Examination procedure
<p>2 oral and 2 written</p>
Examination procedure notes
<p>Due prove e scritte e due prove orali, intermedie e a fine corso,</p>
Prerequisites
First year undergraduate students in Mathematics and Physics of the Scuola Normale (mandatory)
Syllabus
Set theory. Cardinality. Axiom of choice.Construction of integer, rational and real numbers. Completeness of R. Limits of sequences. Limit points, upper and lower limits. Cauchy criterion, infinite limits. Numerical series and convergence criteria.Topology of Rn.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. Totaldifferential 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.
Bibliographical references
Lecture notes will be provided, based on the text "Complementi di Matematica" by Luigi Ambrosio, Carlo Mantegazza and Fulvio Ricci, published by Edizioni della Normale