\contentsline {section}{\numberline {1}Teoria delle curve piane}{1}{section.1}
\contentsline {subsection}{\numberline {1.1}Esempi di curve}{5}{subsection.1.1}
\contentsline {subsection}{\numberline {1.2}Lunghezza di una curva}{6}{subsection.1.2}
\contentsline {subsection}{\numberline {1.3}Retta tangente ad una curva}{14}{subsection.1.3}
\contentsline {subsection}{\numberline {1.4}Superficie}{16}{subsection.1.4}
\contentsline {subsubsection}{\numberline {1.4.1}Piano tangente}{20}{subsubsection.1.4.1}
\contentsline {subsubsection}{\numberline {1.4.2}Area di superficie}{22}{subsubsection.1.4.2}
\contentsline {subsection}{\numberline {1.5}Ascisse curvilinee}{27}{subsection.1.5}
\contentsline {subsection}{\numberline {1.6}Curve geometriche e analitiche}{29}{subsection.1.6}
\contentsline {subsection}{\numberline {1.7}Massimo e minimo vincolato}{35}{subsection.1.7}
\contentsline {section}{\numberline {2}Misurabilita' secondo Jordan}{39}{section.2}
\contentsline {subsection}{\numberline {2.1}Integrale multiplo}{42}{subsection.2.1}
\contentsline {subsubsection}{\numberline {2.1.1}Proprieta'}{44}{subsubsection.2.1.1}
\contentsline {subsubsection}{\numberline {2.1.2}Teorema della media}{45}{subsubsection.2.1.2}
\contentsline {subsection}{\numberline {2.2}Cilindroidi a tre dimensioni}{47}{subsection.2.2}
\contentsline {subsection}{\numberline {2.3}Insieme normale}{48}{subsection.2.3}
\contentsline {subsection}{\numberline {2.4}Formule di riduzione}{49}{subsection.2.4}
\contentsline {subsection}{\numberline {2.5}Solido di rotazione}{54}{subsection.2.5}
\contentsline {subsection}{\numberline {2.6}Baricentro e momento}{54}{subsection.2.6}
\contentsline {subsection}{\numberline {2.7}Domini regolari}{60}{subsection.2.7}
\contentsline {section}{\numberline {3}Integrale improprio}{70}{section.3}
\contentsline {subsection}{\numberline {3.1}Integrale generalizzato}{74}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Integrale illimitato}{77}{subsection.3.2}
\contentsline {section}{\numberline {4}Integrali curvilinei}{79}{section.4}
\contentsline {subsection}{\numberline {4.1}Baricentro e momento curvilinei}{81}{subsection.4.1}
\contentsline {section}{\numberline {5}Forme differenziali lineari}{82}{section.5}
\contentsline {subsection}{\numberline {5.1}Integrale curvilineo della f.d.l.}{85}{subsection.5.1}
\contentsline {subsubsection}{\numberline {5.1.1}Integrale di frontiera}{96}{subsubsection.5.1.1}
\contentsline {section}{\numberline {6}Equazioni differenziali ordinarie}{100}{section.6}
\contentsline {subsection}{\numberline {6.1}Problema di Cauchy}{101}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}Equazioni di ordine uno}{104}{subsection.6.2}
\contentsline {subsubsection}{\numberline {6.2.1}A variabili separate}{104}{subsubsection.6.2.1}
\contentsline {subsubsection}{\numberline {6.2.2}Omogenee}{109}{subsubsection.6.2.2}
\contentsline {subsubsection}{\numberline {6.2.3}Lineari}{111}{subsubsection.6.2.3}
\contentsline {subsubsection}{\numberline {6.2.4}Di Bernoulli}{115}{subsubsection.6.2.4}
\contentsline {subsection}{\numberline {6.3}Equazioni lineari}{121}{subsection.6.3}
\contentsline {subsubsection}{\numberline {6.3.1}Con coeff. costanti}{134}{subsubsection.6.3.1}
\contentsline {subsubsection}{\numberline {6.3.2}Algoritmo risolutivo}{138}{subsubsection.6.3.2}
\contentsline {section}{\numberline {7}*}{140}{section.7}