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## MATHEMATICAL ANALYSIS II

CODE 90440 2017/2018 6 credits during the 1st year of 9273 Electronic Engineering and Information Technology (L-8) GENOVA MAT/08 Italian GENOVA (Electronic Engineering and Information Technology ) 2° Semester This unit is a module of:

## AIMS AND CONTENT

### LEARNING OUTCOMES

The course "Mathematical Analysis II" aims to provide students with some basic mathematical tools useful for engineering and application-oriented topics.

### AIMS AND LEARNING OUTCOMES

Topics of this course include parametric curves, functions of several variables and limits, partial derivatives, differentiability, gradient vector, Hessian matrix, unconstrained optimization in several variables, first order differential equations, higher order linear differential equations, multiple integration with change of variables across different coordinate systems, line and surface integrals, series of real numbers, series of functions.

### TEACHING METHODS

`Lectures for both theory and practices (exercises).`

### SYLLABUS/CONTENT

1. Parametric curves.

2. Functions of several variables (scalar and vectorial fields), limits and continuity. Directional derivatives. Differentiable functions. Necessary Necessary and sufficient conditions for differentiability. Derivatives of composite functions. Derivatives of higher order, Schwarz Theorem and Taylor polynomial in several variables. Unconstrained maxima and minima of scalar fields, necessary and sufficient conditions, Hessian matrix.

3. Metric spaces and sequences of functions (hints). Fixed-point Theorem (hints)..

4. Differential equations of the first order, with separable variables, linear, homogeneous, Bernoulli and Riccati types. Existence and uniqueness theorem (hints). Linear differential equations. Linear differential equations of higher order with constant coefficients, homogeneous and non-homogeneous,

5. Integration of functions of several variables. measurable sets. Double integrals. Surface areas and integrals. Triple integrals. Applications, center of gravity.

6. Numerical series. Convergence criteria for constant sign numerical series. Numerical alternating series and absolutely convergent series. Series of functions. Pointwise, absolute, uniform and total convergence criteria. Derivation and integration of several functions (hints). Power series, radius of convergence. Taylor series.

Workbook: Laura Recine - Maurizio Romeo, Esercizi di analisi matematica - Volume II, Maggioli Editore.

## TEACHERS AND EXAM BOARD

### Exam Board

ENRICO CALCAGNO (President)

ERNESTO DE VITO (President)

CLAUDIO ESTATICO (President)

MAURIZIO ROMEO

## LESSONS

### TEACHING METHODS

`Lectures for both theory and practices (exercises).`

### Class schedule

MATHEMATICAL ANALYSIS II

## EXAMS

### EXAM DESCRIPTION

Written exam and oral exam.

### ASSESSMENT METHODS

The written exam consists in the resolution of four exercises regarding four different topics of the course.
The oral exam focuses mainly on the theory (i.e., definitions, theorems and proofs), but in some cases you will be asked to solve an exercise of a type already studied and solved during the lessons. The oral examination is restricted to students who have previously passed the written test.

### Exam schedule

Date Time Location Type Notes
17/01/2018 09:00 GENOVA Scritto 17/1 AULA B5 6/2 AULA E1 13/6 AULA G1 29/6 AULA G1 23/7 AULA G1
24/01/2018 09:00 GENOVA Orale 24/1 AULA G1 14/2 AULA B5 20/6 AULA B5 12/7 AULA B5 26/7 AULA G1 13/9 AULA B5
06/02/2018 09:00 GENOVA Scritto 17/1 AULA B5 6/2 AULA E1 13/6 AULA G1 29/6 AULA G1 23/7 AULA G1
14/02/2018 09:00 GENOVA Orale 24/1 AULA G1 14/2 AULA B5 20/6 AULA B5 12/7 AULA B5 26/7 AULA G1 13/9 AULA B5
13/06/2018 09:00 GENOVA Scritto 17/1 AULA B5 6/2 AULA E1 13/6 AULA G1 29/6 AULA G1 23/7 AULA G1
20/06/2018 09:00 GENOVA Orale 24/1 AULA G1 14/2 AULA B5 20/6 AULA B5 12/7 AULA B5 26/7 AULA G1 13/9 AULA B5
29/06/2018 09:00 GENOVA Scritto Aula G1
12/07/2018 09:00 GENOVA Orale 24/1 AULA G1 14/2 AULA B5 20/6 AULA B5 12/7 AULA B5 26/7 AULA G1 13/9 AULA B5
23/07/2018 09:00 GENOVA Scritto 17/1 AULA B5 6/2 AULA E1 13/6 AULA G1 29/6 AULA G1 23/7 AULA G1
26/07/2018 09:00 GENOVA Orale 24/1 AULA G1 14/2 AULA B5 20/6 AULA B5 12/7 AULA B5 26/7 AULA G1 13/9 AULA B5
07/09/2018 14:00 GENOVA Scritto 7/9 AULA E1
13/09/2018 09:00 GENOVA Orale 24/1 AULA G1 14/2 AULA B5 20/6 AULA B5 12/7 AULA B5 26/7 AULA G1 13/9 AULA B5

### FURTHER INFORMATION

Prerequisitesi: Analisi Matematica I.

Attendance: Recommended.