mˈɛnɪəv ðə kɹˈɪɾɪkəl θˈiəɹəmz ʌv vˈɛktɚ kˈælkjʊləs dʒˈɛnɚɹəlˌaɪz ˈɛlɪɡəntli tə stˈeɪtmənts ɐbˌaʊt ðɪ ˌɪntᵻɡɹˈeɪʃən ʌv dˌɪfɚɹˈɛnʃəl fˈɔːɹmz ˌɔn mˈænɪfˌoʊldz.
Many of the critical theorems of vector calculus generalize elegantly to statements about the integration of differential forms on manifolds.