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16954 - Mathematics 2

Academic Year 2024/2025

  • Moduli: Giovanni Paolini (Modulo 1) Roberto Pagaria (Modulo 2)
  • Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Materials Science (cod. 5940)

Learning outcomes

At the end of the course, the student possesses basic knowledge of differential and integral calculus for functions of multiple real variables and is acquainted with the main methods for solving differential equations. The student develops a habit for scientific reasoning and sensitivity in analyzing mathematical models. Moreover, they are capable of conducting a detailed study of functions, sequences, and series, both numerical and functional.

Course contents

  • Real-valued functions of several variables. Partial derivatives and directional derivatives for functions of several variables.
  • Differential. Gradient and its properties. Higher-order derivatives. Hessian.
  • Differential calculus for functions of several variables with vector values. Jacobian.
  • Critical points. Lagrange multipliers.
  • Integration for functions of several variables. Polar, spherical, and cylindrical coordinates.
  • Parametric curves and line integrals. Parametric surfaces and surface integrals.
  • Vector fields. Line integral of a vector field. Potential of a vector field.
  • Flux. Divergence theorem. Stokes' theorem.
  • Differential forms. Closed forms and exact forms. Generalized Stokes' theorem.
  • Elements of probability and statistics.

    • Readings/Bibliography

    • Marco Bramanti, Carlo D. Pagani, Sandro Salsa: Analisi matematica 2 (Zanichelli)
    • Marco Bramanti, Fulvia Confortola, Sandro Salsa: Matematica per le scienze (Zanichelli)
    • Simonetta Abenda: Analisi Matematica (Esculapio)
    • Simonetta Abenda: Esercizi di Analisi Matematica (Esculapio)

    Teaching methods

    Lectures and exercises in the classroom with slides and/or blackboard (traditional or electronic).

    Assessment methods

    The assessment is carried out through a written exam. The exam can be taken in a traditional format at the end of the course, or divided into a midterm test during the course (covering the first part of the syllabus) combined with a second test covering the remainder of the material during the first official exam session.

    During all exam sessions, it is not allowed to consult notes.

    Teaching tools

    Blackboard (traditional or electronic) and projector.

    Office hours

    See the website of Giovanni Paolini

    See the website of Roberto Pagaria