Activity  Credits  Period  Academic staff 

Teoria 1  3  I sem. 
Sisto Baldo

Teoria 2  5  I sem. 
Giandomenico Orlandi

Esercitazioni  4  I sem. 
Antonio Marigonda

Activity  Day  Time  Type  Place  Note 

Teoria 1  Tuesday  11:30 AM  1:30 PM  lesson  Lecture Hall F  from Oct 4, 2016 to Oct 4, 2016 
Esercitazioni  Monday  1:30 PM  4:30 PM  lesson  Not defined  from Oct 18, 2016 to Oct 18, 2016 
Topics treated in this course are: Calculus for functions of several variables, sequences and series of functions, ordinary differential equations, Lebesgue measure and integral. Emphasis will be given to examples and applications.
i) Calculus in several variables. Neighborhoods in several variables, continuity in several variables, directional derivatives, differential of functions in several variables, Theorem of Total Differential, gradient of scalar functions, Jacobian matrix for vectorvalued functions, level curves of scalar functions. Parametrized surfaces, tangent and normal vectors, changes of coordinates. Higher order derivatives and differentials, Hessian matrix, Schwarz's Theorem, Taylor's Series.
(ii) Optimization problems for functions in several variables. Critical points, free optimization, constrained optimization, Lagrange's Multiplier Theorem, Implicit and inverse function theorem, Contraction Principle.
(iii) Integral of functions in several variables. Fubini and Tonelli theorems, integral on curves, change of variables formula.
(iv) Integral of scalar function on surfaces, vector fields, conservatice vector fields, scalar potentials, curl and divergence of a vector fields, introduction to differential forms, closed and exact forms, Poincare lemma, GaussGreen formulas.
(v) Flux through surfaces, Stokes' Theorem, Divergence Theorem
(vi) Introduction to metric spaces and normed spaces, spaces of functions, sequence of functions, uniform convergence, function series, total convergence, derivation and integration of a series of functions.
(vii) Introduction to Lebesgue's Measure Theory. Measurable sets and functions, stability of measurable functions, simple functions, approximation results, Lebesgue integral. Monotone Convergence Theorem, Fatou's Lemma, Dominated convergence Theorem and their consequences.
(viii) Ordinary differential equation, existence and uniqueness results, CauchyLipschitz's Theorem. Extension of a solution, maximal solution, existence and uniqueness results for systems of ODE, linear ODE of order n, Variation of the constants method,
other resolutive formulas.
(ix) Fourier's series for periodic functions, convergence results, application to solutions of some PDE.
The final exam consists of a written test followed, in case of a positive result, by an oral test. The written test consists of some exercises on the program.
The oral test will concentrate mainly but not exclusively on the theory.
Activity  Author  Title  Publisher  Year  ISBN  Note 
Esercitazioni  Giuseppe De Marco  Analisi 2. Secondo corso di analisi matematica per l'università  Lampi di Stampa (Decibel Zanichelli)  1999  8848800378  
Esercitazioni  M. Conti, D. L. Ferrario, S. Terracini, G. Verzini  Analisi matematica. Dal calcolo all'analisi, Vol. 1 (Edizione 1)  Apogeo  2006  88503221  
Esercitazioni  V. Barutello, M. Conti, D.L. Ferrario, S. Terracini, G. Verzini  Analisi matematica. Dal calcolo all'analisi Vol. 2  Apogeo  2007  88503242  
Esercitazioni  Conti M., Ferrario D.L., Terracini S,. Verzini G.  Analisi matematica. Dal calcolo all'analisi. Volume 1.  Apogeo  
Esercitazioni  Conti F. et al.  Analisi Matematica, teoria e applicazioni  McGrawHill, Milano  2001  8838660026  
Esercitazioni  Giuseppe de Marco  Analisi uno. Primo corso di analisi matematica. Teoria ed esercizi  Zanichelli  1996  8808243125  
Esercitazioni  Giuseppe de Marco  Analisi Zero, presentazione rigorosa di alcuni concetti base di matematica per i corsi universitari (Edizione 3)  Edizione Decibel/Zanichelli  1997  9788808198310 
Data from AA 2016/2017 are not available yet