This book is the result of some lengthy reflections on how to present the aspects of the theory to the students of Vector Analysis of the three-year degree course in physics of the university of Roma "La Sapienza" and how to integrate the theory with exercises (done in class or proposed in the course) that stimulate reflection in order to favor the absorption of concepts and statements. The topics covered in these notes are the traditional contents of the second year mathematics analysis programs for the degree courses in physics, Engineering or Mathematics: sequences and series of functions, differential calculus for functions of several variables, curves and surfaces in space, free and constrained maxima and minima for functions of several variables, curvilinear integrals of functions and vector fields, differential forms, multiple integrals, surface integrals, ordinary differential equations. Furthermore, some theoretical complements are reported that usually do not appear in the vector analysis texts. The exercises and problems presented illustrate and broaden the theory presented and are completely and in detail performed.
Questo libro nasce da alcune lunghe riflessioni su come presentare gli aspetti della teoria agli studenti di Analisi Vettoriale del corso di laurea triennale in Fisica dell’Università di Roma La Sapienza e di come integrare la teoria con esercizi (svolti a lezione o proposti alle esercitazioni del corso) che stimolino la riflessione in modo da favorire l’assorbimento di concetti ed enunciati. Gli argomenti trattati in queste note coprono i contenuti tradizionali dei programmi di Analisi Matematica del secondo anno per i corsi di laurea in Fisica, Ingegneria o Matematica: successioni e serie di funzioni, calcolo differenziale per funzioni di più variabili, curve e superfici nello spazio, massimi e minimi liberi e vincolati per funzioni di più variabili, integrali curvilinei di funzioni e di campi vettoriali, forme differenziali, integrali multipli, integrali superficiali, equazioni differenziali ordinarie. Inoltre sono riportati alcuni complementi di teoria che solitamente non compaiono nei testi di analisi vettoriale. Gli esercizi e i problemi presentati illustrano e ampliano la teoria esposta e sono completamente e dettagliatamente svolti.
Esercizi svolti di Analisi Vettoriale e complementi di teoria / Lanzara, Flavia; Montefusco, Eugenio. - STAMPA. - (2017), pp. 1-343.
Esercizi svolti di Analisi Vettoriale e complementi di teoria
Flavia Lanzara;Eugenio Montefusco
2017
Abstract
This book is the result of some lengthy reflections on how to present the aspects of the theory to the students of Vector Analysis of the three-year degree course in physics of the university of Roma "La Sapienza" and how to integrate the theory with exercises (done in class or proposed in the course) that stimulate reflection in order to favor the absorption of concepts and statements. The topics covered in these notes are the traditional contents of the second year mathematics analysis programs for the degree courses in physics, Engineering or Mathematics: sequences and series of functions, differential calculus for functions of several variables, curves and surfaces in space, free and constrained maxima and minima for functions of several variables, curvilinear integrals of functions and vector fields, differential forms, multiple integrals, surface integrals, ordinary differential equations. Furthermore, some theoretical complements are reported that usually do not appear in the vector analysis texts. The exercises and problems presented illustrate and broaden the theory presented and are completely and in detail performed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.