Architecture

Curves: Definitions, tangent of a curve, concatenation of curves, equivalent curves, tangent vector and unit tangent vector, regular curve, length of a curve. Functions of Several Variables: Elements of topology in RN, domain of functions of several variables, limits and continuity, derivatives, differentiability, tangent plane, gradient, directional derivatives, gradient formula, differentiation of composite functions, second derivatives, Schwarz's theorem. Optimization: Absolute extrema and the Weierstrass theorem, relative extrema, free extrema and Fermat's theorem, Hessian matrix associated with a function of two variables, study of maxima and minima using the Hessian matrix, basics of constrained optimization. Integral Calculus for Functions of Several Variables: Definition of double integral, normal domains, formulas for reducing double integrals, polar coordinates, change of variables for double integrals, basics of triple integrals. Ordinary Differential Equations: Definitions and examples, general integral, Cauchy problems, first-order separable variable equations, first-order linear homogeneous and non-homogeneous equations, formula for the general integral, second-order linear homogeneous equations, structure of the general integral, linear equations with constant coefficients (homogeneous), characteristic equation, linear equations with constant coefficients (non-homogeneous), structure of the general integral, method of similarity. Line Integrals and Vector Fields: Definitions and examples, first- and second-kind line integrals, conservative fields and potentials, characterization of conservative fields via work, irrotational fields in R2, simply connected domains, irrotational and conservative fields, extension to R3, basics of surfaces.

Istituzioni di Matematica I

G. Crasta, A. Malusa, "Matematica 2: teoria ed esercizi" N. Fusco, P. Marcellini, C. Sbordone, “Elementi di Analisi Matematica 2” M. Bramanti, C. Pagani, S. Salsa, “Analisi Matematica 2”

Attendance is strongly recommended.

The exam consists of a written exam (also with theoretical questions) and an oral exam (at the professor's discretion).

G. Crasta, A. Malusa, "Matematica 2: teoria ed esercizi" N. Fusco, P. Marcellini, C. Sbordone, “Elementi di Analisi Matematica 2” M. Bramanti, C. Pagani, S. Salsa, “Analisi Matematica 2”

electronic blackboard and/or traditional blackboard and/or writing tablet

Istituzioni di Matematica I

G. Crasta, A. Malusa, "Matematica 2: teoria ed esercizi" N. Fusco, P. Marcellini, C. Sbordone, “Elementi di Analisi Matematica 2” M. Bramanti, C. Pagani, S. Salsa, “Analisi Matematica 2”

Attendance is strongly recommended.

The exam consists of a written exam (also with theoretical questions) and an oral exam (at the professor's discretion).

G. Crasta, A. Malusa, "Matematica 2: teoria ed esercizi" N. Fusco, P. Marcellini, C. Sbordone, “Elementi di Analisi Matematica 2” M. Bramanti, C. Pagani, S. Salsa, “Analisi Matematica 2”