Università Roma Tre

Definite integrals of a single variable: definition as a limit of Riemann sums and as an "area with sign". Primitives and indefinite integrals. The fundamental theorem of calculus. Integration methods by parts and by substitution. Integrals of rational functions. Curvilinear integrals of differential forms. Closed and conservative vector fields. Multiple integrals: Fubini's theorem, integration over normal domains. Changes of variables in double and triple integrals. First-order ordinary differential equations: linear and separable variable equations. Second order linear differential equations with constant coefficients, homogeneous and non-homogeneous. Introduction to the wave equation.

Suggested books (not mandatory):
- D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Ed. Ambrosiana.
- P. Marcellini, C. Sbordone: Elementi di Calcolo, Liguori Editore. In alternativa, degli stessi autori: Calcolo, Liguori Editori.