.Giaquinta, G.Modica, Note di Analisi Matematica, Funzioni di una
variabile, Pitagora Editrice, Bologna, 2005.
M.Giaquinta, G.Modica, Note di Analisi Matematica, Funzioni di piu'
variabili, Pitagora Editrice, Bologna, 2006.
M.Bramanti, C.Pagani, S.Salsa, Analisi matematica 1, Zanichelli, 2008.
P.Benevieri, Esercizi di Analisi Matematica I, Citta' Studi, 2007.
Course program
Program
Numbers. Functions and graphs of functions. Limits and continuity. Differential calculus for functions of one variable. Riemann integral and the fundamental theorem of calculus. Computation of some integrals. Exponential
growth and decay. Simple harmonic motion. Second order ODE with constant coefficients. Complex numbers. Taylor formula and approximation. Finite sums. Limits of sequences. Topology in the context of metric spaces. Continuous functions on metric spaces. Curves. Differential calculus for functions of several variables. Submanifolds and immersed surfaces, Implicit functions. Constrained critical points. Gradient flow. A few facts from measure and Lebesgue integration theory. Fubini and change of variable theorems.
A few classical multiple integrals. Measuring the area of a surface. Conservative and irrotational fields. Gauss—Green's formulas. Divergence. Rotor.