Università Roma Tre

INTEGRATION IN ONE VARIABLE
The notion of area. Riemann sums and definite integral. The fundamental theorem of calculus. Integration techniques: integral by subbstitution and by parts; integral of rational functions. Area enclosed by curves. The mean value of a function. Improper integrals.
Length of a curve and curvilinear integral.

ORDINARY DIFFERENTIAL EQUATIONS
Separable differential equations. Linear first order differential equations. Second order differential equations with constant coefficients. Vectorial fields. The theorem of existence and uniqueness. The Euler method.

INTEGRALS IN TWO OR MORE VARIABLES
The notion of volume. Integrals in planar domains and in the three-dimensional space. Surface area and integral on a surface.
Change of variables. The divergence theorem, Green's theorem and Stokes' theorem.

PARTIAL DIFFERENTIAL EQUATIONS
The wave and heat equations on an interval.

- D. Benedetto, M. Degli Espositi, C. Maffei, Matematica per le scienze della vita.
- P. Marcellini, C. Sbordone, Calcolo.
- P. Marcellini, C. Sbordone, Esercitazioni di Analisi Matematica I, prima parte e seconda parte.

Area and distance; Integrals; Fundamental Theorem of Calculus; Techniques of integration; Approximation of integrals; Arc length; Area of a surface of revolution; Volume of a solid of revolution; Multiple integrals; changes of variables; Surface integrals; Divergence, Greens' and Stokes' Theorems; Ordinary and Partial differential equations

1. D.Benedetto, M.Degli Esposti, C.Maffei; Matematica per le scienze della vita; Casa Editrice Ambrosiana
2. Paolo Marcellini, Carlo Sbordone; Calcolo; Liguori Editore
3. James Stewart; Calculus - Early trascendentals; Ed. Thomson