B024548 - MATHEMATICAL ANALYSIS

Italian

Real and complex numbers
Functions of one variable
Limits
Derivatives
Taylor's formula
Riemann's integral
Improper integrals
Numerical sequences and series.
Elements of point set topology
Functions of several variables
Partial and directional derivatives, continuity and differentiability, free and constrained extrema.
Double and triple integrals
Parametric curves
Line and surface integrals
Ordinary differential equations
Method of separation of variables and linear equations

Textbooks:
Anichini G. - Conti G., Analisi Matematica 1,Pearson Education, 2008.
Anichini G. - Conti G., Analisi Matematica 2,Pearson Education, 2010.

Textbooks recommended for exercises:
Benevieri P., Esercizi di Analisi Matematica, Ed. De Agostini.
Marcellini P. - Sbordone C., Esercitazioni di Matematica 1, Liguori
Editore.
Marcellini P. - Sbordone C., Esercitazioni di Matematica 2, Liguori
Editore.
Salsa S. - Squellati A., Esercizi di Analisi Matematica 1, Zanichelli.
Salsa S. - Squellati A., Esercizi di Analisi Matematica 2, Zanichelli.

Other texts :
Bertsch M. - Dal Passo R. - Giacomelli L., Analisi Matematica, McGraw Hill, Milano 2007.
Giaquinta M. - Modica G., Note di Analisi Matematica. Funzioni di una variabile, Pitagora Editrice, Bologna 2005.
Giaquinta M. - Modica G., Note di Analisi Matematica. Funzioni di piu'
variabili, Pitagora Editrice, Bologna 2006.

Se also: http://www.dma.unifi.it/~pera

Knowledge and understanding of both mathematical principles and the role of mathematical sciences as a tool for the analysis and the problem solving of mechanical engineering problems. Knowledge of the principles of computer science and the algorithmic and numerical approach to problems.
The training goal is the acquisition of a good disposition to the theoretical approach and to the logical-formal rigor through the elaboration of some concepts of differential and integral calculus in one and several variables, improving students' skills concerning calculation techniques.

Basic notions of high school mathematics courses. In particular: formal calculus, polynomials, algebraic equations and inequalities, elements of analytic geometry, and of trigonometry

The course has two terms consisting in theoretical lectures alternated with tutorials.

More information about the course is available at the following link http://www.dma.unifi.it/~pera

The course has two parts. The exam is performed at the end of the second term. It consists in a written text and in a subsequent oral exam. At the end of the first term an intermediate not mandatory written test is performed.
The student has to develop capability in applying and understanding knowledge related to mathematical methods - with particular reference to differential and integral calculus, geometry, linear algebra, numerical calculation, linear programming, probability and statistics - to model, analyze and solve engineering problems, also with the help of IT tools.

The detailed program of the course is available at the following link
http://www.dma.unifi.it/~pera