MATHEMATICAL ANALYSIS II

To understand, learn, and use the fundamental tools of mathematical analysis II, as series of functions, free and constrained optimization, differential forms, multiple integrals, and (systems of) differential equations. To highlight their role in the mathematical modeling of classical problems arising from Physics. Be able to interpret and build simple mathematical models.

Classroom lectures and exercises.

Sequences and series of functions. Metric spaces and functions between metric spaces. Differential calculus for functions of several variables. Curves and surfaces. Implicit functions and applications. Line integrals and differential forms. Ordinary differential equations. Measure and integral. Surface integrals.

M. Bramanti – C.D. Pagani – S. Salsa, Analisi matematica 2, Zanichelli Editore, Bologna, 2009.

G. Di Fazio – P. Zamboni, Analisi Matematica Due, Monduzzi Editore, Bologna, 2008.

N. Fusco – P. Marcellini – C. Sbordone, Analisi Matematica due, Liguori Editore, Napoli, 1996.

P. Marcellini – C. Sbordone, Esercitazioni di Matematica, Vol. II, Liguori Editore, Napoli, 1988.

W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, Singapore, 1976.