Learning outcomes of the course unit
Completes the mathemathical work begun in the MATHEMATICS I course, providing students additional skills useful in understanding how mathematics may be applied to the other subjects in the degree course.
Course contents summary
Implicit functions. Dini's theorem. Ordinary differential equations. Linear first order diffential equations. Initial-value problems. Linear differential equations with constant coefficients. Simple numerical methods of integration. Parametric representations of curves and surfaces. Regular curves and surfaces. Line integrals. Vector fields. Conservative fields and potential functions. Language of differential forms. Double integrals, triple integrals and surface integrals. Flow of a vector field through a surface. Divergence theorem. Power series. Complex exponential function. Euler's formulas. Vector spaces. Linear transformations. Eigenvalues and eigenvectors. Diagonalisation of square matrices.
M. Bramanti, C.D. Pagani, S. Salsa, MATEMATICA (Calcolo infinitesimale e Algebra Lineare), Zanichelli, Bologna, 2004.
M. Bertsch, Istituzioni di Matematica, Bollati Boringhieri, Torino.
G. Zwirner, Istituzioni di Matematiche (parti 1^ e 2^), Cedam, Padova.
Frontal lectures and exercises.
The exam consists of written and oral tests.