# MATHEMATICS 2 AND EXERCISES

## Learning outcomes of the course unit

The course of Mathematics II and Exercises is designed to provide tools and mathematical methods useful for applications.

The theoretical treatment of the fundamental concepts will be followed by examples and exercises.

We expect that at the end of the course the students have the following abilities:

- to know the main properties of multi-variable functions, multiple integrals, series of functions and Fourier/Laplace transforms;

- to apply the correct tools to solve exercises;

- to express the contents in a clear way, even in the oral exam, owing to a formally correct mathematical language;

- to use the acquired knowledge to solve problems even in different frames (Physics, Chemical Physicis, and so on).

The course of Mathematics II and Exercises is designed to provide tools and mathematical methods useful for applications.

The theoretical treatment of the fundamental concepts will be followed by examples and exercises.

## Prerequisites

Matematica I ed Esercitazioni (Mathematics I and Exercises)

Matematica I ed Esercitazioni (Mathematics I and Exercises)

## Course contents summary

The course of Mathematics II and Exercises is designed to provide tools and mathematical methods useful for several applications.

The course of Mathematics II and Exercises is designed to provide tools and mathematical methods useful for several applications.

## Course contents

- Functions of several real variables: limits; continuity and differentiability; maxima and minima.

- Curves and surfaces: integrals.

- Series; functions series; Fourier series; power series: convergence properties and sum of the series.

- Fourier and Laplace transforms: definitions, properties, basic rules and applications to differential problems.

- Functions with complex variable: examples, and Cauchy-Riemann conditions.

- Functions of several real variables: limits; continuity and differentiability; maxima and minima.

- Curves and surfaces: integrals.

- Series; functions series; Fourier series

- Fourier and Laplace transforms: definitions, properties, basic rules and applications to differential problems.

- Functions with complex variable: examples, and Cauchy-Riemann conditions.

## Recommended readings

M. Bramanti, C. D. Pagani, S. Salsa: Matematica (Calcolo Infinitesimale e Algebra lineare), Zanichelli Ed., in particular from Chapter 10 to Chapter 14

or, equivalently,

M. Bramanti, C. D. Pagani, S. Salsa: Analisi Matematica 2, Zanichelli Ed., in particular from Chapter 3 to Chapter 7.

M. Bramanti, C. D. Pagani, S. Salsa: Matematica (Calcolo Infinitesimale e Algebra lineare), Zanichelli Ed., in particular from Chapter 10 to Chapter 14

or, equivalently,

M. Bramanti, C. D. Pagani, S. Salsa: Analisi Matematica 2, Zanichelli Ed., in particular from Chapter 3 to Chapter 7.

## Teaching methods

Lectures with theoretical explanations and several exercises

Lectures with theoretical explanations and several exercises

## Assessment methods and criteria

The knowledge and understanding of the topics of the course will be verified through a written and oral exam.

- Written exam: exercises on the main arguments of the course (steady points of multi-variable functions, conservative vector fields, double or triple integrals, power series, differential problems solved owing to Fourier or Laplace transforms).

During the course there will be two written "intermediate exams" that, if both with a positive result, allow the students to do directly the oral exam.

- Oral exam: questions on the theoretical arguments of the course and on the methods used to solve the exercises.

The knowledge and understanding of the topics of the course will be verified through a written and oral exam.