In this section, we examine Green\u2019s theorem, which is an extension of the Fundamental Theorem of Calculus to two dimensions. Green\u2019s theorem has two forms: a circulation form and a flux form, both of which require region [latex]D[\/latex]\u00a0in the double integral to be simply connected. However, we will extend Green\u2019s theorem to regions that are not simply connected.<\/p>\r\n
Put simply, Green\u2019s theorem relates a line integral around a simply closed plane curve [latex]C[\/latex]\u00a0and a double integral over the region enclosed by [latex]C[\/latex]. The theorem is useful because it allows us to translate difficult line integrals into more simple double integrals, or difficult double integrals into more simple line integrals.<\/p>","rendered":"
In this section, we examine Green\u2019s theorem, which is an extension of the Fundamental Theorem of Calculus to two dimensions. Green\u2019s theorem has two forms: a circulation form and a flux form, both of which require region [latex]D[\/latex]\u00a0in the double integral to be simply connected. However, we will extend Green\u2019s theorem to regions that are not simply connected.<\/p>\n
Put simply, Green\u2019s theorem relates a line integral around a simply closed plane curve [latex]C[\/latex]\u00a0and a double integral over the region enclosed by [latex]C[\/latex]. The theorem is useful because it allows us to translate difficult line integrals into more simple double integrals, or difficult double integrals into more simple line integrals.<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t