, derivable functions, differentiable functions, Taylor’s formula, expansion of elementary functions, primitives and indefinite integrals, methods of indefinite integration, definite integrals, fundamental theorem of integral calculus, first order differential equations, Cauchy’s problem and theorem, resolution of linear first order differential equations and separable variables equations, linear differential equations with constant coefficients of order n.

     

    RECOMMENDED READING/BIBLIOGRAPHY

    F. Parodi, T. Zolezzi, Appunti di Analisi matematica, ECIG, 2007
    R. A. Adams, Calcolo differenziale 1 & 2, Casa Editrice Ambrosiana, 2007
    A. Bacciotti, F. Ricci, Lezioni di Analisi Matematica 1 e 2, Levrotto & Bella, 1991.
    M. Bramanti, C. Pagani, S. Salsa, Analisi matematica 1 e 2 Zannichelli, 2008

    M.Baronti-F.De Mari-R.Van Der Putten-I.Venturi: Calculus Problems, Springer

    TEACHERS AND EXAM BOARD

    Exam Board

    MARCO BARONTI (President)

    CLAUDIO ESTATICO

    ROBERTUS VAN DER PUTTEN (President Substitute)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    The final exam consists of a written test and an oral exam. The student must obtain an evaluation of at least 12/30 in the written test  to access the oral exam.

    ASSESSMENT METHODS

    During the written test the student will have to solve some exercises concerning the study of functions and  the differential problem. During the oral examination the student must highlight critical analytical skills and must be able to apply the main theorems for the solution of  easy exercises.

    Exam schedule

    Date Time Location Type Notes