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## MATHEMATICAL ANALYSIS 1

CODE 56585 2017/2018 12 credits during the 1st year of 8720 Mechanical Engineering (L-9) GENOVA MAT/05 Italian GENOVA (Mechanical Engineering) Annual

## AIMS AND CONTENT

### LEARNING OUTCOMES

The course aims at providing the student with basic operative knowledge on differential and integral calculus for functions of one and two real variables, with some attention to mathematical rigour. Some of the founding elements of mathematical modeling are developed in the second half of the course, such as the elementary theory of ordinary differential equations.

### TEACHING METHODS

Lectures and practice

### SYLLABUS/CONTENT

Functions of one real variable. Real numbers, the oriented real line. The Cartesian plane, graphs of elementary functions. Operations on functions and their graphical interpretation. Monotonicity. Composition and inversion. Powers, exponentials and logarithms. Supremum and infimunm. Sequences and series: the basic notions and examples. Limits of functions. Infinitesimal and infinite functions. Continuous functions and their local and global, derivative, derivation rules. Derivatives of elementary functions. Sign of derivatives in the study of monotonicity and convexity. The classical theorems of Rolle, Cauchy, Lagrange and de l'Hôpital. Taylor expansions and applications to critical points. Definite and indefinite integrals.

Functions of two (or more) real variables. Continuity, directional and partial derivatives, gradient.  Differentiability and tangent plane. Level sets. Local minima and maxima: second order derivatives and the Hessian. Schwartz’s theorem.

Differential equations. Separation of variables.  The existence and uniqueness theorem for the Cauchy problem. Linear first and second order differential equations: solving methods. General solution for the linear equation.

A. Bacciotti, F. Ricci, Lezioni di Analisi Matematica 1 e 2, Levrotto & Bella, 1991.

C. Canuto, A. Tabacco, Analisi Matematica 1 e 2, Springer-Verlag Italia, 2003.

F.De Mari, Dispense di Analisi Matematica 1, http://www.dima.unige.it/~demari/DIDA.html

## TEACHERS AND EXAM BOARD

### Exam Board

MANUEL MONTEVERDE (President)

EMANUELA SASSO (President)

ENRICO CALCAGNO

FILIPPO DE MARI CASARETO DAL VERME

## LESSONS

### TEACHING METHODS

Lectures and practice

### Class schedule

MATHEMATICAL ANALYSIS 1

## EXAMS

### Exam schedule

Date Time Location Type Notes
15/01/2018 09:00 GENOVA Scritto
13/02/2018 09:00 GENOVA Scritto
15/02/2018 09:00 GENOVA Compitino
12/06/2018 09:00 GENOVA Compitino
18/06/2018 09:00 GENOVA Scritto
17/07/2018 09:00 GENOVA Scritto
12/09/2018 09:00 GENOVA Scritto