MATHEMATICS 2 PART 2
Learning outcomes of the course unit
Furnish the basic mathematical instruments to treat elementary physical or mathematical problems inherents real or vector valued functions of many real variables.
Knowledge of basic elements of Mathematical Analysis of real valued functions of one real variable.
Course contents summary
Differential calculus for real and vector valued functions of many real variables. Optimizazion. Line integrals. Riemann integration. Surface integrals.
REAL VALUED FUNCTIONS OF MANY REAL VARIABLES. Limits. Continuity. Partial Derivatives. Differentiability. Hessian matrix. Taylor formula. Vector valued functions. Jacobian matrix. Implicit functions.
OPTIMIZAZION. Weierstrass theorem (en). Stationary points. Quadratic forms. Sufficient conditions of min/max. Optimizazion with constraints. Lagrange theorem.
LINE INTEGRALS. Regular curves. Line integrals of first and second type.
RIEMANN INTEGRATION OF MANY VARIABLES FUNCTIONS. Measurable sets. Integration techniques.
SURFACE INTEGRALS. Gauss-Green Lemma.
C. Canuto - A. Tabacco, Analisi matematica I, Springer Italia C. Canuto - A. Tabacco, Analisi matematica II, Springer Italia
Any other text of Mathematical Analysis inherents to real or vector valued functions of many real variables.
Assessment methods and criteria
The examination combines write text and oral discussion