16954 - Mathematics 2

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.

The differential. The gradient and its properties. Higher-order derivatives. The Hessian.

Differential calculus for vector-valued functions of several variables. The 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.

Flow. Divergence theorem. Stokes' theorem.

Differential forms. Closed forms and exact forms. Generalized Stokes' theorem.

Some 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 on the blackboard. Slides might be used in exceptional circumstances.

Assessment methods

A closed book (no notes allowed) written examination. The exam can be taken at the end of the course, or it may be divided into a midterm examination during the course (covering the first part of the syllabus) combined with a second examination covering the remainder of the material during the first official exam session.

Teaching tools

Blackboard and textbooks.

Office hours

See the website of Nicola Tito Pagani