First year students in Mathematics, Physics and Chemistry
Metric spaces, completeness and the contraction theorem.
Sequences and series of functions, pointwise and uniform convergence.
Power series. Limits of derivatives and integrals.
Functions of several real variables. Partial and directional derivatives. Differential. Total
differential theorem. Hessian matrix.
A few hints on functions from Rn to Rm, Jacobian matrix, differentiation of composite functions.
Implicit functions. Regular curves. Conservative vector fields and potentials.
Differential equations and Cauchy problems. Local existence and uniqueness theorem. Linear differential equations and systems.
Goal of the lectures is to introduce students to basic topics but under an advanced and stimulating viewpoint, offering relevant additional elements with respect to traditional courses.