Integrative teaching
Franco Flandoli
Exercises
Examination procedure
Written and oral exam
Prerequisites
First year students in Biology and Chemistry
Syllabus
Basics of Mathematics
Logic and sets; natural, integer, rational and real numbers.
Analysis
Sequences and Series
Limit and convergence; Cauchy sequences.
Metric and Topological Spaces
Open and closed sets; neighborhoods.
Limits and Continuity
Limits of real functions; lim sup and lim inf; continuity and Weiestrass theorem.
Differential Canculus
Rolle, Cauchy, Lagrange and De L'Hopital theorems; Taylor formula and series.
Integration
Riemann integral; fundamental theorem of calculus.
Functions of Many Variables
Continuity; partial derivatives; gradient; differential and differentiability; critical points and Hessian.
Bibliographical references
Notes given by the teacher.
Mariano Giaquinta, Giuseppe Modica, Analisi matematica, Volume 1: Funzioni di una variabile. Pitagora, 1998.
Carlo Domenico Pagani, Sandro Salsa, Analisi matematica 1, Second edition. Zanichelli, 2015